Global navigation satellite systems performance analysis

Global navigation satellite systemsperformance analysis and augmentation strategies in aviation

Roberto Sabatini1 Terry Moore2 and Subramanian Ramasamy1

1RMIT University School of Engineering ndash Aerospace Engineering and Aviation Discipline Bundoora VIC 3083 Australia

2University of Nottingham Nottingham Geospatial Institute Nottingham NG7 2TU United Kingdom

A B S T R A C T

In an era of significant air traffic expansion characterised by a rising congestion of the radiofrequency spectrum and a widespread introductionof Unmanned Aircraft Systems (UAS) Global Navigation Satellite Systems (GNSS) are being exposed to a variety of threats including signalinterferences adverse propagation effects and challenging platform-satellite relative dynamics Thus there is a need to characterize GNSSsignal degradations and assess the effects of interfering sources on the performance of avionics GNSS receivers and augmentation systemsused for an increasing number of mission-essential and safety-critical aviation tasks (eg experimental flight testing flightinspectioncertification of ground-based radio navigation aids wide area navigation and precision approach) GNSS signal deteriorationstypically occur due to antenna obscuration caused by natural and man-made obstructions present in the environment (eg elevated terrainand tall buildings when flying at low altitude) or by the aircraft itself during manoeuvring (eg aircraft wings and empennage masking theon-board GNSS antenna) ionospheric scintillation Doppler shift multipath jamming and spurious satellite transmissions Anyone of thesephenomena can result in partial to total loss of tracking and possible tracking errors depending on the severity of the effect and the receivercharacteristics After designing GNSS performance threats the various augmentation strategies adopted in the Communication NavigationSurveillanceAir Traffic Management and Avionics (CNS+A) context are addressed in detail GNSS augmentation can take many forms butall strategies share the same fundamental principle of providing supplementary information whose objective is improving the performanceandor trustworthiness of the system Hence it is of paramount importance to consider the synergies offered by different augmentationstrategies including Space Based Augmentation System (SBAS) Ground Based Augmentation System (GBAS) Aircraft BasedAugmentation System (ABAS) and Receiver Autonomous Integrity Monitoring (RAIM) Furthermore by employing multi-GNSSconstellations and multi-sensor data fusion techniques improvements in availability and continuity can be obtained SBAS is designed toimprove GNSS system integrity and accuracy for aircraft navigation and landing while an alternative approach to GNSS augmentation is totransmit integrity and differential correction messages from ground-based augmentation systems (GBAS) In addition to existing space andground based augmentation systems GNSS augmentation may take the form of additional information being provided by other on-boardavionics systems such as in ABAS As these on-board systems normally operate via separate principles than GNSS they are not subject tothe same sources of error or interference Using suitable data link and data processing technologies on the ground a certified ABAS capabilitycould be a core element of a future GNSS Space-Ground-Aircraft Augmentation Network (SGAAN) Although current augmentationsystems can provide significant improvement of GNSS navigation performance a properly designed and flight-certified SGAAN could playa key role in trusted autonomous system and cyber-physical system applications such as UAS Sense-and-Avoid (SAA)

1 Introduction

The origins of Global Navigation Satellite Systems (GNSS) dateback to the early 1960s when the United States Department ofDefense initiated the development of systems for threendashdimensional position determination [1] After the US Navysuccessfully tested the first satellite navigation system calledTRANSIT the Space Division of the US Air Force initiated aprogram known as Project 621B that evolved into the NavigationSignal Time and Range (NAVSTAR) program In 1973 the USDefense Navigation Satellite System (DNSS) was created whichwas later referred to as NAVSTAR Global Positioning System(GPS) Various GNSS systems are currently in service or underdevelopment The US GPS and the Russian GLONASS(Globalnaya Navigazionnaya Sputnikovaya Sistema) haveachieved their Full Operational Capability (FOC) back in the1990rsquos [2] Other GNSS systems that are currently at the advanceddevelopment or deployment stages include the EuropeanGALILEO and the Peoplersquos Republic of China BEIDOUNavigation Satellite System (BDS) GNSS systems typically usesignals 20 dB below the ambient noise floor and despite severalresearch efforts devoted to interference detection and mitigationstrategies at receiver and platform level (mostly for militaryapplications) no effective solution has been implemented so far inthe civil aviation context Thus there is a need to characterizeGNSS signal degradations and assess the effects of interferingsources on the performance of avionics GNSS receivers andDifferential GNSS (DGNSS) systems used for an increasingnumber of mission-essential and safety-critical aviation tasks (eg

experimental flight testing flight inspectioncertification ofground-based radio navigation aids wide area navigation andprecision approach)

GNSS signal deteriorations typically occur due to antennaobscuration caused by natural and man-made obstructions presentin the environment (eg elevated terrain and tall buildings whenflying at low altitude) or by the aircraft itself during manoeuvring(eg aircraft wings and empennage masking the on-board GNSSantenna) ionospheric scintillation Doppler shift multipathjamming and spurious satellite transmissions Anyone of thesephenomena can result in partial to total loss of tracking and possibletracking errors depending on the severity of the effect and thereceiver characteristics Tracking errors especially if undetectedby the receiver software can result in large position errors Partialloss of tracking results in geometry degradation which in turnaffects position accuracy Consequently GNSS alone does notalways provide adequate performance in mission-essential andsafety-critical aviation applications where high levels of accuracyand integrity are required

GNSS augmentation can take many forms but all share the samefundamental principle of providing supplementary informationwhose objective is improving the performance andortrustworthiness of the system GNSS augmentation benefits in theaviation domain can be summarized as follows

Increased runway access more direct en-route flightpaths and new precision approach services

Reduced and simplified avionics equipment

Potential elimination of some ground-based navigationaids (VOR ILS etc) with cost saving to Air NavigationService Providers (ANSPs)

This paper is organised as follows Section 2 provides a detaileddiscussion on GNSS aviation applications followed by adescription of models for GNSS performance threats in Section 3Section 4 presents the different augmentation strategies and theidentification of a pathway to a future GNSS Space-Ground-Avionics Augmentation Network (SGAAN) is discussed in Section5 an investigation of the potential of GNSS augmentationtechniques to support trusted autonomous Unmanned AircraftSystem (UAS) applications is presented in Section 6 Theconclusions of this article are summarised in Section 7 andrecommendations for future research are highlighted in Section 8

2 GNSS Aviation Applications

Although different GNSS systems employ diversified hardwareand software features all systems are composed by a spacesegment a control segment and a user segment (Fig 1) The spacesegment includes the satellites required for global coverage Thesesatellites are predominantly in Intermediate Circular Orbit (ICO)

at nominal altitudes of 19100 km (GLONASS) 20184 km (GPS)and 23222 km (GALILEO) from the Earthrsquos surface

BDS also employs satellites in Geostationary Orbit (GEO) andInclined Geosynchronous Orbit (IGSO) The user segment includesthe large variety of GNSS receivers developed for air ground andmarine navigation positioning applications The control segmentincludes one or more Control and Processing Stations (CPSs)connected to a number of Ground Monitoring Stations (GMSs) andantennae located around the globe for Telemetry Tracking andCommand (TTampC) signals downuplink and navigationintegritysignals uplink to the satellites The GMS antennae passively trackall GNSS satellites in view collecting ranging signals from eachsatellite This information is passed on to the CPS where thesatellite ephemeris and clock parameters are estimated andpredicted Additionally satellite integrity data are analysed andappropriate integrity flags are generated for faultyunreliablesatellites The ephemerisclock and integrity data are then up-linked to the satellite for retransmission in the navigation messageThe satellite clock drift is corrected so that all transmitted data aresynchronised with GNSS time

SpaceSegment

ControlSegment

UserSegment

Satellite TTampC Data

NavigationIntegrity Data

Satellite Navigation Signals

Constellation Monitoring Data

Ground Monitoring Station

Satellite TTampC Link

NavigationIntegrity Uplink

ControlProcessing Station

Legend

Fig 1 GNSS segments

The fundamental equation is the following

ݐ ேௌௌ minus௦ݐ= ௦ݐ߂ (1)

where ݐ ேௌௌ is the GNSS time ௦ݐ is the satellite time and ௦ݐ߂ is thedifference between satellite and GNSS time The corrections areapplied to the last term of equation (1) typically using polynomialcoefficients and a relativistic correction term The correctionequation can be written as

௦ݐ߂ = + ଵ(ݐ ேௌௌminusݐ) + ଶ(ݐ ேௌௌminusݐ)ଶ + ݐ߂ (2)

where ଵ and ଶ are the polynomial coefficients for phasefrequency and age offset ݐ߂ is the relativistic correction term andݐ is the time of transmission of the corrections

Typically the ephemeris corrections are obtained through anestimation of the Cartesian co-ordinates of the satellites along theorbits by integrating the equations of motion For integritypurposes suitable Fault Detection Isolation and Recovery (FDIR)techniques are employed In particular the health status of thesatellite subsystems is continuously monitored (satellite payloadbus solar arrays battery power and the level of propellant used formaneuvers) and any anomaly must be promptly detected andresolved When needed spare satellites can be activated The

Signal-in-Space (SIS) is also constantly monitored to guarantee therequired performance standards Despite the significanttechnological enhancements recently introduced in controlsegment integrity features current GNSS systems have limitedFDIR capability In most cases several minutes or even hours arerequired to provide the required integrity information (ie usedonot use signals) to GNSS users Obviously this is not acceptablefor mission-essential and safety-critical aviation applications

21 GNSS Observables

There are basically three types of GNSS observables that can beused in aviation GNSS receivers pseudorange carrier phase andDoppler observable Pseudoranges are commonly used in real-time aircraft navigation and can provide an accuracy ranging fromabout 20 m (single frequency receivers) to about 2 m in DifferentialGNSS (DGNSS) positioning The carrier phases are traditionallyused in high precision trajectory determination applications (egTSPI systems for flight test and flight inspection) and can achievesub-centimetre accuracy However it is also quite common to usecombinations of pseudoranges and carrier phase measurementsboth in real-time and post mission applications Moreover it hasbecome common practice to take advantage of various

combinations of the original phase observation such as doubledifferences and triple differences

211 Pseudorange Observable

The concept of pseudoranging is based on measuring differencebetween the time of transmission of the code from the satellite andthe epoch of reception of the same signal at the receiver antennaThis is achieved by correlating identical pseudorandom noise(PRN) codes generated by the satellitersquos clock with thosegenerated internally by the receiverrsquos own clock If this timedifference is multiplied by the speed of propagation of the radiowave a range value is obtained which is the distance between thesatellite and the receiverrsquos antenna referring to the epoch ofobservation Both receiver and satellite clock errors affect thepseudoranges Therefore they differ from the actual geometricdistance corresponding to the epochs of emission and receptionThe general pseudorange equation is

(ݐ) = ݐ) ݐminus

) times (3)

where represents the actual measurement ݐ denotes the

nominal time of the receiver clock at receptionݐ denotes thenominal time of the satellite clock at emission and denotes thespeed of light Equation (3) would correspond to the actualdistance between the satellite and receiverrsquos antenna if there wereno clock biases the signal travelled through vacuum and there wasno multipath effect The clock drifts can be represented by thefollowing expressions

ݐ=ݐ + ݐ (4)

ݐ ݐ= + ݐ (5)

where the symbol ݎ denotes the true time and the terms ݐ andareݐ the receiver and satellite clock errors respectively Takingthese errors and biases into account the complete expression forthe pseudorange becomes

(ݐ) = ൫ݎݐminusݎݐ

൯ minus ݐ) minus ܫ+(ݐ(ݐ) +

(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (6)

Therefore

(ݐ) = ߩ

(ݐ) minus ݐ) minus ܫ+(ݐ(ݐ) +

(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (7)

where ܫ(ݐ) and k

pk tT are the ionospheric and tropospheric

delays depending on varying conditions along the path of thesignal The symbols (ݐ) and

(ݐ) denote the receiver

and satellite hardware code delays respectively The symbol

(ݐ) denotes the multipath of the codes which depends on

the geometry of the antenna and satellite with respect tosurrounding reflective surfaces The term ߝ denotes the random

measurement noise The term ߩ(ݐ) is the actual geometric

distance between the receiverrsquos antenna and the satellite at aspecific epoch and therefore

ߩ(ݐ) = ඥ(ݑminus 2(ݑ + minusݒ) ݒ )2 + minusݓ) 2(ݓ (8)

The terms (ݓݒݑ) are the approximate Cartesian co-ordinatesof the receiver and ݓݒݑ) ) denote the position of the satelliteat the epoch of transmission With reference to Fig 2 assuming aconstant receiver clock error ݐ for measurements to any satelliteand omitting all other error terms in Eq (6) the following systemof equations is formed

⎩⎪⎨

⎪⎧

ଵ(ݐ) = ඥ(ݑଵminus )ଶݑ + minusଵݒ) )ଶݒ + minusଵݓ) minus)ଶݓ ݐ

ଶ(ݐ) = ඥ(ݑଶminus )ଶݑ + minusଶݒ) )ଶݒ + minusଶݓ) minus)ଶݓ ݐ

ଷ(ݐ) = ඥ(ݑଷminus )ଶݑ + minusଷݒ) )ଶݒ + minusଷݓ) minus)ଶݓ ݐ

ସ(ݐ) = ඥ(ݑସminus )ଶݑ + minusସݒ) )ଶݒ + minusସݓ) minus)ଶݓ ݐ

(9)

Therefore the co-ordinates of the user receiver (and GNSS time)can be derived from the simultaneous observation of four (or more)satellites If more than four satellites are visible a least-squaresolution can be determined The GNSS receiver calculates itsposition in an Earth-Centred Earth Fixed (ECEF) Cartesian co-ordinate system (typically using WGS84) These co-ordinates maybe expressed to some other system such as latitude longitude andaltitude if desired Solution of the system (equation 9) requiresmeasurement of the pseudoranges to four different satellites TheGNSS receiverrsquos computer may be programmed to solve directlythe navigation equations in the form given above However thecomputation time required to solve them may be too long for manyapplications

O

hRe

(xk yk zk)

(x2 y2 z2)

(x3 y3 z3)

XE YE

ZE

(x4 y4 z4)

(x1 y1 z1)

GreenwitchMeridian

Equator

North Pole

Fig 2 Navigation solution in the ECEF co-ordinate system (at time zerothe XE axis passes through the North Pole and the YE axis completes the

right-handed orthogonal system

As an alternate approach these equations may be approximated bya set of four linear equations that the GPS receiver can solve usinga much faster and simpler algorithm The system of equations (9)can be rewritten in the form

(ݐ) = ඥ(ݑminus 2(ݑ + ݒ) minus ݒ )2 + minusݓ) 2(ݓ + (10)

(i = 1 2 3 4)

where ݒݑ and ݓ represent the co-ordinates of the ith satellite = ݐ and the units have been chosen so that the speed of lightis unity Linearization of equation (10) can proceed as describedin [3 4] The resulting set of linearized equations relates thepseudorange measurements to the desired user navigationinformation as well as the userrsquos clock bias

ቀ௨௨

ቁ∆ݑ + ቀ

௩௩

ቁ∆ݒ + ቀ

௪௪

ቁ∆ݓ + ∆ = ∆ (11)

(i = 1 2 3 4)

where ݓݒݑ are the nominal (a priori best-estimate) valuesof ݓݒݑ and ݑ∆ ݒ∆ ݓ∆ ∆are the corrections to thenominal values is the nominal pseudorange measurement tothe ith satellite ∆ is the difference between actual and nominalrange measurements The quantities on the right-hand side aresimply the differences between the actual measured pseudorangesand the predicted measurements which are supplied by the userrsquoscomputer based on knowledge of the satellite position and currentestimate of the userrsquos position and clock bias Therefore thequantities to be computed ݑ∆) ݒ∆ ݓ∆ ∆) are the correctionsthat the user will make to the current estimate of position and clock

time bias The coefficients of the quantities on the left-hand siderepresent the direction cosines of the LOS vector from the user tothe satellite as projected along the Cartesian co-ordinate system

212 Carrier Phase Observable

The carrier phase observable is the difference between the receivedsatellite carrier phase and the phase of the carrier generated by thereceiver oscillator The same error sources that affectpseudoranges are responsible for the errors which determine thepositional accuracy achieved with carrier phases [5] Clearly themathematical formulation of any specific error component isdifferent from the pseudorange case (ie phase measurementerrors instead of range measurement errors) Since the antennacannot sense the number of whole carrier waves between thesatellite and the receiver (called the integer ambiguity) an extraparameter is inserted in the carrier phase equation

ߔ

= (ݐ)ߔ minus (ݐ)ߔ +

+ ఃܫ (ݐ) minus

(ݐ)

+ ః (ݐ) + ః (ݐ) +

(ݐ) + ఃߝ (12)

The symbols (ݐ)ߔ and (ݐ)ߔ denote the phase of the receivergenerated signal and the phase of the satellite signal respectivelyat the epoch t of satellite signal reception The symbol

is the

integer ambiguity The terms ఃܫ (ݐ) and

(ݐ) are the ionospheric

and tropospheric delays The ionospheric delay factor has anegative value because the carrier phase progresses when travellingthrough the ionosphere Furthermore the tropospheric factor isconverted in cycles multiplying by where is the nominalfrequency and c is the speed of light in vacuum The symbols

ః (ݐ) and (ݐ) refer to the receiver and satellite hardware

delays respectively The symbol ః (ݐ) denotes the multipath

effect and ఃߝ denotes the carrier phase measurement noiseAssuming synchronisation of the satellite and receiver clocksomitting other error sources (receiver phase tracking circuits localoscillator multipath and measurement noise) and taking intoaccount both the time of transmission and reception of the signalthe equation for the phase observation between a satellite i and areceiver A can be written as [6]

ߔ( ) = (ݐ)ߔ minus )ߔ ) (13)

where ߔ( ) is the phase reading (phase at receiver A of the signal

from satellite i at time ) (ݐ)ߔ is the received signal (phase of thesignal as it left the satellite at time t) and )ߔ ) is the generatedsignal phase (phase of the receiverrsquos signal at time ) If ߩ

(ݐ)is the range between receiver and satellite we have

=ݐ minusఘಲ(௧)

(14)

Therefore

(ݐ)ߔ = ൬ߔ minusఘಲ(௧)

൰ (15)

(ݐ)ߔ = )ߔ ) minusడః(௧)

ௗ௧ถ

timesఘಲ(௧)

+⋯ (16)

(ݐ)ߔ = )ߔ ) minus timesఘಲ(௧)

+⋯ (17)

and finally

ߔ( ) = )ߔ ) minus

ߩ(ݐ) minus )ߔ ) +

(18)

where ߔ( ) is the phase reading (degree or cycles) )ߔ ) is the

emitted signal

ߩ(ݐ) is the total number of wavelengths )ߔ )

is the generated signal and is the integer ambiguity The carrier

phase measurement technique typically uses the difference

between the carrier phases measured at a reference receiver and auser receiver This is therefore an inherently differential technique

213 Doppler Observable

The equation that associates the transmitted frequency from thesatellite with the received frequency is

=

ଵାᇲ

(19)

where is the received frequency denotes the emittedfrequency from the satellite primeݎ denotes the radial velocity in thesatellite-receiver direction and denotes the speed of light invacuum The Doppler frequency shift is given by thedifference minus The radial velocity rrsquo is the actual rate ofchange in the satellite-receiver distance and it is given by

=ᇱݎ minusೖ

ೖ∙ (20)

The integrated Doppler count between two epochs ଵݐ and ଶݐ isgiven by

(௧భ௧మ) = int ( minus )ݐ௧మ

௧భ(21)

More information about the Doppler observable and on some of itspractical uses can be found in the literature [7 8]

22 GNSS Error Sources

In the following paragraphs the error sources affectingpseudorange and carrier phase measurements are described Theerror sources can be classified into the five broad categories aslisted below

Receiver Dependent Errors Clock Error Noise and

Resolution

Ephemeris Prediction Errors

Satellite Dependent Errors Clock Offset and Group

Delays

Propagation Errors Ionospheric Delay Tropospheric

Delay and Multipath

User Dynamics Errors

221 Receiver Dependent Errors

Most receivers employ quartz clocks to measure GNSS time whichare not as accurate as the atomic clocks of the satellites Thereforethere is an offset between the receiver and satellite clocks calledreceiver clock error This error affects both the measurement of thesignal flight time and the calculation of the satellitersquos position attime of transmission Measurement Noise is a random error whichdepends entirely on the electronic components of the receiverReceivers for very precise measurements are designed to minimisethis error Both noise and resolution errors can be reduced by usingappropriate filtering techniques Theoretically receiver noise canbe removed by averaging the measurements but only over fairlylong periods of observation time

222 Ephemeris Prediction Errors

The ephemeris data are required for both pseudorange and phasecomputations These errors are due to incorrect estimation of thesatellites ephemeris at the CPS A model for evaluating these errors(Fig 3) is obtained by considering the three components of thevector representing the difference between estimated and truedistance Along Track (ATK) Across Track (XTK) and Radial(RAD) The maximum error is experienced when the satellite hasan elevation of 0deg on the receiver horizon and the line-of-sight(LOS) user-satellite lies on the geometric plane containing ATK

In general the error can be expressed as a function of the threecomponents in the form

ܧ = ܦܣ ߙݏ + ߚݏߙݏܭܣ + ߚݏߙݏܭ (22)

where ߙ is the angle between the LOS user-satellite and the satellitevertical and ߚ is the angle between the ATK direction and the planecontaining the LOS and the satellite vertical The US DoD preciseephemeris is calculated from actual observation to the satellitesfrom a network of ground stations distributed around the world Itis produced several days after the observation period and isavailable only to authorised users Other non-DoD organisationsproduce precise ephemeris both globally and locally by suitablemodelling of all forces and moments acting on the satellites Orbitrelaxation techniques can be developed within GNSS softwareThese techniques solve for orbital errors in the broadcast ephemerisand produce improved relative positioning [9-12]

223 Satellite Dependent Errors

Corrections to the drift of the satellite atomic clocks are computedby the CPS and then broadcasted to the users in the navigationmessage The effect of satellite clock offset is negligible in mostpositioning applications (using the polynomial coefficientscorrections computed at the CPS it is possible to reduce this errordown to 1 part per 1012) The residual error is due to the fact thatcorrections from the CPS are periodic and not continuous GroupDelays are the delays typical of the satellite electronic circuitsThey are estimated on the ground before the satellites are launchedand corrections are included in the navigation message

RAD

XTK

ATK

Rs

Ru

LOS

Fig 3 Error components in ephemeris estimation

224 Propagation Errors

As discussed propagation errors include both ionospheric andtropospheric delays As the satellite signal passes through theionosphere it is delayed for two reasons [13] Firstly because ittravels through a non-vacuum material (propagation delay) thusthe Pseudo Random Noise (PRN) codes are delayed while thecarrier phase is advanced when passing through the ionosphericlayers Secondly because it bends due to refraction for manyapplications the error caused by the bending effect can beconsidered negligible if the signals are transmitted by satelliteswith an elevation of 15deg or more The ionospheric delay isdependent primarily on the number of electrons that the signalencounters along its propagation path It is therefore dependentboth on the ionosphere characteristics (variable during the day andwith seasons) and the path angle (elevation angle of the satellite)It is possible to approximately evaluate the ionospheric delay usingthe following equation [13]

∆= 4031ா

మ(23)

where ܥܧ is the total electron content integrated along the LOSto the satellite in units of electronsm2 is the frequency in Hz and is the speed of light TEC varies with time and depends on thelocation of the ionosphere lsquopiercedrsquo by the LOS to the satellite Atthe L1 frequency (157542 MHz) equation (23) can be written fora satellite that is not at the zenith [14]

∆= 0162ி∙ாೡ

(24)

where ௩ܥܧ is the ܥܧ value for a vertical column located at thepierce point in units of 1016 electrons per m2 and ܨ is the obliquityfactor Assuming that the active region of the ionosphere can berepresented by a thin shell at an elevation of 350 km the obliquitycan be approximately expressed as a simple function of theelevation angle in degrees (ܧ) of the satellite at the receiverrsquosantenna [14]

ܨ = 1 + 274 ∙ 10(96 minus ଷ(ܧ (25)

Depending on the receiver design different models can be adoptedto calculate the correction terms to be applied to the pseudorangebefore solving the navigation equations Particularly L1 code-range receivers use a sinusoidal model of the ionosphere (calledKlobuchar model) which takes into account the variations of theionospheric layers (low over night rapidly getting higher afterdawn getting slightly higher during the afternoon and rapidlygetting lower after sunset) The sinusoidal parameters (amplitudeand period) are transmitted in the navigation message Therelevant equations are the following [15]

ܦܫ = +ܥܦ ቂݏܣଶగ(௧ ః )

ቃ( (ݕ (26)

ܦܫ = )ܥܦ ℎݐ) (27)

where ܦܫ (Ionospheric Vertical Delay) is expressed in nsec ܥܦis the constant night-day offset (5 nsec) ܣ is the amplitude (whosevalue is between 10 and 100 nsec) ߔ is the constant phase offset(1400 hours) ݐ is the local time and is the period The twofactors ܣ and are transmitted as coefficients of a cubic equation

representing a model of the ionosphere with varying latitude Asthe delay also depends on obliquity of the path elevation isincluded as an additional factor in the equation

ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)

where ܦܫ is the Total Ionospheric Delay (nsec) and ܧ is theelevation angle of the satellites over the horizon As the ionosphereis dispersive at radio frequencies two signals at differentfrequencies will be delayed by different amounts Thereforedouble frequency GNSS receivers (eg GPS P-code receivers) canmeasure the difference (Δ) between the time of reception of L1(157542 MHz) and L2 (122760 MHz) and evaluate the delayassociated with both of them For L1 we have

∆ ଵ = Δቀಽభ

ಽమቁଶ

minus 1൨ଵ

(29)

where

∆ =ସଷଵ∙ா

మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)

The troposphere is the lower part of the atmosphere (up to about 50km) and its characteristics depend on local humidity temperatureand altitude The tropospheric delay for a given slant range can bedescribed as a product of the delay at the zenith and a mappingfunction which models the elevation dependence of thepropagation delay In general the total Slant Tropospheric Delay(STD) is given by the sum of a Slant Hydrostatic Delay (SHD) anda Slant Wet Delay (SWD) and both of them can be expressed by arelevant Zenith Tropospheric Delay (ZTD) and a MappingFunction (MF) The SHD (or ldquodry componentrdquo) account for about90 of the total tropospheric delay and accurate estimations arenormally available On the other hand the ldquowet componentrdquo(SWD) estimations are generally less accurate and there is asignificant variability depending on the actual modelsimplemented Table 1 shows some typical values of thetropospheric delay for various elevation angles [13]

Table 1 Tropospheric delay for varying elevation angle

Elevation Angle [deg] Dry Component [m] Wet Component [m]

90 23 02

30 46 04

10 130 12

5 260 23

The total STD is given by

ܦ = ܦܪ + ܦ (31)

ܦ = ுܨܯtimesܦܪ + ௐܨܯtimesܦ (32)

where andܦܪ areܦ the zenith hydrostatic delay and zenithwet delay respectively =ܦ) +ܦܪ (ܦ ுܨܯ and ௐܨܯ aretheir corresponding ݏܨܯ There are many modelsܦ and ݏܨܯcurrently used in GNSS positioning applications Popular modelsinclude the empiricalܦ models developed by Saastamoinen [16and 17] Hopfield [18 and 19] and by the University of NewBrunswick [20] Popular MFs include the ones described by Chao[21] Ifadis [22] Herring [23] Niell [24] and Boehm [25]

225 Multipath Errors

GNSS signals may arrive at the receiver antenna via differentpaths due to reflections by objects along the path Such effect isknown as multipath The reflected signal will have a different pathlength compared to the direct signal therefore it will give a biaseddistance measurement (Fig 4) Multipath depends on theenvironment surrounding the receiver and on the satellitegeometry Typically multipath will be greater for low elevation

satellites and code multipath is much greater than carrier phasemultipath [26] For code measurements the multipath error canreach a theoretical value of 15 times the chip rate So for instancethe GPS CA code chip rate is 2931 metre and the maximummultipath error is about 43965 metres However values of lessthan 2-3 metres are the norm and upper values of 15 metres arerarely observed For carrier phase the maximum theoreticalmultipath error is a quarter of the wavelength This equates toabout 5 centimetres for the GPS L1 and L2 frequencies althoughtypical values are less than 1 centimetre [27] Multipath can beaccurately modelled and removed only at static points by takingobservations at the same points and at the same hour on consecutivedays This however is possible in a dynamic environment Othertechniques use Signal-to-Noise Ratio (SNR) and signalphasefrequency information to detect and quantify multipath

DirectSignal

MultipathSignal

GNSS Antenna

Fig 4 Multipath error

Despite several technological advances and research effortsaddressing multipath detection and mitigation techniques this isstill a major error source in GNSS applications Techniques suchas the Narrow Correlator [28] the Double DeltaStrobe Correlator[29] or the Vision Correlator by Fenton and Jones [30] are notcapable of eliminating the multipath-related errors completely

226 User Dynamics Error

There are various errors due to the dynamics of a GNSS receiverThese errors range from the physical masking of the GNSS antennato the accuracy degradation caused by sudden accelerations of theantenna If carrier phase is used the resulting effect of ldquocycleslipsrdquo is the need for re-initialisation (ie re-determination of theinteger ambiguities) In general a distinction is made betweenmedium-low and high dynamic platforms

23 UERE Vector

The User Equivalent Range Error (UERE) is an error vector alongthe line-of-sight user-satellite given by the projection of all systemerrors The value of this vector can be reduced only by carefuldesign of the receiver since there is nothing the users of non-augmented GNSS receivers can do to reduce other error sourcesThe UERE is generally measured in metres and is given as either a1-sigma error (often denoted as (ߪ or a 2-sigma error (95) Theportion of the UERE allocated to the space and control segments iscalled the User Range Error (URE) and is defined at the phasecentre of the satellite antenna The portion of the UERE allocatedto the User Equipment is called the UE Error (UEE) Specificallythe UERE is the root-sum-square of the URE and UEE When SAwas on typical values of the UERE vector for GPS were below 10m (95) for P(Y) code receivers and about 33 m (95) for CAcode receivers With SA turned off the UERE of CA code

receivers is typically less than 20 metres with the actual valuedominated by ionospheric and multipath effects Dual-frequencyreceivers (with the capability of removing almost entirely theionospheric errors) typically experience smaller UEREs Users ofthe new modernised GPS civilian signals as well as future users ofGALILEO and BEIDOU will be able to use multiple frequenciesto compensate for the ionospheric errors and thereby to achievelower UEREs In GNSS systems the UERE values are stronglydependent on the time elapsed since the last upload from the controlsegment As an example Fig 5 shows the GPS StandardPositioning Service (SPS) UERE variation with time [31] In GPSnormal operations the time since last upload is limited to no morethan one day The smallest UERE and best SIS accuracy willgenerally occur immediately after an upload of fresh NAV messagedata to a satellite while the largest UERE and worst SIS accuracywill usually be with the stalest NAV message data just prior to thenext upload to that satellite

Days Since Last Upload

20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m

Fig 5 UERE variation with time in normal and extended operations [31]

The metric used to characterize whether the NAV message databeing transmitted by a satellite is fresh or stale is the age of data(AOD) where the AOD is the elapsed time since the controlsegment generated the satellite clockephemeris prediction used tocreate the NAV message data upload The AOD is approximatelyequal to the time since last upload plus the time it took the ControlSegment to create the NAV message data and upload it to thesatellite For Normal Operations (NOP) the GPS UERE budgetand the traditional SPS SIS accuracy specifications apply at eachAOD Because the largest UERE and worst SIS accuracy usuallyoccur with the oldest NAV message data the UERE budget andtraditional SPS SIS accuracy specifications are taken as applyingat the maximum AOD For reference the GPS UERE budgets forSPS receivers at zero AOD at maximum AOD in normaloperations and at 145 day AOD in extended operations are shownin Table 2 The breakout of the individual segment components ofthe UERE budgets shown in this table is given for illustrationpurposes only assuming average receiver characteristics Theactual GPS SPS ranging accuracy standards are better specified interms of the UEE and URE components and the overall errorbudget is dependent on a number of assumptions conditions andconstraints Table 3 lists the error budgets and typical UEE valuesapplicable to airborne CA-code GPS receivers in normal operatingconditions Table 4 lists the condition and criteria that apply to theURE budgeting

24 DOP Factors

Ranging errors alone do not determine GNSS positioning accuracyThe accuracy of the navigation solution is also affected by therelative geometry of the satellites and the user This is describedby the Dilution of Precision (DOP) factors The four linearized

equations represented by Eq (9) can be expressed in matrixnotation as

൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦

ଵଵߚ ଵଶߚ ଵଷߚ 1ଶଵߚ ଶଶߚ ଶଷߚ 1ଷଵߚ ଷଶߚ ଷଷߚ 1ସଵߚ ସଶߚ ସଷߚ 1

൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦

ЄଵЄଶЄଷЄସ

൪ (33)

where an error vector has been added to account for pseudorangemeasurement noise plus model errors and any unmodelled effects(eg SA) and ߚ is the direction cosine of the angle between the

LOS to the ith satellite and the jth co-ordinate

Table 2 GPS single frequency CA code UERE budgetAdapted from [31]

Segment Error Source

UERE Contribution [95][m]

ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability

Group Delay Stability

Differential Group DelayStability

Satellite AccelerationUncertainty

Other Space SegmentErrors

00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control

ClockEphemerisEstimation

ClockEphemerisPrediction

ClockEphemeris CurveFit

Iono Delay Model Terms

Group Delay TimeCorrection

Other Control SegmentErrors

20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User

Ionospheric DelayCompensation

Tropospheric DelayCompensation

Receiver Noise andResolution

Multipath

Other User SegmentErrors

NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10

95 System UERE (SPS)127-212

170-241

388

Table 3 Typical UEE error budget (95) Adapted from [31]

Error SourceTraditionalSpec Single

Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay

CompensationNA NA NA 08

TroposphericDelay

Compensation39 40 39 10

Receiver Noiseand Resolution

29 20 20 04

Multipath 24 05 02 02

Other Errors 10 10 10 08

UEE [m] 95 55 46 45 16

Assuming benign conditions [31]

Table 4 SPS SIS URE accuracy standards Adapted from [31]

SIS Accuracy Standard Conditions and Constraints

Single-Frequency CA-Code

le 78 m 95 Global Average URE during Normal

Operations over all AODs


Operations at Zero AOD


Operations at Any AOD

For any healthy SPS SIS

Neglecting single-frequencyionospheric delay model errors

Including group delay timecorrection errors at L1

Including inter-signal bias (P(Y)-code to CA-code) errors at L1



Operations

le 30 m 9979 Worst Case Single Point Average

URE during NormalOperations





Standard based on measurementinterval of one year average ofdaily values within the service

volume

Standard based on 3 servicefailures per year lasting no more

than 6 hours each


le 388 m 95 Global Average URE during

Extended Operations after 14Days without Upload


Equation (33) can be written more compactly as

=ݎ +ҧݔܤ Є (34)

where ܤ is the 4 4 solution matrix (ie matrix of coefficients ofthe linear equation) ҧisݔ the user position and time correctionvector equivҧݔ [߂ݓ߂ݒ߂ݑ߂]

ݎ is the pseudorangemeasurement difference vector equivݎ) ߂] ଵ߂ ଶ߂ ଷ߂ ସ ]) and Єis the vector of measurement and other errors (Єequiv [Єଵ Єଶ Єଷ Єସ ])

The GNSS receiver (or post-processing software) solves the matrixequation using least squares or a Kalman Filter (KF) The solutionis

=ҧݔ ܤ)minus ܤଵ(ܤ (35)

The new term in the above equation is the weight matrix ( ) thatcharacterizes the differences in the errors of the simultaneousmeasurements as well as any correlations that may exist amongthem The weight matrix is given by

= ߪଶܥ (36)

where ܥ is the covariance matrix of the pseudorange errors andߪ

ଶ is a scale factor known as the a priori variance of unit weightApplying the law of propagation of error (also known as thecovariance law) we obtain

௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)

௫ܥ = ൫ܥܤଵܤ൯

ଵ(38)

where ௫ܥ is the covariance matrix of the parameter estimates If weassume that the measurement and model errors are the same for all

observations with a particular standard deviation (ߪ) and that theyare uncorrelated we can write

ܥ = ଶߪܫ (39)

where ܫ is the identity matrix Therefore the expression for ௫ܥsimplifies to

௫ܥ = ߪଵ(ܤܤ)ଶ = ߪܦ

ଶ (40)

The term r represents the standard deviation of the pseudorange

measurement error plus the residual model error which is assumedto be equal for all simultaneous observations If we further assumethat the measurement error and the model error components are allindependent then we can simply root-sum-square these errors toobtain the value ofߪ Based on the definition of UERE givenabove we can use the 1-sigma UERE for ߪ The elements ofmatrix D are a function of receiver-satellite geometry only Theexplicit form of this matrix is

ܦ = ൦

ଵଵܦ ଵଶܦ ଵଷܦ ଵସܦଶଵܦ ଶଶܦ ଶଷܦ ଶସܦଷଵܦ ଷଶܦ ଷଷܦ ଷସܦସଵܦ ସଶܦ ସଷܦ ସସܦ

൪ (41)

The DOP factor can be defined as follows

ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)

where d is the dimension of the DOP factor The diagonal elementsof C୶ത are the estimated receiver coordinate and clock-offsetvariances and the off-diagonal elements (ie covariances) indicatethe degree to which these estimates are correlated The explicitform of the C୶ത matrix is

௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)

The various DOP values can be expressed as functions of thediagonal elements of the ௫ܥ matrix or of the ܦ matrix Convertingthe Cartesian co-ordinates in matrix form to more convenient localgeodetic coordinates we have

തതതതܥ =

⎣⎢⎢⎡ேߪ

ଶ ோߪ ேுߪ ேߪாேߪ ாߪ

ଶ ாுߪ ாߪுேߪ ுாߪ ுߪ

ଶ ுߪߪ ே ߪ ா ߪ ு ߪ ଶ⎦

⎥⎥⎤

(44)

Table 5 shows the relationship between the DOP factors and thediagonal elements of the തതതതܥ matrix and of the ܦ matrix inequation (42) It is also evident that

ܦ = ଶܦܪradic + ଶܦ (45)

ܦܩ = ଶܦradic + ଶܦ (46)

The PDOP is very frequently used in navigation This is because itdirectly relates error in GNSS position to errors in pseudo-rangemeasurements to the satellites According to the definitions givenabove the 1-sigma Estimated Position and Time Errors (EPE andETE) of a GNSS receiver can be calculated using the PDOP (EPEin 3D) the HDOP (EPE in 2D) or the TDOP In general we have

ଷܧܧ = ߪ ߪ= ܦ (47)

ଶܧܧ = ுߪ ܦܪߪ= (48)

ܧܧ = ߪ ߪ= ܦ (49)

Table 6 shows the relationship between the EPE3D and the Figureof Merit (FOM) This parameter is frequently used in avionics

GNSS receivers to provide an indication of the quality ofinformation provided by GNSS

Table 5 DOP expressions

DOP Factor D Matrix Formulation C Matrix Formulation

Geometric DOP (GDOP) ܦܩ = ඥܦଵଵ + ଶଶܦ + ଷଷܦ + ସସܦ

ܦܩ

=1

ߪඥߪே

ଶ + ாߪଶ + ுߪ

ଶ + ߪ ଶ

Position DOP (PDOP) ܦ = ඥܦଵଵ + ଶଶܦ + ଷଷܦ ܦ =1

ߪඥߪே


ଶ

Horizontal DOP (HDOP) ܦܪ = ඥܦଵଵ + ଶଶܦ ܦܪ =1

ߪඥߪே

ଶ + ாߪଶ

Vertical DOP (VDOP) ܦ = ඥܦଷଷ ܦ =1

ߪඥ ுߪ

ଶ =ுߪ

ߪ

Time DOP (TDOP) ܦ = ඥܦସସ ܦ =1

ߪඥ ߪ ଶ =

ߪ

ߪ

Table 6 GNSS figure of merit

FOM Est Position Error 3-D (m) Est Time Error

1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms

There is a proportionality between the PDOP and the reciprocalvalue of the volume V of a particular tetrahedron formed by thesatellites and the user position (Fig 6)

Unit Sphere

Tetrahedron

Antenna

A

B D

C

Fig 6 PDOP tetrahedron construction

In Fig 6 four unit-vectors point toward the satellites and the endsof these vectors are connected with 6 line segments It can in factbe demonstrated that the PDOP is the RSS (ie square root of thesum of the squares) of the areas of the 4 faces of the tetrahedrondivided by its volume (ie the RSS of the reciprocals of the 4altitudes of the tetrahedron) [32] Therefore we can write

ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)

At a particular time and location the four satellites shown inFig 6 have determined elevations and azimuths with respect to thereceiver From these satellite positions the components(ݖݕݔ) of the unit vectors to the satellites can be determinedUsing the Pythagorean theorem the distances between the ends ofthe unit vectors can be determined Knowing these distances atetrahedron can be constructed (Fig 7) and the four altitudes of thetetrahedron can be measured

D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4

S1 = Area ABCS2 = Area BCDS3 = Area CDAS4 = Area ABD

Fig 7 ldquoCut and foldrdquo tetrahedron for PDOP determination

There is no approximation associated with the geometricexpression Any residual error in PDOP determination is only dueto construction of the tetrahedron and measurement of the altitudesIf the angleܣܥܣ in Fig 7 is small one can recognise that the PDOPwill be large (poor) even without measuring the altitudes since thisleads to a tetrahedron having a small volume From the geometricdefinition of PDOP we deduce that it is optimal from the userrsquospoint of view (ie low PDOP) to select the four satellites giving alarge volume of the tetrahedron (and a small RSS of the areas ofthe 4 faces of the tetrahedron) This can be obtained primarily by

selecting a combination of satellites far from each other anduniformly distributed around the receiver The condition for themaximum volume is with a satellite at the zenith and the other threeseparated by 120deg (azimuth) and low over the horizon Thiscondition however would degrade the signal quality due to thelonger propagation paths (ie a compromise between signalquality and accuracy of the solution is therefore necessary) Afurther consequence of the above construction is that if the ends ofthe unit vectors are coplanar (a not unusual circumstance) thePDOP becomes infinite and a position is not obtainable This isthe reason for which the various GNSS constellations have beendesigned so that there are almost always 6-7 satellites in viewanywhere on Earth giving an alternate choice of the 4 satellites tobe utilised If m satellites are in view the number of possiblecombinations is

=

ସ( ସ)(51)

In most GNSS receivers the number of combinations alsocorresponds to the number of PDOPGDOP computationsnecessary for selection of the best satellite geometry Somesystems can automatically reject prior performing positioningcalculations subsets of satellites with associated DOP factorsbelow pre-set thresholds

25 GNSS Performance Requirements in Aviation

The aviation community has devoted great efforts to therationalization and standardization of the navigation performanceparameters and requirements thus specifying the so-calledRequired Navigation Performance (RNP) that an airbornenavigation system must achieve [33 34] Accuracy integrityavailability and continuity are used to describe the RNP foroperations in various flight phases and within specified classes ofairspace The four parameters used to characterize the navigationsystems performance are summarized [35]

Accuracy The accuracy of an estimated or measuredposition of a craft (vehicle aircraft or vessel) at a given timeis the degree of conformance of that position with the trueposition velocity andor time of the craft Since accuracy isa statistical measure of performance a statement ofnavigation system accuracy is meaningless unless it includesa statement of the uncertainty (eg confidence level) inposition that applies

Integrity Integrity is the measure of the trust that can beplaced in the correctness of the information supplied by anavigation system Integrity includes the ability of thesystem to provide timely warnings to users when the systemshould not be used for navigation

Continuity The continuity of a system is the ability of thetotal system (comprising all elements necessary to maintaincraft position within the defined area) to perform its functionwithout interruption during the intended operation Morespecifically continuity is the probability that the specifiedsystem performance will be maintained for the duration of aphase of operation presuming that the system was availableat the beginning of that phase of operation

Availability The availability of a navigation system is thepercentage of time that the services of the system are usableby the navigator Availability is an indication of the abilityof the system to provide usable service within the specifiedcoverage area Signal availability is the percentage of timethat navigation signals transmitted from external sources areavailable for use It is a function of both the physicalcharacteristics of the environment and the technicalcapabilities of the transmitter facilities

In aviation applications accuracy is a measure of the differencebetween the estimated and the true or desired aircraft positionunder nominal fault-free conditions It is normally expressed as95 bounds on Horizontal and Vertical position errors [34] In theavionics context there are two distinguished types of accuracy thatmust be considered the accuracy relative to the navigation systemalone and the accuracy achieved by the combination of navigationand flight control systems This second type of accuracy is calledTotal System Error (TSE) and is measured as deviation from therequired flight trajectory In large commercial aircraft and severalmilitary aircraft the required flight trajectory and associatedguidance information is computed by a Flight Management System(FMS) and constantly updated based on ATM and weatherinformation The navigation system estimates the aircraft statevector (ie position velocity attitude and associated rates)determines the deviation from the required flight trajectory andsends these information either to the cockpit displays or to anAutomatic Flight Control System (AFCS) The error in theestimation of the aircraftrsquos position is referred to as NavigationSystem Error (NSE) which is the difference between the aircraftrsquostrue position and its displayed position The difference betweenthe desired flight path and the displayed position of the aircraft iscalled Flight Technical Error (FTE) and accounts for aircraftdynamics turbulence effects human-machine interface etc Asillustrated in Fig 8 the TSE is obtained as the vector sum of theNSE and the FTE

Required Flight Trajectory

Indicated Flight Trajectory

Actual Flight Trajectory

FTE

TSENSE

Fig 8 Navigation accuracy in aviation applications

The integrity risk can be conveniently defined as the probability ofproviding a signal that is out of tolerance without warning the userin a given period of time It is typically derived from the high-levelTarget Level of Safety (TLS) which is an index generallydetermined through historic accident data against which thecalculated risk can be compared to judge whether the operation ofthe system is safe or not The navigation integrity requirements invarious flight phasesoperational tasks have been specified byICAO in terms of three key performance indicators the probabilityof failure over time (or per single approach) the Time-To-Alert(TTA) and the HorizontalVertical Alert Limits The TTA is themaximum allowable time elapsed from the onset of the systembeing out of tolerance until the equipment enunciates the alert Thealert limits represent the largest horizontal and vertical positionerrors allowable for safe operations They are defined as follows[36]

Horizontal Alert Limit (HAL) the HAL is the radius of a circle inthe horizontal plane (the local plane tangent to the WGS-84ellipsoid) with its center being at the true position that describesthe region that is required to contain the indicated horizontalposition with the required probability for a particular navigationmode

Vertical Alert Limit (VAL) the VAL is half the length of asegment on the vertical axis (perpendicular to the horizontal planeof the WGS-84 ellipsoid) with its center being at the true positionthat describes the region that is required to contain the indicated

vertical position with the required probability for a particularnavigation mode

According to these definitions in order to assess the navigationsystem integrity the NSE must be determined first and checkedagainst the Alert Limits (ALs) applicable to the current flightoperational phase However since the NSE is not observable bythe pilot or by the avionics on board the aircraft another approachto evaluate the system integrity has to be adopted The standardapproach consists in estimating the worst-case NSE andconfronting this value with the corresponding AL These limits forNSE are known as Protection Levels (PLs) and represent high-confidence bounds for the NSE Similarly to the positioning errors

the PLs are stated in terms of Horizontal and Vertical components(HPL and VPL)

Table 7 lists the required level of accuracy integrity continuity andavailability defined by ICAO for the different aircraft flight phasesVarious applicable national and international standrads have beenused in this compilation [37-41]

An additional performance indicator that is often used tocharacterise avionics GNSS receivers is the Time-To-First-Fix(TTFF) The TTFF accounts for the time elapsed from the GNSSreceiver switch-on until the output of a navigation solution isprovided to the user within the required performance boundaries(typically in terms of 2D3D accuracy)

Table 7 Aviation GNSS Signal-in-Space Performance Requirements [37-41]

TYPE OFOPERATION

HORVERTACCURACY

(95)CONTINUITY AVAILABILITY INTEGRITY TTA HAL VAL

En Route Oceanic 3700mNA1 minus 10ସhr to

1 minus 10hr099 to 099999 1 minus 10hr 5 min 7408mNA

En RouteContinental

3700mNA1 minus 10ସhr to


En Route Terminal 740mNA1 minus 10ସhr to

1 minus 10hr099 to 099999 1 minus 10hr 15 s 1852mNA

APV-I 16m20 m 1 minus 8 times 1015 s 099 to 09991 minus 2 times 10

App10 s 40m50 m

APV-II 16m8 m 1 minus 8 times 1015 s 099 to 09991 minus 2 times 10

App6 s 40m20m

Category I 16m4m 1 minus 8 times 1015 s 099 to 0999991 minus 2 times 10

App6 s 40m10m

Category II 69m2m 1 minus 4 times 1015 s 099 to 099999 1 minus 10ଽ15 s 1 s 173m53m

Category III 62 m2 m

1 minus 2 times 1030 s(lateral)

1 minus 2 times 1015 s(vertical)

099 to 099999

1 minus 10ଽ30 s(lateral)

1 minus 10ଽ15 s(vertical)

1 s 155m53m

The TTFF is commonly broken down into three more specificscenarios as defined in the GPS equipment guide

Cold Start The receiver has no recent Position Velocity and Time(PVT) data estimates and no valid almanac data Therefore it mustsystematically search for all possible satellites in the sky Afteracquiring a satellite signal the receiver can obtain the almanac data(approximate information relative to satellites) based on which theprocess of PVT estimation can start For instance in the case ofGPS receivers manufacturers typically claim the factory TTFF tobe in the order of 15 minutes

Warm Start The receiver has estimates of the current time within20 seconds the current position within 100 km and its velocitywithin 25 ms and it has valid almanac data Therefore it mustacquire each satellite signal and obtain the satellites detailedephemeris data

Hot Start The receiver has valid PVT almanac and ephemerisdata enabling a rapid acquisition of satellite signals The timerequired by a receiver in this state to calculate a position fix is alsocalled Time-to-Subsequent-Fix (TTSF) TTSF is particularlyimportant in aviation applications due to frequent satellite datalosses caused by high dynamics aircraft manoeuvres

In aviation applications GNSS alone does not guarantee the levelof performance required in several flight phases and operationaltasks In particular GNSS fails to deliver sufficient accuracy andintegrity levels for mission-critical and safety-critical operationssuch as precision approachauto-landing avionics flight test and

flight inspection Therefore appropriate augmentation strategiesmust be implemented to accomplish these challenging tasks usingGNSS as the primary source of navigation data

3 GNSS Threats in Aviation

To meet the stringent SIS performance requirements of GNSS inthe aviation context (Table 7) it is essential to detect isolate andpossibly predict GNSS data degradations or signal lossesexperienced by the aircraft during its mission This concept appliesboth to civil and military (manned and unmanned) aircraftalthough in different flight and operational tasks Suitablemathematical models are therefore required to describe the maincauses of GNSS signal outagesdegradations including Dopplershift interferencejamming antenna obscuration adverse satellitegeometries Carrier-to-Noise ratio (CN0) reductions (fading) andmultipath (ie GNSS signals reflected by the Earthrsquos surface or theaircraft body)

31 Antenna Obscuration

Due to the manoeuvres of the aircraft the wings tail and fuselagewill obscure some satellites during the flight Fig 9 shows theGNSS satellite obscuration algorithm

Taking into account the aircraft shape (eg using a CATIA 3-Dmodel) the aircraft flight dynamics (pitch roll and yaw variations)and the geometric displacement of the GNSS satellites in view theAntenna Obscuration Matrixes (AOMs) can be generated for the

different flight conditions Besides the AOM other factorsinfluence the satellite visibility In general a satellite isgeometrically visible to the GNSS receiver only if its elevation inthe antenna frame is above the Earth horizon and the antennaelevation mask

Fig 9 GNSS satellite obscuration analysis

It should be noted that even high performance avionics GNSSantennae have gain patterns that are typically below -3dB at about5 degrees elevation and as a consequence their performancebecome marginal below this limit (Fig 10)

17-Feb-201239copy Roberto Sabatini 2012 39

Antenna Gain (dB)

Elevation

Fig 10 Avionics antenna gain pattern (L1 frequency)

In order to determine if a satellite is obscured the LOS of thesatellite with respect to the antenna phase centre has to bedetermined To calculate the satellite azimuth and elevation withrespect to the antenna transformation matrix between ECEF (EarthCentred Earth Fixed) and antenna frame must be applied This isobtained from

ா =

lowast ே lowast ா

ே (52)

where is the transformation matrix between the aircraft body

frame and the antenna frame ே is the transformation matrix from

ENU (East-North-Up) to body frame and ாே is the ECEF to ENU

transformation matrix

32 GNSS Signal

The received signal strength is affected by a number of factorsincluding transmitter and receiver characteristics propagationlosses and interferences When necessary the various factorscontributing to the GNSS link budget and signal degradations dueto interference can be combine Multipath induced effects areconsidered separately The ratio of total carrier power to noiseܥ in dB-Hz is the most generic representation of receivedsignal strength This is given by

ேబ= ௧+ +௧ܩ minusܩ minus௦ܮ ܮ minus minusܮ ߪ minus (dB) (53)

where

is the transmitted power level (dBw)

௧ܩ is the satellite antenna gain (dBic)

ܩ is the receiver antenna gain toward the satellite

௦ܮ is the free space loss

ܮ is the atmospheric attenuation (dry-air)

ܮ is the rainfall attenuation

ߪ is the tropospheric fading

is the receiver noise figure

As an example Table 8 shows the expected ܥ for a receivertracking a GPS satellite at zenith given a typical noise powerdensity of -205 dBW-Hz [75] The values of ܥ listed in Table14 should be compared against the values required to acquire andtrack GPS signals These thresholds are heavily dependent onreceiver design and for most commercial GNSS receivers they arein the order of 28-33 dB-Hz for acquisition and 25-30 dB-Hz tomaintain tracking lock [42 43] Current generation avionics GNSSreceivers which are designed to operate in high dynamicsconditions typically exhibit better CN0 thresholds [44 45]

Table 8 Nominal receiver GPS signal power and received CN0 [43]

SV Block

IIR-MIIFFrequency P or P(Y) CA or L2C

Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C

L1 435 dB-Hz 465 dB-Hz


The link budget calculated from equation (55) only refers to thedirect GNSS signal received from a satellite Multipath effectswhich are due to the geometric and reflective characteristics of theenvironment surrounding the GNSS antenna are not included inthis calculation and are discussed separately The L-band antennaon-board a GNSS satellite is designed to radiate the composite L-band signals to the users on and near the Earth In the case of GPS(Fig 11) the satellite viewing angle from edge-to-edge of the Earthis about 277 degrees [46] The satellite antenna is designed toilluminate the Earthrsquos surface with almost uniform signal strengthThe path loss of the signal is a function of the distance from theantenna phase centre to the surface of the earth The path loss isminimum when the satellite is directly overhead (90deg elevation)and is maximum at the edges of the coverage area (satellite at thehorizon)

Fig 11 GPS satellite antenna coverage

The difference in signal strength caused by this variation in pathlength is about 21 dB and the satellite antenna gain can beapproximated by

(ܤ)௧ܩ = 25413 lowast ܧݏ minus 25413 (54)

where E is the elevation angle Similarly the avionics antenna gainpattern shown in Fig 8 can be approximated by

(ܤ)ܩ = 98756 lowast ܧݏ minus 47567 (55)

33 Radiofrequency Interference

Intentional and unintentional RF interference (jamming) can resultin degraded navigation accuracy or complete loss of the GNSSreceiver tracking Jammers can be classified into three broadcategories Narrowband Jammers (NBJ) Spread SpectrumJammers (SSJ) and Wideband Gaussian Jammers (WGJ) Inmission-essential and safety-critical GNSS applications bothintentional and unintentional jamming must be detected in theGNSS receiver and accounted for in the integrity augmentationarchitecture Fortunately a number of effective jamming detectionand anti-jamming (filtering and suppression) techniques have beendeveloped for military GNSS applications and some of them arenow available for civil use as well An overview of thesetechniques is presented in [49] The JS performance of a GNSSreceiver at its tracking threshold can be evaluated by the followingequation [1]

=ܬ 10 ቂଵ

ଵబభ( బ)frasl ಾ minus

ଵ

ଵబభ( బ)frasl ቃ (56)

where Q is the processing gain adjustment factor (1 for NBJ 15for SSJ and 2 for WGJ) Rୡ is the code chipping rate (chipssec)and ெ(ܥ) ூே is the receiver tracking threshold (dB-Hz) Sincethe weak limit in an avionics receiver is the carrier tracking loopthreshold (typically the PLL) this threshold is usually substitutedfor ெ(ܥ) ூே During some experimental flight test activities withunaided L1 CA code avionics receivers it was found that in alldynamics conditions explored and in the absence of jamming aܥ) )frasl of 25 dB-Hz was sufficient to keep tracking to the satellites[44 45] Using this 25 dB-Hz tracking threshold the ܬperformance of the GPS receiver considering one of the satellitestracked (PRN-14) during the descent manoeuvre was calculatedThe calculated C for PRN-14 was approximately 37 dB-HzUsing these ܬ values the minimum range in metres from ajamming source can be calculated from

=ఒೕ

ସగ൬10

ಶೃುೕషುೕశಸೕషಽ

మబ ൰ (57)

where ܧ ௧ is the effective radiated power of the jammer (dBw)

lis the wavelength of jammer frequency (m) is the received

(incident) jamming power level at threshold = +ܬ ௦ (dBw)

௦is the minimum received (incident) signal power (dBw) isܩ

the GNSS antenna gain toward jammer (dBic) and isܮ the

jammer power attenuation due to receiver front-end filtering (dB)

34 Atmospheric Effects

GNSS signal frequencies (L-band) are sufficiently high to keep theionospheric delay effects relatively small On the other hand theyare not so high as to suffer severe propagation losses even in rainyconditions However the atmosphere causes small but non-negligible effects that must be taken into account The majoreffects that the atmosphere has on GNSS signals include [42]

Ionospheric group delaycarrier phase advance

Tropospheric group delay

Ionospheric scintillation

Tropospheric attenuation

Tropospheric scintillation

The first two effects have a significant impact on GNSS dataaccuracy but do not directly affect the received signal strength(ܥ) Ionospheric scintillation is due to irregularities in theelectron density of the Earthrsquos ionosphere (scale size fromhundreds of meters to kilometres) producing a variety of localdiffraction and refraction effects These effects cause short-termsignal fading which can severely stress the tracking capabilities ofa GNSS receiver Signal enhancements can also occur for veryshort periods but these are not really useful from the GNSSreceiver perspective Atmospheric scintillation effects are moresignificant in the equatorial and sub-equatorial regions and tend tobe less of a factor at European and North-American latitudes

Signal scintillation is created by fluctuations of the refractiveindex which are caused by inhomogeneity in the medium mostlyassociated to solar activity At the GNSS receiver location thesignal would exhibit rapid amplitude and phase fluctuations aswell as modifications to its time coherence properties The mostcommonly used parameter characterizing the intensity fluctuationsis the scintillation index ସ defined as [47]

ସ = ටlangூమranglangூrangమ

langூrangమ(58)

where I is the intensity of the signal (proportional to the square ofthe signal amplitude) and lang rang denotes averaging The scintillationindex S4 is related to the peak-to-peak fluctuations of the intensityThe exact relationship depends on the distribution of the intensityAccording to [47] the intensity distribution is best described by theNakagami distribution for a wide range of ସ values TheNakagami density function for the intensity of the signal is givenby

(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)

where the Nakagami ldquom-coefficientrdquo is related to the scintillationindex S4 by

=ଵ

ௌరమ (60)

In formulating equation (61) the average intensity level of ܫ isnormalized to be 1 The calculation of the fraction of time that thesignal is above or below a given threshold is greatly facilitated bythe fact that the distribution function corresponding to theNakagami density has a closed form expression which is given by

(ܫ) = int ݔ(ݔ)ூ

=

Γ( ூ)

Γ( )(61)

where Γ( )and Γ (ܫ ) are the incomplete gamma functionand gamma function respectively Using the above equation it ispossible to compute the fraction of time that the signal is above orbelow a given threshold during ionospheric events For examplethe fraction of time that the signal is more than dB below themean is given by(10ଵ) and the fraction of time that the signalis more than dB above the mean is given by 1 ndash (10 ଵ)Scintillation strength may for convenience be classified into threeregimes weak moderate or strong [47] The weak valuescorrespond to ସ lt 03 the moderate values from 03 to 06 and thestrong case for ସ gt 06 The relationship between ସ and theapproximate peak-to-peak fluctuations ௨ (dB) can be

approximated by

௨ = 275 times ସଵଶ (62)

Table 9 provides a convenient conversion between ସ and theapproximate peak-to-peak fluctuations ௨ (dB)

Table 9 Empirical conversion table for scintillation indicesAdapted from [47]

Scintillation regime [dB]

Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275

Geographically there are two zones of intense scintillation one athigh latitudes and the other centred within plusmn20deg of the magneticequator as shown in Fig 12 Severe scintillation has been observedin these two sectors while in the middle latitudes scintillationoccurs exceptionally such as during geomagnetic storms In theequatorial sector there is a pronounced night-time maximum ofactivity For equatorial scintillation peak activity around the vernalequinox and high activity at the autumnal equinox have beenobserved

Fig 12 Depth of scintillation fading at 15 GHz during solar maximumand minimum years [47]

In order to predict the intensity of ionospheric scintillation onEarth-space paths the International Telecommunication Union(ITU) recommend that the Global Ionospheric Scintillation Model(GISM) be used [47] The GISM permits one to predict the ସ

index the depth of amplitude fading as well as the rms phase andangular deviations due to scintillation as a function of satellite andground station locations date time and working frequency

Tropospheric attenuation in the GNSS frequency bands isdominated by oxygen and the effects of other chemical species canbe neglected for most applications Oxygen attenuation (ܣ) is in theorder of 0035 dB for a satellite at zenith and its variation withelevation angle (ܧ) can be approximated by [75]

(ܧ)ܣ cong

௦ாାସଷ(dB)3ݎ lt ܧ lt 10 (63)

(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)

These formulae provide acceptable results only if ܧ gt 3 degreesHowever since several other errors affects measurements fromsatellites with elevation below 5 degrees a software mask istypically employed in avionics GNSS receivers to exclude thesesatellites form the navigation computations [45] Troposphericrainfall attenuation has a minor effect in the GNSS frequencybands For instance at a frequency of 2 GHz the attenuation forhigh rainfall rates is less than 001 dBkm (rainfall attenuation

below 2 GHz is even less) Tropospheric scintillation is caused byirregularities (primarily turbulence) causing variations of therefractive index This effect varies with time frequency andelevation angle For small omnidirectional antennas such as GNSSantennas the CCIR provided the following expression for the long-term RMS amplitude scintillation [46]

ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)

where is the frequency in GHz The Noise Figure ( ) is related

to the system noise temperature ( ௦௬௦) in Kelvin as follows [48]

= 10 ቀ1 +ೞೞ

బቁ (dB) (66)

where = 290K = 246 dB-K ௦௬௦ for antenna plus receiver can

be computed using the Friis formula Typical values for state-

of-the-art GPS receivers are between 2 and 4 dB

35 Doppler Shift

Doppler shift is the change in frequency of the received signal thatis experienced when the observer (aircraft) moves relative to thesignal source (satellite) The magnitude of the frequency shiftproduced in the signal received from the nth satellite is a functionof the relative velocity measured along the satellite-aircraft LOSThe Doppler shift of the nth satellite signal frequency is given by

∆ = ቀ|௩ሬሬሬሬሬ|∓|௩ሬሬሬሬ|

ቁ ݏ (67)

where ሬሬሬሬݒ is the nth satellite velocity component along the LOS ሬሬሬሬݒis the aircraft velocity projection along the LOS is the speed oflight [ [ଵݏ is the GNSS signal frequency [Hz] and is theangle between the aircraft velocity vector and the nth satellite LOSIn a practical aviation application an optimisation process can beinitiated aiming to avoid any further observed increase in Dopplershift In particular the presented algorithm studies the variations ofሬሬሬሬݒ and ሬሬሬሬݒ for each tracked satellite and imposes geometricconstraints to the trajectory that are accounted for in the trajectoryoptimisation process With reference to the geometry illustrated inFig 13 the following trigonometric relationship holds true

Ԧcosݒ) )sinܧ= Ԧcosݒ prime (68)

where Ԧݒ is the aircraft velocity vector isܧ the elevation angle ofthe nth satellite is the relative bearing of the aircraft to thesatellite and prime is the azimuth of the LOS projection in theantenna plane

Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ

Fig 13 Reference geometry for Doppler shift analysis

From equations (67) and (68) the aircraft-satellite relativegeometric conditions that maximise or minimise Doppler shift canbe determined In particular combining the two equations theDoppler shift is given by


ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)

The above equation shows that both the elevation angle of thesatellite and the aircraft relative bearing to the satellite affect themagnitude of the Doppler shift In particular reductions of ܧ leadto increases in Doppler shift while prime drives increments ordecrements in Doppler shift depending on the size of the angle andthe direction of the aircraft velocity vector By inspecting Fig 14it is evident that a relative bearing of 90deg and 270deg would lead to anull Doppler shift as in this case there is no component of theaircraft velocity vector ሬሬሬሬݒ) in this case) in the LOS to the satelliteHowever in all other cases (ie neԦݒ (ሬሬሬሬݒ such a component wouldbe present and this would lead to increments or decrements inDoppler shift depending on the relative directions of the vectors Ԧݒand ሬሬሬሬݒ This fact is better shown in Fig 14 where a steady flightwithout loss of generality is assumed

χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ

Fig 14 Reference geometry for Doppler shift manoeuvre corrections

As the time required for typical aircraft heading changemanoeuvres is much shorter than the timeframe associate tosignificant satellite constellation changes each satellite can beconsidered stationary in the body reference frame of themanoeuvring aircraft Therefore during manoeuvres leading toDoppler shift an initial aircraft velocity vector పሬሬሬcanݒ be consideredto define path constraints that avoid further signal degradation orloss This can be performed by imposing that the aircraft increasesthe heading rates towards the directions ሬሬሬሬݒ or ሬሬሬሬݒ- and minimisesthe heading rates towards the directions ெሬሬሬሬሬݒ and ெሬሬሬሬሬݒ- The choice ofሬሬሬሬorݒ ሬሬሬሬݒ- is based simply on the minimum required heading change(ie minimum required time to accomplish the correction)Regarding the elevation angle (ܧ) dependency of Doppler shiftequation (69) shows that minimising the elevation angle becomesan objective also in terms of Doppler trajectory optimisation

36 Multipath Analysis

Multipath is caused by the interference of multiple reflections(from the ground and the aircraft structure) with the direct signaltransmitted by the satellite and represents a major source of errorin GNSS observations The level and characteristics of multipathdepend on the geometry of the environment surrounding theantenna the reflectivity of nearby objectsterrain and the satelliteelevation angle In order to build a reliable multipath model acombination of signal analysis and geometric ray-tracing methodswas adopted

ࢼ

Fig 15 GNSS signal phases

From Fig 15 the and phase error for a single refection can berepresented as a function of direct and multipath signal amplitudesand the multipath relative phaseߚ [49]

= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)

ݐ ൫ߜథ൯= ௦ఉ

ା ௦ఉ(71)

where ௗܣ is the direct signal amplitude ܣ is multipath signalamplitude and ߚ is the phase of the multipath Fig 16 shows thatboth the multipath phase andߚ the multipath amplitude affect thereceived signal Therefore we require a multipath model tosimulate these two factors considering the reflections from theairframe and from the ground The commonly adoptedAeronautical Multipath Channel (AMC) model developed duringthe ESA-SDS research [50 51]

=

+

-

ࢼ = deg ࢼ = deg ࢼ = ૡdeg

Fig 16 Variation of ܣ as function of the angle ߚ

Fig 17 illustrates the overall structure of the AMC model Letℎ(ݐ ) be the impulse response of the multipath channel modelThen ℎ(ݐ ) is given by [50]

ℎ(ݐ ) = 1 + sum ඥ ଷୀଵ lowast (ݐ) lowast minusݐ)ߜ ) (72)

where is the echo power of the th path The signal (ݐ) is anoise signal with power and a power spectral density N(f)

( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)

where ܤ is the noise bandwidth From the multipath channel modelin Fig 17 the wing reflection the fuselage reflection and theground-echo are the main components of the multipath signal

Fig 17 AMC model structure

Fig 18 shows the geometric reflection model The incoming waveis emitted from point is the receiver location and is thereflection point is a defined point on the reflecting surface andn stands for a unit vector normal to the surface

R

T

Reference

Reflecting SurfaceV

Sn

R image

Fig 18 Geometric reflection model

In ray-tracing the reflection point and the defined point shouldsatisfy the equation

(minus ) times = 0 (74)

and the line equation connecting and

= + timesݐ ൫ minus ൯ (75)

where isݐ a parameter between 0 and 1 Combining Eqs (74) and(75)is given by

= +timestimes

times൫ோ ൯൫ minus ൯ (76)

The corresponding extra path lengthܮ ௌ due to specularreflection is then

ܮ ௌ = |minus | + | minus | minus |minus | (77)

In our wing reflection model the wing is assumed to be flat ByGaussian Doppler spectrum theory the power of the wing echospectrum is assumed to be [52]

(ௗ) = 20 lowast ൬ଵ

ඥଶగఙమlowast

మ

మమ൰ (78)

where the deviation ߪ = 38 Hz The wing reflection signal delaycan be calculated from

௪(ݐ) =ଶlowastlowast௦(ா)

బ(79)

where L is the antenna height from the wing ܧ is the elevationangle (degrees) and ܥ is the speed of light The fuselage isassumed to be a cylinder and the power of the fuselage echospectrum is given by [52]

(ܤ) = 20 lowast ଵ[ ଵ lowast (మlowast|| ) minus minus ଷ] (80)

where ଵ ଶ and ଷ are the fuselage geometric coefficientsPrevious research showed that the fuselage reflectioncharacteristics change very little by increasing the fuselage radius[51] Ground reflection becomes important only during the landingphase when the aircraft is in close proximity of the terrainAssuming a Gaussian distributed ground reflection amplitude withzero mean the ground-echo power is given by

(ௗ) = 20 lowast logଵ൬ଵ


మ

మమ൰ (81)

where in this case the deviation ߪ = 38 Hz Assuming that theterrain is flat

௨ௗ(ݐ) =ଶlowastlowast௦(ா)

బ(82)

where ℎ is the aircraft altitude and ܧ is the elevation angleObviously this basic ground-echo model can be expanded to takeinto account various terrain and man-made building geometriesAs discussed in [42] GNSS receivers can effectively reject mostof the multipath signal if the differential delay ∆τ gt 15 μs for theCA code and 015 μs for the P(Y) code As a consequence theregion of potential ground-echo multipath problems for the CAcode is

ℎ lowast ݏ (ܧ) lt (ݏߤ15) lowast ܥ = 4485 (83)

Simulation and flight test activities performed on various aircrafthave showed that the fuselage reflections are normally the maincontributors to the airframe multipath [53 54] In most conditionsthe effects of signals reflected from the aircraft wings arecomparatively smaller [50 51] In particular it has been found thatthe airframe multipath ranging error budget can be minimised byplacing the GNSS antenna 5 (or more) centimetres above thehighest point on the aircraft fuselage Furthermore it has beenobserved that the effect of ground-echo signals translate into asudden increase of the multipath ranging error of up to two ordersof magnitude with respect to the airframe multipath errors aloneDuring a low-level military aircraft flight trial it was found that theground-multipath ranging error reached a value of about 140metres when the aircraft was flying at an altitude of 300 feet AGLover flat terrain with a roll angle exceeding 45 degrees [44 45] Itmust be pointed out however that such particular flight conditionsare only likely to be encountered in military aircraft and someunmanned aircraft applications Due to the flight profilerequirements and manoeuvring constraints of typical airliners theground multipath contributions can be normally neglected in thesecases According to the Standard Multipath Error Model (SMEM)research [55] and experimental validation activities performed inthe US on various types of civil airliners [56] the airframemultipath ranging error s ௨௧௧ associated to a satellite

observation can be calculated directly as a function of the satelliteelevation angle

sݑ ݐ ℎݐ = 013 + 053ቀminus

ܧ

10ቁ

(84)

This model was endorsed by the ICAO GNSS panel and includedin the Minimum Operational Performance Standards (MOPS) forthe Local Area Augmentation System (LAAS) and for the WideArea Augmentation System (WAAS) by the Radio TechnicalCommission for Aeronautics (RTCA) [36 41 56 57]

37 Receiver Tracking Errors

A dedicated analysis of the GNSS receiver tracking performance isrequired to analyse the dynamic stress errors signal fading ܥ)reduction) and interferences ܬ) increase) When the GNSS codeandor carrier tracking errors exceed certain thresholds thereceiver loses lock to the satellites Since both the code and carriertracking loops are nonlinear especially near the threshold regionsonly Monte Carlo simulations of the GNSS receiver in differentdynamics and SNR conditions can determine the receiver trackingperformance [58] Nevertheless some conservative rule-of-thumbsapproximating the measurement errors of the GNSS tracking loopscan be employed for this analysis Numerous sources ofmeasurement errors affect the carrier and code tracking loops It isimportant to analyse the dominant error sources in each type oftracking loop Considering a typical avionics GNSS receiveremploying a two-quadrant arctangent discriminator the PhaseLock Loop (PLL) threshold is given by [1]

ߪ3 = +ߪ3 ߠ le 45deg (85)

where ߪ is the 1-sigma phase jitter from all sources except

dynamic stress error and ߠ is the dynamic stress error in the PLLtracking loop Expanding the above equation the 1-sigmathreshold for the PLL tracking loop becomes [1]

ߪ = ඥߪ௧ଶ + జߪ

ଶ + ߠଶ +

ఏ

ଷle 15deg (86)

where ௧ߪ is the 1-sigma thermal noise జߪ is the variance-

induced oscillator phase noise and ߠ is the Allan-variance jitter

The PLL thermal noise is often thought to be the only carriertracking error since the other sources of PLL jitter may be eithertransient or negligible The PLL thermal noise jitter is computed asfollows

௧ߪ =ଷ

ଶగට

బ(1 +

ଵ

ଶబ) (degrees) (87)

where ܤ is the carrier loop noise bandwidth (Hz) is the

carrier to noise power ratio ( = 10(ேబ)ଵ for CN

expressed in dB-Hz) and T is the predetection integration time(seconds) ܤ and ܥ can be derived from the SNR modeldescribed earlier in this section Determination of the vibration-induced oscillator phase noise is a complex analysis problem Insome cases the expected vibration environment is so severe thatthe reference oscillator must be mounted using vibration isolatorsin order for the GPS receiver to successfully operate in PLL Theequation for vibration induced oscillator jitter is

జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)

where is the L-band frequency (Hz) జ( )is the oscialltorvibration sensitivity of ∆ per g as a function of which isthe random vibration modulation frequency (Hz) ( ) is thepower curve of the random vibration as a function of (gଶHz)and g is the gravity acceleration Usually the oscillator vibrationsensitivityజ( ) is not variable over the range of the randomvibration modulation frequency then the above equation can besimplified to

జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)

The equations used to determine Allan deviation phase noise areempirical They are stated in terms of what the requirements are forthe short-term stability of the reference oscillator as determined bythe Allan variance method of stability measurement The equationfor second-order loop short-term Allan deviation is

ଶߠ = 144ఙಲ (ఛ)lowastಽ

(rad) (90)

The equation for thirdndashorder loop short-term Allan deviation forPLL is

ଷߠ = 160ఙಲ (ఛ)lowastಽ

(rad) (91)

where )ߪ ) is the Allan deviation-induced jitter (degrees) isthe L-band input frequency (Hz) is the short-term stability gatetime for Allan variance measurement (seconds) and ܤ is the noisebandwidth Usually )ߪ ) can be determined for the oscillator andit changes very little with gate time For example assuming theloop filter as a third-order with a noise bandwidth B୬ = 18 Hz andthe gate time τ = 1B୬ = 56 ms the Allan deviation is found tobe σ(τ) = 10ଵ The dynamic stress error depends on the loopbandwidth and order In a third-order loop the dynamic stress erroris [1 54]

ଷߠ =ௗయோௗ௧య

ఠబయ =

ௗయோௗ௧య

ቀಳ

బళఴరఱቁయ = 04828

యೃ

య

య (degrees) (92)

where is the LOS range to the satellite ଶݐଶ is themaximum LOS acceleration dynamics (degsଶ) w is the loop filternatural radian frequency and B୬is the noise bandwidth For the L1frequency the term ଷݐଷ = (98sଷ) times (360degcycle) times(157542 times 10 cycless)= 185398degsଷ Frequency jitter dueto thermal noise and dynamic stress error are the main errors in aGNSS receiver Frequency Lock Loop (FLL) The receivertracking threshold is such that the 3-sigma jitter must not exceedone-fourth of the frequency pull-in range of the FLL discriminatorTherefore the FLL tracking threshold is [1 54]

ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)

where ௧ிߪ3 is the 3-sigma thermal noise frequency jitter and f isthe dynamic stress error in the FLL tracking loop The aboveequation shows that the dynamic stress frequency error is a 3-sigmaeffect and is additive to the thermal noise frequency jitter Thereference oscillator vibration and Allan deviationndashinducedfrequency jitter are small-order effects on the FLL and areconsidered negligible The 1-sigma frequency jitter threshold is1(12T) = 00833T Hz The FLL tracking loop jitter due to thermalnoise is

௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)

where ܨ is 1 at highܥ and 2 near the threshold ௧ிߪ isindependent of CA or P(Y) code modulation and loop order Sincethe FLL tracking loop involves one more integrator that the PLLtracking loop of the same order the dynamic stress error is [54]

=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)

Regarding the code tracking loop a conservative rule-of-thumb forthe Delay Lock Loop (DLL) tracking threshold is that the 3-sigmavalue of the jitter due to all sources of loop stress must not exceedthe correlator spacing ( ) expressed in chips Therefore [54]

ߪ3 = ௧ߪ3 + le (chips) (96)

where σ୲ୈis the 1-sigma thermal noise code tracking jitter Re isthe dynamic stress error in the DLL tracking loop The DLLthermal noise code tracking jitter is given by

௧ߪ = ටସிభௗ

మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)

where Fଵis the DLL discriminator correlator factor (1 for timeshared tau-dithered earlylate correlator and 05 for dedicated earlyand late correlators) is the correlator spacing between earlyprompt and late ܤ is the code loop noise bandwidth and ଶܨ is theDLL dicriminator type factor (1 for earlylate type discriminator

and 05 for dot product type discriminator) The DLL tracking loopdynamic stress error is given by

=ೃ

ఠబ (chips) (98)

where dR୬ dt୬ is expressed in chipssecn The PLL FLL and DLLerror equations described above allow determining the CN

corresponding to the tracking threshold of the receiver A genericcriterion applicable to GNSS augmentation systems is

௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)

where (ܥ) is the minimum carrier-to-noise ratio for PLLcarrier tracking ிis(ܥ) the is the minimum carrier-to-noiseratio for FLL carrier tracking and is(ܥ) the minimumcarrier-to-noise ratio for DLL code tracking

4 GNSS Augmentation

In aviation applications GNSS alone does not guarantee the levelof performance required in several flight phases and operationaltasks In particular GNSS fails to deliver sufficient accuracy andintegrity levels for mission safety-critical operations such asprecision approachauto-landing avionics flight test and flightinspection Therefore appropriate augmentation strategies must beimplemented to accomplish these challenging tasks using GNSS asthe primary source of navigation data Furthermore when GNSS isemployed as primary means of navigation some form ofaugmentation is necessary to satisfy accuracy integrityavailability and continuity requirements

41 Differential GNSS

Differential GNSS (DGNSS) techniques can be used to addressaccuracy requirements Specifically in the case of GPSdifferential techniques have been developed which can provideaccuracies comparable with current landing systems A variety ofLocal Area DGNSS (LAD) and Wide Area DGNSS (WAD)networks have been proposed over the past twenty years and someLADWAD systems have achieved the levels of maturity requiredto enter the market Due to the existence of a copious literature onGPSGNSS basic principles and applications these will not becovered in this thesis DGNSS was developed to meet the needs ofpositioning and distance-measuring applications that requiredhigher accuracies than stand-alone GNSS could deliver DGNSSinvolves the use of a control or reference receiver at a knownlocation to measure the systematic GNSS errors and by takingadvantage of the spatial correlation of the errors the errors can thenbe removed from the measurement taken by moving or remotereceivers located in the same general vicinity There have been awide variety of implementations described for affecting such aDGNSS system The intent is to characterise various DGNSSsystems and to compare their strengths and weaknesses Twogeneral categories of DGNSS systems can be identified those thatrely primarily upon the code measurements and those that relyprimarily upon the carrier phase measurements Using carrierphase high accuracy can be obtained (centimetre level) but thesolution suffers from integer ambiguity and cycle slips Whenevera cycle slip occurs it must be corrected for and the integerambiguity must be re-calculated The pseudorange solution is morerobust but less accurate (2 to 5 m) As it is not affected by cycleslips there is no need for re-initialisation A typical DGNSSarchitecture is shown in is shown in Fig 19

Corrections

DataLink

DGNSS Reference

Receiver

Surveyed GNSSAntenna

Data link

GNSS

DGNSS Ground Station

Receiver

Fig 19 Typical DGNSS system architecture

The system consists of a Reference Receiver (RR) located at aknown location that has been previously surveyed and one or moreDGNSS User Receivers (URs) The RR antenna differentialcorrection processing system and data link equipment (if used) arecollectively called the Reference Station (RS) Both the UR andthe RR data can be collected and stored for later processing or sentto the desired location in real time via the data link DGNSS isbased on the principle that receivers in the same vicinity willsimultaneously experience common errors on a particular satelliteranging signal In general the UR (mobile receiver) usesmeasurements from the RR to remove the common errors In orderto accomplish this the UR must simultaneously use a subset or thesame set of satellites as the reference station The DGNSSpositioning equations are formulated so that the common errorscancel The common errors include signal path delays through theatmosphere and satellite clock and ephemeris errors For PPSusers the common satellite errors are residual system errors thatare normally present in the PVT solution For SPS users thecommon satellite errors also include the intentionally added errorsfrom SA Errors that are unique to each receiver such as receivermeasurement noise and multipath cannot be removed withoutadditional recursive processing (by the reference receiver userreceiver or both) to provide an averaged smoothed or filteredsolution Various DGNSS techniques are employed depending onthe accuracy desired where the data processing is to be performedand whether real-time results are required If real-time results arerequired then a data link is also required For applications withouta real-time requirement the data can be collected and processedlater The accuracy requirements usually dictate whichmeasurements are used and what algorithms are employed In thecase of Differential GPS (DGPS) accuracy is independent ofwhether SPS or PPS is being used although real-time PPS DGPScan have a lower data rate than SPS DGPS because the rate ofchange of the nominal system errors is slower than the rate ofchange of SA However the user and the Reference Station mustbe using the same service (either PPS or SPS) The clock andfrequency biases for a particular satellite will appear the same toall users since these parameters are unaffected by signalpropagation or distance from the satellite The pseudorange anddelta-range (Doppler) measurements will be different for differentusers because they will be at different locations and have differentrelative velocities with respect to the satellite but the satellite clockand frequency bias will be common error components of thosemeasurements The signal propagation delay is truly a commonerror for receivers in the same location but as the distance betweenreceiversrsquo increases this error gradually de-correlates and becomesindependent The satellite ephemeris has errors in all threedimensions Therefore part of the error will appear as a commonrange error and part will remain a residual ephemeris error Theresidual portion is normally small and its impact remains small for

similar observation angles to the satellite The first acceptedstandard for SPS DGPS was developed by the Radio TechnicalCommission for Maritime Services (RTCM) Special Committee-104 [59-61] The data interchange format for NATO users ofDGPS is documented in STANAG 4392 The SPS reversionarymode specified in STANAG 4392 is compatible with the RTCMSC-104 standards The standards are primarily intended for real-time operational use and cover a wide range of DGPS measurementtypes Most SPS DGPS receivers are compatible with the RTCMSC-104 differential message formats DGPS standards foraeronautical use were originally developed by the RTCA allowSpecial Category-I (SCAT-I) precision approach using range-codedifferential These standards were contained in RCTA documentDO-217 and intended only for limited use until an internationalstandard could be developed for precision approach [62] Morerecently the two separate standards were developed by RTCA forGPS WAASLAAS These standards define the minimumoperational performance requirements for different WAASLAASimplementation types allowing WAAS operations down to CAT-I[63] and LAAS operations down to CAT-IIIb [64 65] There aretwo primary variations of the differential measurements andequations One is based on ranging-code measurements and theother is based on carrier-phase measurements There are alsoseveral ways to implement the data link function DGNSS systemscan be designed to serve a limited area from a single referencestation or can use a network of reference stations and specialalgorithms to extend the validity of the DGNSS technique over awide area The result is that there is a large variety of possibleDGNSS system implementations using combinations of thesedesign features

411 Ranging-Code DGNSS

Ranging-code differential techniques use the pseudorangemeasurements of the RS to calculate pseudorange or positioncorrections for the UR The RS calculates pseudorange correctionsfor each visible satellite by subtracting the ldquotruerdquo range determinedby the surveyed position and the known orbit parameters from themeasured pseudorange The UR then selects the appropriatecorrection for each satellite that it is tracking and subtracts thecorrection from the pseudorange that it has measured The mobilereceiver must only use those satellites for which corrections havebeen received If the RS provides position corrections rather thanpseudorange corrections the corrections are simply determined bysubtracting the measured position from the surveyed position Theadvantage of using position corrections is obviously the simplicityof the calculations The disadvantage is that the reference receiverand the user receiver must use the exact same set of satellites Thiscan be accomplished by coordinating the choice of satellitebetween the RR and the UR or by having the RS compute aposition correction for each possible combination of satellites Forthese reasons it is usually more flexible and efficient to providepseudorange corrections rather than position corrections RTCANATO STANAG and RTCM standards are all based onpseudorange rather than position corrections The pseudorange orposition corrections are time tagged with the time that themeasurements were taken In real-time systems the rate of changeof the corrections is also calculated This allows the user topropagate the corrections to the time that they are actually appliedto the user position solution This reduces the impact of datalatency on the accuracy of the system but does not eliminate itentirely SPS corrections become fully uncorrelated with the usermeasurements after about 2 minutes Corrections used after twominutes may produce solutions which are less accurate than stand-alone SPS GPS PPS corrections can remain correlated with theuser measurements for 10 minutes or more under benign (slowlychanging) ionospheric conditions There are two ways ofpseudorange data processing post-mission and real-timeprocessing The advantage of the post-mission solution over the

real-time one is that it is more accurate because the user can easilydetect blunders and analyse the residuals of the solution On theother hand the main disadvantage of the post-mission solution isthat the results are not available immediately for navigation Thetypical algorithm of the ranging-code DGNSS post-processedsolution used in flight test and inspection tasks is the doubledifference pseudorange

Fig 20 shows the possible pseudorange measurements betweentwo receivers (k and l) and two satellites (p and q) If pseudoranges1 and 2 from Fig 22 are differenced then the satellite clock errorand satellite orbit errors will be removed If SA is active (not thepresent case) it will be removed completely only if the signalsutilised in each receiver are transmitted exactly at the same timeThe residual error from SA is not a problem for post-processedpositioning where it is easy to ensure that the differencing is donebetween pseudoranges observed at the same time Anyatmospheric errors will also be reduced significantly with singledifferencing The basic mathematical model for single differencepseudorange observation is the following

minus

= ߩ

minus ߩ

minus ݐ) minus +(ݐ minus

+ minus

+ Δߝ (104)

where

is the pseudorange measurementߩdenotes the

geometric distance between the stations and satellite ݐ denotesthe receiverrsquos clock offsets denotes the receiverrsquos hardware

code delays

denotes the multipath of the codes Δߝ denotes

the measurement noise and is the velocity of light

DGNSS User Receiver(Receiver k)

DGNSS Reference Receiver(Receiver l)

1

2

3

4

Satellite p Satellite q

Fig 20 Pseudorange Differencing

Equation (104) represents the single difference pseudorangeobservable between receivers There are four unknowns in theabove equation assuming that the co-ordinates of station k areknown and that the difference in clock drifts is one unknownHence four satellites are required to provide four single differenceequations in order to solve for the unknowns Single differenceswith code observations are frequently used in relative (differential)navigation Using all pseudoranges shown in Fig 22 differencesare formed between receivers and satellites Double differencesare constructed by taking two between-receiver single differencesand differencing these between two satellites This procedureremoves all satellite dependent receiver dependent and most of theatmospheric errors (if the distance between the two receivers is nottoo large) The derived equation is

minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where

denotes the total effect of multipath There are three

unknowns in the above equation (the co-ordinates of station l) anda minimum of four satellites is required to form a minimum of three

double difference equations in order to solve for the unknownsUsing the propagation of errors law it is shown that the doubledifference observables are twice as noisy as the pure pseudoranges

ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)

but they are more accurate because most of the errors are removedIt is to be note that multipath remains because it cannot bemodelled and it is independent for each receiver

412 Carrier-phase DGNSS

Carrier-phase DGNSS techniques use the difference between thecarrier phases measured at the RR and UR A double-differencingtechnique is used to remove the satellite and receiver clock errorsThe first difference is the difference between the phasemeasurement at the UR and the RR for a single satellite Thiseliminates the satellite clock error which is common to bothmeasurements This process is then repeated for a second satelliteA second difference is then formed by subtracting the firstdifference for the first satellite from the first difference for thesecond satellite This eliminates both receiver clock errors whichare common to the first difference equations This process isrepeated for two pairs of satellites resulting in three double-differenced measurements that can be solved for the differencebetween the reference station and user receiver locations This isinherently a relative positioning technique therefore the userreceiver must know the reference station location to determine itsabsolute position

The single difference observable is the instantaneous phasedifference between two receivers and one satellite It is alsopossible to define single differences between two satellites and onereceiver Using the basic definition of carrier-phase observablepresented above the phase difference between the two receivers Aand B and satellite is given by

Φ ( ) = Φ

( ) minusΦ( ) (107)

and can be expressed as

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)

where Φ( ) = Φ( ) minusΦ( ) =

- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)

Hence with four satellites and

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)

The double difference is formed from subtracting two singledifferences measured to two satellites and The basic doubledifference equation is

Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=

- and the only unknowns being the double-

difference phase ambiguity

and the receiver co-ordinates Thelocal clock error is differenced out Two receivers and foursatellites and will give 3 double difference equationscontaining the co-ordinates of the receiver A ( ) and B

( ) and the unknown integer ambiguities

and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)

Therefore the double difference observation equation can bewritten as [6]

Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =

(Φ minusΦୡ) + ݒ (118)

where ( ) are the co-ordinates of receiver A ( )are the co-ordinates of receiver B (ଵଶଷ) are the integerambiguities ܥ is correction term (Φ minusΦୡ) is the observedminus the computed observable and ݒ is the residual Fromequation (113) the unknown receiver co-ordinates can becomputed It is necessary however to determine the carrier phaseinteger ambiguities (ie the integer number of completewavelengths between the receiver and satellites) In surveyingapplications this integer ambiguity can be resolved by starting withthe mobile receiver antenna within a wavelength of the referencereceiver antenna Both receivers start with the same integerambiguity so the difference is zero and drops out of the double-difference equations Thereafter the phase shift that the mobilereceiver observes (whole cycles) is the integer phase differencebetween the two receivers An alternative is to place the mobilereceiver at a surveyed location In this case the initial difference isnot necessarily zero but it is readily calculated For aviationapplications where it is not possible to bring the referencemobileantennas together or to position the aircraft at a surveyed locationthe reference and mobile receivers must solve for the ambiguitiesindependently as part of an initialisation process For theseapplications it is essential to be able to solve for integer ambiguityat an unknown location and while in motion In this case solvingfor the integer ambiguity usually consists of eliminating incorrectsolutions until the correct solution is found A good initial estimateof position (such as from ranging-code differential) helps to keepthe initial number of candidate solutions small Redundantmeasurements over time andor from extra satellite signals are usedto isolate the correct solution This version of the carrier-phaseDGNSS technique is typically called Real-Time Kinematic (RTK)GNSS If carrier track or phase lock on a satellite is interrupted(cycle slip) and the integer count is lost then the initialisationprocess must be repeated for that satellite Causes of cycle slips canrange from physical obstruction of the antenna to suddenaccelerations of the aircraft Output data flow may also beinterrupted if the receiver is not collecting redundant measurementsform extra satellites to maintain the position solution If a preciseposition solution is maintained re-initialisation for the lost satellitecan be very rapid Developing a robust and rapid method ofinitialisation and re-initialisation is the primary challenge facingdesigners of RTK systems that have to deal with safety criticalapplications such as aircraft precision approach A description oftechniques for solving ambiguities both in real-time and post-processing applications together with information about cycleslips repair techniques can be found in the literature [66-78]

42 Data Link Implementations

DGNSS can be implemented in several different ways dependingon the type of data link used The simplest way is no data link at

all For non-real-time applications the measurements can bestored in the receiver or on suitable media and processed at a latertime In most cases to achieve surveying accuracies the data mustbe post-processed using precise ephemeris data that is onlyavailable after the survey data has been collected Similarly forsome test applications the cost and effort to maintain a real-timedata link may be unnecessary Nevertheless low-precision real-time outputs can be useful to confirm that a test is progressingproperly even if the accuracy of the results will be enhanced laterDifferential corrections or measurements can be uplinked in real-time from the reference station to the users This is the mostcommon technique where a large number of users must be servedin real-time For military purposes and proprietary commercialservices the uplink can be encrypted to restrict the use of theDGNSS signals to a selected group of users Differentialcorrections can be transmitted to the user at different frequenciesWith the exception of satellite data links there is generally a trade-off between the range of the system and the update rate of thecorrections As an example Table 10 lists a number of frequencybands the range and the rate at which the corrections could beupdated using the standard RTCM SC-104 format [59-61]

Table 10 Possible DGNSS data link frequencies

Frequency Range [Km]Update Rate

[sec]

LF (30 - 300 kHz) gt 700 lt 20

MF (300 kHz - 3 MHz) lt 500 5 ndash 10

HF ( 3 MHz - 25 MHz) lt 200 5

VHF (30 MHz - 300MHz)

lt 100 lt 5

L Band (1 GHz - 2GHz)

Line of Sight Few Seconds

An uplink can be a separate transmitterreceiver system or theDGNSS signals can be superimposed on a GPS-link L-bandranging signal The uplink acts as a pseudo-satellite or ldquopseudoliterdquoand delivers the ranging signal and DGNSS data via the RF sectionof the user receiver much in the same way the GPS navigationmessage is transmitted The advantages are that the additionalranging signal(s) can increase the availability of the positionsolution and decrease carrier-phase initialisation time Howeverthe RS and URrsquos become more complex and the system has a veryshort range (a few kilometres at the most) This is not only becauseof the line of sight restriction but also the power must be kept lowin order to avoid interference with the real satellite signals (ie thepseudolite can become a GPS jammer if it overpowers the GPSsatellite signals) A downlink option is also possible from the usersto the RS or other central collection point In this case thedifferential solutions are all calculated at a central location This isoften the case for test range applications where precise vehicletracking is desired but the information is not used aboard thevehicle The downlink data can be position data plus the satellitetracked or pseudorange and deltarange measurements or it can bethe raw GPS signals translated to an intermediate frequency Thetranslator method can often be the least expensive with respect touser equipment and therefore is often used in munitions testingwhere the user equipment may be expendable

421 DGNSS Accuracy

Controlled tests and recent extensive operational use of DGNSShave repeatedly demonstrated that DGNSS (pseudorange) providesaccuracies in the order of 3 to 10 metres This figure is largelyirrespective of receiver type whether or not SA is in use and overdistances of up to 100 NM from the reference station [45 79] WithKinematic DGNSS (KDG) positioning systems requiring theresolution of the carrier phase integer ambiguities whilst on the

move centimetre level accuracy can be achieved [6 80-83] Mostcurrent applications of DGNSS use L1 CA code pseudorange asthe only observable with achieved accuracies of 1 to 5 m in real-time Other applications use dual frequency pseudoranges (egCA and P code from GPS) or combinations of pseudorange andcarrier phase observables Various techniques have been developedthat achieve increased accuracy at the expense of increasedcomplexity A possible classification scheme of these techniques ispresented in Table 11

Precise DGNSS (PDG) can achieve accuracies below 1 m usingdual-frequency psudorange measurements and Very PreciseDGNSS (VPDG) taking advantage of both dual frequency codeand carrier phase observables is capable of On-The-Fly (OTF)ambiguity resolution [69 70] At the moment Ultra-PreciseDGNSS (UPDG) using carrier phase observables with integerambiguities resolved is only utilised in flight testing flightinspection and other non-real-time aviation applications In theabsence of Selective Availability (SA) the major sources of errorfor stand-alone ranging-code GNSS are

Ephemeris Error

Ionospheric Propagation Delay

Tropospheric Propagation Delay

Satellite Clock Drift

Receiver Noise and clock drift

Multipath

Table 11 Classification of DGNSS techniques

Name Description RMS

DGNSSSingle frequency pseudorange (eg

GPS CA code)1 - 5 m

PDGDual frequency pseudorange (eg GPS

P code)01 - 1 m

VPDG Addition of dual band carrier phase 5 - 30 cm

UPDGAbove with integer ambiguities

resolvedlt 2 cm

Table 12 lists the error budgets from the above sources giving anestimation of the possible improvements provided by L1 ranging-code DGNSS [82] The error from multipath is site dependent andthe value in Table 12 is only an example The receiver clock driftis not mentioned in Table 12 because it is usually treated as anextra parameter and corrected in the standard solutionFurthermore it does not significantly add to differential errorsMultipath and receiver noise errors cannot be corrected byDGNSS It is worth to mention that the errors introduced bySelective Availability (SA) which is currently off would becorrected by DGNSS techniques For users near the referencestation the respective signal paths to the satellite are close enoughtogether that the compensation of Ionospheric and TroposphericDelays (ITD) is almost complete As the user to RS separation isincreased the different ionospheric and tropospheric paths to thesatellites can be far enough apart that the ionospheric andtropospheric delays are no longer common errors Thus as thedistance between the RS and user receiver increases theeffectiveness of the atmospheric delay corrections decreases

Table 12 Error sources in DGNSS

Error SourceStand Alone GNSS

[m]L1 CA CodeDGNSS [m]

Ephemeris 5 - 20 0 ndash 1

Ionosphere 15 - 20 2 ndash 3

Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2

The ephemeris error is effectively compensated unless it has quitea large out-of-range component (eg 1000 metres or more due toan error in a satellite navigation message) Even then the error willbe small if the distance between the reference receiver and userreceiver is small Finally the satellite clock error is compensatedas long as both reference and user receivers employ the samesatellite clock correction data As already mentioned thecorrelation of the errors experienced at the RS and the user locationis largely dependent on the distance between them As theseparation of the user from the RS increases so does the probabilityof significant differing ionospheric and tropospheric conditions atthe two sites Similarly the increasing separation also means thata different geometrical component of the ephemeris error is seenby the RR and UR This is commonly referred to as ldquoSpatialDecorrelationrdquo of the ephemeris and atmospheric errors In generalthe errors are likely to remain highly correlated for users within350 km of the RS However if the distance is greater than 250 kmthe user will obtain better results using correction models forionospheric and tropospheric delay [45 79] Additionally practicalDGNSS systems are typically limited by the data link to aneffective range of around 170 km Table 13 shows the error budgetdetermined for a SPS DGPS system with increasing distances fromthe RR [45]

Table 13 DGNSS L1 pseudorange errors with increasing distancefrom RS

Error Sources 0 NM 100 NM 500NM

1000 NM

Space Segment

Clock Errors (ft) 0 0 0 0

Control Segment

Ephemeris Errors(ft)

0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222

Since the RR noise and multipath errors are included in thedifferential corrections and become part of the userrsquos error budget(root-sum-squared with the user receiver noise and multipatherrors) the receiver noise and multipath error components in thenon-differential receiver can be lower than the correspondent errorcomponents experienced in the DGNSS implementation Anothertype of error introduced in real-time DGNSS positioning systemsis the data linkrsquos ldquoage of the correctionsrdquo This error is introduceddue to the latency of the transmitted corrections (ie thetransmitted corrections of epoch ݐ arrive at the moving receiver atepoch These corrections are not the correct ones because theywere calculated under different conditions Hence the co-ordinates of the UR would be slightly offset

DGNSS systems that compensate for accuracy degradations overshort distances (typically up to the RS-UR Line-of-Sight (LOS)employing VUHF datalinks) are referred to as Local Area DGNSS(LAD) DGNSS systems covering large geographic areas arereferred to as Wide Area DGNSS (WAD) systems They usuallyemploy a network of reference receivers that are coordinated toprovide DGNSS data over a wide coverage area Such systemstypically are designed to broadcast the DGNSS data via satellitealthough a network of ground transmission sites is also feasible Auser receiver typically must employ special algorithms to derivethe ionospheric and tropospheric corrections that are appropriatefor its location from the observations taken at the various referencesites

Various countries including the United States Canada EuropeJapan China India and Australia have developed LADWADsystems Some of these systems transmit DGNSS data fromgeostationary satellites for use by commercial navigation usersincluding the aviation community Some commercial DGNSSservices also broadcast data from multiple reference stations viasatellite However several such systems remain a group of LADrather than WAD systems This is because the reference stationsare not integrated into a network allowing the user accuracy todegrade with distance from the individual reference sites

43 Real Time Kinematics (RTK) and Precise Point Positioning

For aviation applications where it is not possible to bring thereferencemobile antennas together or to position the aircraft at asurveyed location the reference and mobile receivers must solvefor the ambiguities independently as part of an initialisationprocess For these applications it is essential to be able to solve forinteger ambiguity at an unknown location and while in motion Inthis case solving for the integer ambiguity usually consists ofeliminating incorrect solutions until the correct solution is foundA good initial estimate of position (such as from ranging-codedifferential) helps to keep the initial number of candidate solutionssmall Redundant measurements over time andor from extrasatellite signals are used to isolate the correct solution This versionof the carrier-phase DGNSS technique is typically called Real-Time Kinematic (RTK) GNSS If carrier track or phase lock on asatellite is interrupted (cycle slip) and the integer count is lost thenthe initialisation process must be repeated for that satellite Causesof cycle slips can range from physical obstruction of the antenna tosudden accelerations of the aircraft Output data flow may also beinterrupted if the receiver is not collecting redundant measurementsform extra satellites to maintain the position solution If a preciseposition solution is maintained re-initialisation for the lost satellitecan be very rapid Developing a robust and rapid method ofinitialisation and re-initialisation is the primary challenge facingdesigners of RTK systems that have to deal with safety criticalapplications such as aircraft precision approach

Although centimetre-level GNSS accuracy is increasingly relevantfor a number of aviation and other Safety-of-Life (SoL)applications the possible adoption of RTK techniques in theaviation context is still being researched and no RTK systems arecontemplated by the current ICAO standards for air navigationFrom an operational perspective the main inconvenience of theRTK technique is that it requires a reference station relatively closeto the user so that the differential ionospheric delay is negligibleHigh-accuracy single-baseline RTK solutions are generally limitedto a distance of about 20 km [84] although test activities haveshown that acceptable results can be achieved over up to 50 km intimes of low ionospheric activity [85]

A way of partially overcoming such inconvenience is the NetworkRTK (NRTK) technique which uses a network of ground referencestations to mitigate atmospheric dependent effects over longdistances The NRTK solution is generally based on between three

and six of the closest reference stations with respect to the user andallows much greater inter-station distances (up to 70-90 km) whilemaintaining a comparable level of accuracy [85]

The Wide Area RTK (WARTK) concept was introduced in the late1990s to overcome the need of a very dense network of referencestations WARTK techniques provide accurate ionosphericcorrections that are used as additional information and allowincreasing the RTK service area In this way the system needsreference stations separated by about 500ndash900 kilometres [86]

Precise Point Positioning (PPP) is a further carrier-phase GNSStechnique that departs from the basic RTK implementation anduses differencing between satellites rather than differencingbetween receivers Clearly in order to be implemented PPPrequires the availability of precise reference GNSS orbits andclocks in real-time Combining the precise satellite positions andclocks with a dual-frequency GNSS receiver (to remove the firstorder effect of the ionosphere) PPP is able to provide positionsolutions at centimetre level [87]

PPP differs from double-difference RTKNRTK positioning in thesense that it does not require access to observations from one ormore close reference stations accurately-surveyed PPP justrequires data from a relatively sparse station network (referencestations thousands of kilometres apart would suffice) This makesPPP a very attractive alternative to RTK especially in long-distanceaviation applications where RTKNRTK coverage would beimpractical However PPP techniques are still not very mature andtypically require a longer convergence time (20-30 minutes) toachieve centimetre-level performance [87] Another possibility isto use local ionospheric corrections in PPP This approach wouldreduce convergence time to about 30 seconds and contribute to anaugmented integrity However they would also require a densityof reference networks similar to that of NRTK [88]

44 Multi-Constellation GNSS

The various GNSSs (GPS GLONASS BDS GALILEO etc)operate at different frequencies they employ various signalprocessing techniques and adopt different multiple access schemesMost of them employ or are planned to progressively transition toCode Division Multiple Access (CDMA) for operations at the L-band frequency of 157542 MHz (L1) This signal originallyintroduced by GPS for Standard Positioning Service (SPS) userswill guarantee interoperability between the various GNSSconstellations with substantial benefits to the existing vastcommunity of GPS users including aviation Signal-in-Space(SIS) interoperability is also being actively pursued on otherfrequencies with a focus on those that are currently allocated toSafety-of-Life (SOL) services From a userrsquos perspective theadvantage to having access to multiple GNSS systems is increasedaccuracy continuity availability and integrity Having access tomultiple satellite constellations is very beneficial in aviationapplications where the aircraft-satellite relative dynamics can leadto signal tracking issues andor line-of-sight obstructions Evenwhen interoperability at SIS level cannot be guaranteed theintroduction of multi-constellation receivers can bring significantimprovements in GNSS performance The literature on this subjectis vast and it is beyond the scope of this paper to address in detailsthe various signal and data processing techniques implemented inGNSS systems

The purpose of GNSS modernisation is to provide more robustnavigationpositioning services in terms of accuracy integritycontinuity and availability by broadcasting more rangingtimingsignals In particular availability will be improved with theemployment of multi-constellation GNSS At the moment (July2017) more than 70 GNSS satellites are already in view It isexpected that about 120 satellites will be available once the variousGNSS systems are fully operational [89-93] The GNSS

constellations and their supported signals are summarised in Table14

Currently there are 31 GPS satellites on-orbit in the Medium EarthOrbit (MEO) The GPS signals can be summarised as follows

L1 (157542 MHz) It is a combination of navigation messagecoarse-acquisition (CA) code and encrypted precision P(Y)code (CA-code is a 1023 bit Pseudo Random Noise (PRN)code with a clock rate of 1023 MHz and P-Code is a very longPRN code (7 days) with a clock rate of 1023 MHz)

L2 (122760 MHz) It is a P(Y) code The L2C code is newlyadded on the Block IIR-M and newer satellites The L2C codeis designed to meet emerging commercialscientific needs andprovides higher accuracy through better ionosphericcorrections

L3 (138105 MHz) It is used by the defence support programto support signal detection of missile launches nucleardetonations and other high-energy infrared events

L4 (1379913 MHz) It is used for studying additionalionospheric correction

L5 (117645 MHz) It is used as a civilian SoL signal Thisfrequency falls into an internationally protected range foraeronautical navigation promising little or no interferenceunder all circumstances

SPS provides civil users with a less accurate positioning capabilitythan PPS using single frequency L1 and CA code only PPS isavailable primarily to the military and other authorized users of theUS (and its allies) equipped with PPS receivers The PPS uses L1and L2 CA and P-codes GPS modernisation comprises a series ofimprovements provided by GPS Block IIR-M GPS Block IIF GPSIII and GPS III Space Vehicle 11+ The M-code signals aremodulated on L1 and L2 The addition of L5 makes GPS a morerobust radionavigation service for many aviation applications aswell as all ground-based users The new L2C signals called as L2civil-moderate (L2 CM) code and L2 civil-long (L2 CL) code aremodulated on the L2 signals transmitted by Block IIR-M IIF andsubsequent blocks of GPS satellite vehicles The M-code is a newmilitary signal modulated on both L1 and L2 signals

The L1C signal was developed by the US and Europe as a commoncivil signal for GPS and GALILEO Other GNSS systems such asBDS and QZSS are also adopting signals similar to L1C The firstL1C signal with be available with the launch of GPS III blocksatellites Backward compatibility will be guaranteed by allowingthe L1C signal to broadcast in the same frequency as the L1 CAsignal

Out of the 30 planned GALILEO satellites 13 are currentlyoperational 2 are under commissioning and 3 act as testbed (notavailable for operational use) GALILEO signals are used toprovide 5 distinct services including Open Service (OS) Safety-of-Life Service (SoLS) Commercial Service (CS) Public RegulatedService (PRS) and Search and Rescue Support Service (SAR) TheSOLS in particular support a number of aviation marine andsurface transport applications The SOLS guarantees a level ofaccuracy and integrity that OS does not offer and it offersworldwide coverage with high accuracy integrity

GALILEO carriers can be classified as E5a (1176450 MHz) E5b(1207140 MHz) and E5ab (full band) which are wide band dataand pilot signals E6 (127875 MHz) and E2-L1-E1 (157542MHz) The GALILEO navigation signals can be classified asfollows

L1F It supports OS (unencrypted)

L1P It supports PRS (encrypted)

E6C It supports CS (encrypted)

E6P It supports PRS (encrypted)

E5a It supports OS (unencrypted)

E5b It supports OS (unencrypted)

Since the GALILEO E2-L1-E1 and E5a signal frequencies are thesame as of L1 and L5 GPS signals both these systems support theirtreatment as a systems of systems [94]

The GLONASS system has 23 satellites in operational conditionIn addition to these M type satellites there are already twomodernised GLONASS-K satellites in operation The moreadvanced GLONASS-KM satellites will be able to provide legacyFDMA signals supporting Open FDMA (OF) and Secured FDMA(SF) services on L1 and L2 as well as CDMA signals on L1 L2and L3 providing Open CDMA (OC) and Secured CDMA (SC)services It could also transmit CDMA signals on the GPS L5frequency (117645 MHz) Advanced features include inter-satellite links laser time transfer capability andor improved clocks[95] Furthermore GNSS integrity information could also bebroadcast in the third civil signal in addition to global differentialephemeris and time corrections supporting Open CDMAModernized (OCM) services BDS (Big DipperCOMPASS) theChinese navigation satellite system provides a regional navigationservices using a two-way timingranging technique BeiDou-2(BDS-2) is expected to be a constellation of 35 satellites offeringbackward compatibility with BeiDou-1 and 30 non-geostationarysatellites These include 27 in MEO and 3 in InclinedGeosynchronous Orbit (IGSO) and 5 in Geostationary Earth orbit(GEO) that will offer complete coverage of the globe The futurefully operational BDS is expected to support two kinds of generalservices including Radio Determination Satellite Service (RDSS)and Radio Navigation Satellite Service (RNSS) The RDSS willsupport computation of the user position by a ground station usingthe round trip time of signals exchanged via GEO satellite whilethe RNSS will support GPS- and GALILEO-like services and isalso designed to achieve similar performances The QZSS providesa regional navigation serviceaugmentation system and is set tobegin operations in 2018 with 3 IGSO satellites and 1 GEOsatellite Specific signals such as L1 sub-meter class Augmentationwith Integrity Function (SAIF) and L6 L-band Experimental (LEX)will be transmitted in addition to the support for L1 CA L2C L5and L1C signals The planned Block II satellites will support theCentimetre Level Augmentation Service and PositioningTechnology Verification Service [96 97] The Indian RegionalNavigation Satellite System (IRNSS) also referred to as NavIC(Navigation with Indian Constellation) comprises of sevensatellites with 4 in IGSO and 3 in GEO Two kinds of services aresupported namely Standard Positioning Service (SPS) andRestricted Service (RS) Both services are carried on L5 (117645MHz) and S band (249208 MHz) The navigation signals areexpected to be transmitted in the S-band (2ndash4 GHz)

The new and modernised GNSS constellations along with thenewly introduced signals are expected to be compatible with otherGNSS systems Compatibility in this context refers to the abilityof global and regional navigation satellite systems andaugmentations to be used separately or together without causingunacceptable interference or other harm to an individual system orservice [98] To support computability among the various GNSSsystems ITU provides a framework for discussions onradiofrequency compatibility Interoperability is anotherconsideration to be taken into account which refers to the abilityof global and regional navigation satellite systems andaugmentations to be used together so as to support services withbetter capabilities than would be achieved by relying solely on theopen signals of one system [98] Common modulation schemescentre frequency signal and power levels as well as geodetic

reference frames and system time steerage standards are defined tosupport interoperability

Table 14 GNSS constellations

Constellation(Global

Regional)

Block andOrbit

Satellites Signals

GPS

IIR (MEO) 12 L1 CA L1L2P(Y)

IIR-M(MEO)

7 L1 CA L1L2P(Y) L2C L1L2M

IIF (MEO) 12 L1 CA L1L2P(Y) L2C L1L2M L5

III (MEO) Yet to belaunched

L1 CA L1CL1L2 P(Y) L2CL1L2 M L5

GALILEOIOV (MEO) 3 E1 E5abab E6

FOC (MEO) 10 E1 E5abab E6

GLONASS

MEO Out ofservice

L1L2 SF and L1OF

M (MEO) 23 L1L2 OF and SF

K1 (MEO) 2 L1L2 OF and SFL3 OC

K2 (MEO) Yet to belaunched

L1L2 OF and SFL1 OC L1 SC L2SC L3 OC

KM (MEO) Yet to belaunched

L1L2 OF and SFL1L2L3 OC andSC L1L3L5OCM

BeiDou-1MEO 4

(experimentaland retired)

B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3

MEO 3 B1-2 B1 B2B3ab

IGSO 2 B1-2 B1 B2B3ab

QZSSI (GEO andIGSO)

2 L1 CA L1C L1L2C L5 L6LEX SAIF

IRNSSIGSO 4 L5S SPS and RS

GEO 3 L5S SPS and RS

45 GNSS Integration with Other Sensors

All GNSS techniques (either stand-alone or differential) sufferfrom some shortcomings The most important are

The data rate of a GNSS receiver is too low and the latencyis too large to satisfy the requirements for high performanceaircraft trajectory analysis in particular with respect to thesynchronisation with external events In addition there mightbe a requirement for high-rate and small latency trajectorydata to provide real-time guidance information to the pilot(eg during fly-over-noise measurements) With the need toprocess radio frequency signals and the complex processingrequired to formulate a position or velocity solution GPSdata rates are usually at 1 Hz or at best 10 Hz (an update rateof at least 20 Hz is required for real-time aviation

applications) [99]

Influences of high accelerations on the GPS receiver clockthe code tracking loop and carrier phase loop may becomesignificant

Signal lsquoloss-of-lockrsquo and lsquocycle slipsrsquo may occur veryfrequently due to aircraft manoeuvres or other causes

SA degrades the positioning accuracy over long distances

High DGNSS accuracy is limited by the distance between thereference station and the user because of the problem ofionosphere in integer ambiguity resolution on-the-fly [100]

Especially in the aviation context there is little one can do toensure the continuity of the signal propagation from the satellite tothe receiver during high dynamic manoeuvres The benefits ofintegrating GNSS with other sensors are significant and diverseBoth absolute measurements such as Position Velocity andAttitude (PVA) which can be directly measured as well as relativemeasurements between the air platform and the environment canbe considered for integration Direct measurements can be obtainedby employing GNSS Inertial Navigation System (INS) digitalmaps etc In case of small UAS GNSS measurements can beintegrated with other navigation sensorssystems including InertialNavigation System (INS) Vision-based Navigation Sensors(VBN) Celestial Navigation Sensors (CNS) Aircraft DynamicsModel (ADM) virtual sensor etc [101] The variety of sensors forintegration is even more expandable for aircraft operating in anurban setting when Signals-of-Opportunity (SoO)-based sources(cellular signal base transceiver stations Wireless Fidelity (Wi-Fi)networks etc) are available [102] Basically each navigationsystem has some shortcomings The shortcomings of GNSS werediscussed above and in the case of INS it is subject to an evergrowing drift in position accuracy caused by various instrumenterror sources that cannot be eliminated in manufacturingassembly calibration or initial system alignment Furthermorehigh quality inertial systems (ie platform systems) tend to becomplex and expensive devices with significant risk of componentfailure By employing these sensors in concert with some adequatedata-fusion algorithms the integrated navigation system can solvethe majority of these problems As an example the integration ofGNSS and INS measurements might solve most of the abovementioned shortcomings the basic update rate of an INS is 50samples per second or higher and an INS is a totally self-containedsystem The combination of GNSS and INS will therefore providethe required update rate data continuity and integrity

Technical considerations for integration of GNSS and other sensorsinclude the choice of system architecture the data-fusionalgorithm and the characterisation and modelling of themeasurements produced by the sensors Integration of othersensors with GNSS can be carried out in many different waysdepending on the application (ie onlineoff-line evaluationaccuracy requirements) Various options exist for integration andin general two main categories can be identified depending on theapplication post-processing and real-time algorithms Thecomplexity of the algorithm is obviously related to both systemaccuracy requirements and computer load capacity

The level of integration and the particular mechanisation of thedata-fusion algorithm are dependent on

The task of the integration process

The accuracy limits

The robustness and the stand alone capacity of eachsubsystem

The computation complexity

For GNSS and INS data fusion the basic concepts of systemintegration can be divided into

Open Loop GNSS aided System (OLGS)

Closed Loop GNSS aided System (CLGS)

Fully Integrated GNSS System (FIGS)

The simplest way to combine GNSS and INS is a reset-onlymechanisation in which GNSS periodically resets the INS solution(Fig 21) In this open-loop strategy the INS is not re-calibrated byGNSS data so the underlying error sources in the INS still drive itsnavigation errors as soon as GNSS resets are interrupted Howeverfor short GNSS interruptions or for high quality INS the errorgrowth may be small enough to meet mission requirements This iswhy platform inertial systems have to be used with OLGS systemsoperating in a high dynamic environment (eg military aircraft)The advantage of the open loop implementation is that in case ofinaccurate measurements only the data-fusion algorithm isinfluenced and not the inertial system calculation itself As thesensors of a platform system are separated from the body of theaircraft by gimbals they are operating normally at their referencepoint zero The attitude angles are measured by the angles of thegimbals The integration algorithm can run internal or external tothe INS but the errors of the inertial system have to be carefullymodelled

The main advantage of GNSS aiding the INS in a closed-loopmechanisation is that the INS is continuously calibrated by thedata-fusion algorithm using the GNSS data Therefore strapdownsensors can be used in a CLGS implementation (Fig 21) Incontrary to platform systems sensors of strapdown INS are notuncoupled from the aircraft body They are operating in adynamically more disturbed environment as there are vibrationsangular accelerations angular oscillations which result in anadditional negative influence to the system performance Inaddition sensors are not operating at a reference point zeroTherefore the errors of the system will increase very rapidly andproblems of numerical inaccuracy in an open loop implementationmay soon increase This is why it is advantageous to loop back theestimated sensor errors to the strapdown calculations in order tocompensate for the actual system errors Consequently the errorsof the INS will be kept low and linear error models can be usedWhen GNSS data is lost due to dynamics or satellite shadowingthe INS can continue the overall solution but now as a highlyprecise unit by virtue of its recent calibration However this systemimplementation can be unstable

The system integration of best accuracy will be of course the fullintegration of GNSS and other sensors which require a data-fusionimplementation at a rawuncorrelated measurements level(Fig 21) As the KF theory asks for uncorrelated measurements[103] it is optimal to use either the raw GPS measurements (iethe range and phase measurements to at least four satellites theephemeris to calculate the satellite positions and the parameters tocorrect for the ionospheric and troposphere errors) or GNSSposition (and velocity) data uncorrelated between update intervals[105] In the first case the receiver clock errors (time offset andfrequency) can be estimated as a part of the filter model Thisapproach has very complex measurement equations but requiresonly one KF mechanisation Moreover its filtering can be mostoptimal since both GNSS errors and INS errors can be includedwithout the instability problems typical of cascade KFs

The other classification commonly in practise to define theintegration techniques is given by

Loose integration It refers to fusion of navigation solutionsProcessed GNSS PVT measurements are used in this type ofintegration

Tight integration It refers to the fusion of navigation

measurements GNSS code and carrier range and phasemeasurements are used in this type of integration

Deepultratight integration It refers to the integration at the

signal processing level which employs raw GNSSradiofrequency signals

(a) (b) (c)

Fig 21 GNSS integration architectures a OLGS b CLGS and c FIGS [107]

The most important distinction to be made is between cascaded andnon-cascaded approaches which correspond as mentioned beforeto aided (OLGS and CLGS) or fully integrated (FIGS)architectures respectively In the cascaded case two filtersgenerally play the role The first filter is a GNSS filter whichproduces outputs (ie position and velocity) which are correlatedbetween measurement times This output is then used as input forthe second filter which is the INS KF As time correlation of thismeasurement input does not comply with the assumptionsunderlying the standard KF [103] it must be accounted for in theright way [106] This complicates the KF design (ie the potentialinstability of cascaded filters makes the design of the integrationKF a very cautious task) However from a hardwareimplementation point of view aided INS (in both OLGS and CLGSconfigurations) results in the simplest solution In the non-cascadedcase there is just a single KF and is generally based on an INS errormodel and supplemented by a GNSS error model The GNSSmeasurements uncorrelated between measurement times aredifferenced with the raw INS data to give measurements of the INSerrors also uncorrelated between measurements times

State-of-the-art data-fusion algorithms such as the traditional KFExtended Kalman Filter (EKF) and the more advanced UnscentedKalman Filter (UKF)multi-hypotheses UKF can be employed forthe integration process In general a KF can be used to estimate theerrors which affect the solution computed in an INS or in a GNSSas well as in the combination of both navigation sensors A KF is arecurrent optimal estimator used in many engineering applicationswhenever the estimation of the state of a dynamic system isrequired An analytic description of KFs and other integrationalgorithms can be found in the literature [103 104] TheKF algorithm is optimal under three limiting conditions the systemmodel is linear the noise is white and Gaussian with knownautocorrelation function and the initial state is known Moreoverthe computing burden grows considerably with increasing numberof states modelled Matrix formulation methods of various typeshave been developed to improve numerical stability and accuracy(eg square root and stabilised formulations) to minimise thecomputational complexity by taking advantage of the diagonalcharacteristics of the covariance matrix (U-D factorisationformulation where U and D are upper triangular and diagonal

matrix respectively) and to estimate state when the state functionsare non-linear (eg EKF) The EKF measurement model is definedas

ݖ = ܪ lowast ݔ + ݒ (119)

where ݖ is the measurement vector ܪ is the design matrix ݔ isthe state vector ݒ is the measurement noise and k is the kth epochof timeݐ The state vector at epoch k+1 is given by

ାଵݔ = Ф୩ lowast ݔ + ܩ lowast ݓ (120)

where Ф୩ is the state transition matrix from epoch k to k+1 ܩ isthe shaping matrix and ݓ is the process noise The algorithm iscomposed of two steps prediction and correction The predictionalgorithm of the EKF estimates the state vector and computes thecorresponding covariance matrix from the current epoch to thenext one using the state transition matrix characterizing the processmodel described by

ାଵ = Ф୩ାଵ

ାФାଵ + (121)

where ାଵ is a predicted value computed and

ା is the updatedvalue obtained after the correction process The process noise at acertain epoch k is characterized by the covariance matrix Theupdating equations correct the predicted state vector and thecorresponding covariance matrix using the collected measurementsis given by

ାଵݔା = ାଵݑାଵܭ (122)

ାଵା = ାଵ

minus ାଵܪାଵܭ ାଵ (123)

where ାଵܭ is the Kalman gain matrix at epoch k+1 and ାଵisݑthe innovation vector at epoch k+1

Post-processing integration of GNSS and INS measurements canbe carried out by means of the Rauch-Tung-Striebel algorithmwhich consists of a KF and a backward smoother The forwardfilter can take into account previous measurements only Thesmoothed estimate utilises all measurements It is evident thatbackward smoothing can only be done off-line The filter estimatesthe state vector together with the error covariance matrix The statevector contains the error components of the inertial navigationsystem The smoothed trajectories and also accurate velocities are

obtained by adding the state vector to the measurements deliveredby the INS The equations of the Rauch-Tung-Striebel algorithmcan be found in [103] Alternatives include the BrysonndashFrazier twofilter smoother Monte Carlo smoother etc The filtering algorithmmost commonly implemented in real-time systems is the BiermanrsquosU-D Factorised KF The U-D algorithm is efficient and providessignificant advantages in numerical stability and precision [103]

Artificial Neural Networks (ANN) could be employed to relax oneor more of the conditions under which the KF is optimal andorreduce the computing requirements of the KF However thedevelopment of an integration algorithm completely based only onneural technology (eg hopfield networks) will lead to a complexdesign and unreliable integration functions Furthermore thissolution is even more demanding than the KF in terms ofcomputing requirements [108] Hence a hybrid network in whichthe ANN is used to learn the corrections to be applied to the stateprediction performed by a rule-based module appears to be the bestcandidate for future navigation sensor integration Techniques foron-line training would allow for real-time adaptation to the specificoperating conditions but further research is required in this fieldIn a hybrid architecture an ANN is used in combination with arule-based system (ie a complete KF or part of it) in order toimprove the availability of the overall system A hybrid networkprovides performances comparable with the KF but with improvedadaptability to non-linearities and unpredicted changes insystemenvironment parameters Compared with the KF thehybrid architecture features the high parallelism of the neuralstructure allowing for faster operation and higher robustness tohardware failures The use of ANN to correct the state variablesprediction operated by the rule-based module avoids computing theKalman gain thus considerably reducing the computing burdenStability may be guaranteed if the output of the network is in theform of correction to a nominal gain matrix that provides a stablesolution for all system parameters The implementation of such afilter however would be sensitive to network topology andtraining strategy An adequate testing activity would therefore berequired In addition to ANN approaches such as the Radial BasisFunction (RBF) neural networks Adaptive Neuron-FuzzyInference System (ANFIS) have been developed to enhanceGNSSINS integration for its improved ability to handle theproblem at hand and to include an expert knowledge base of a fuzzysystem and adaptive membership functions characterising therelationship between the inputs and outputs

46 GNSS Integrity Augmentation

According to the US Federal Radionavigation Plan ldquointegrity is ameasure of the trust that can be placed in the correctness of theinformation supplied by a navigation system Integrity includes theability of the system to provide timely warnings to users when thesystem should not be used for navigationrdquo This definition is verycomprehensive but unfortunately it is too generic and this is whymany research efforts were undertaken in the past to better specifythe GNSS integrity performance metrics Previous research haseffectively developed and applied statistical criteria to inflate thenavigation error bounds in specific flight phases So whileaccuracy is typically specified at 95 (2σ) confidence level integrity requirements normally refer to percentiles of 99999(6σ) or higher depending on the particular phase of flightapplication [109] The intention behind this is to keep theprobability of hazardous events (that could possibly put at riskhuman lives) extremely low From a system performanceperspective integrity is intended as a real-time decision criterionfor using or not using the system For this reason it has been acommon practice to associate integrity with a mechanism or set ofmechanisms (barriers) that is part of the integrity assurance chainbut at the same time is completely independent of the other parts ofthe system for which integrity is to be assured

Consequently the concepts of Alert Limit Integrity RiskProtection Level and Time to Alert were introduced and arecurrently reflected in the applicable ICAO SARPs and in the RTCAstandards for WAAS and LAAS These integrity performancemetrics are

Alert Limit (AL) The alert limit for a given parametermeasurement is the error tolerance not to be exceeded withoutissuing an alert

Time to Alert (TTA) The maximum allowable time elapsedfrom the onset of the navigation system being out of toleranceuntil the equipment enunciates the alert

Integrity Risk (IR) Probability that at any moment theposition error exceeds the AL

Protection Level (PL) Statistical bound error computed so asto guarantee that the probability of the absolute position errorexceeding said number is smaller than or equal to the targetintegrity risk

As discussed above integrity is the ability of a system to providetimely warnings to users when the system should not be used fornavigation [110] In general it is essential to guarantee that with aspecified probability P either the horizontalvertical radial positionerror does not exceed the pre-specified thresholds (HALVAL) oran alarm is raised within a specified TTA interval when thehorizontalvertical radial position errors exceed the thresholds Todetect that the error is exceeding a threshold a monitor functionhas to be installed within the navigation system This is also thecase within GNSS systems in the form of the ground segmentHowever for GNSS systems TTA is typically in the order ofseveral hours that is even too long for the cruise where a TTA of60 seconds is required (an autoland system for zero meter verticalvisibility must not exceed a TTA of 2 seconds) Various methodshave been proposed and practically implemented for stand-aloneGNSS integrity monitoring A growing family of suchimplementations already very popular in aviation applicationsincludes the so called Receiver Autonomous Integrity Monitoring(RAIM) techniques Regarding DGNSS it should be underlinedthat it does more than increasing GNSS positioning accuracy italso contributes to enhancing GNSS integrity by compensating foranomalies in the satellite ranging signals and navigation datamessage The range and range rate corrections provided in theranging-code DGNSS correction message can compensate forramp and step type anomalies in the individual satellite signalsuntil the corrections exceed the maximum values or rates allowedin the correction format If these limits are exceeded the user canbe warned not to use a particular satellite by placing ldquodo-not-userdquobit patterns in the corrections for that satellite (as defined inSTANAG 4392 or RTCARTCM message formats) or by omittingthe corrections for that satellite

As mentioned before step anomalies will normally cause carrier-phase DGNSS receivers to lose lock on the carrier phase causingthe reference and user receivers to reinitialise UR noiseprocessing anomalies and multipath at the user GPS antennacannot be corrected by a DGNSS system These errors are includedin the overall DGNSS error budget Errors in determining ortransmitting the satellite corrections may be passed on to thedifferential user if integrity checks are not provided within the RSThese errors can include inaccuracies in the RS antenna locationthat bias the corrections systematic multipath due to poor antennasighting (usually in low elevation angle satellites) algorithmicerrors receiver inter-channel bias errors receiver clock errors andcommunication errors For these reasons typical WAD and LADRS designs also include integrity checking provisions to guaranteethe validity of the corrections before and after broadcast

In the aviation context various strategies have been developed forincreasing the levels of integrity of DGNSS based

navigationlanding systems These include both Space BasedAugmentation Systems (SBAS) and Ground Based Augmentation

Systems (GBAS) to assist aircraft operations in all flight phases(Fig 22)

SBAS

GBAS

Fig 22 GBAS and SBAS services Adapted from [111]

These systems are effectively WAD and LAD systems that employrespectively DGNSS vector correction (SBAS) and scalar(pseudorange) correction techniques (GBAS) Some informationabout SBAS and GBAS relevant to this thesis are provided in thefollowing sections of this chapter However before examining thecharacteristics of GNSS integrity augmentation systems it is usefulto recall the definitions relative to Failure Detection and Exclusion(FDE)

Fig 23 shows the different conditions associated with FDE Thevarious FDE events are defined as follows [41]

Alert An alert is defined to be an indication that is providedby the GPS equipment when the positioning performanceachieved by the equipment does not meet the integrityrequirements

Positioning failure A positioning failure is defined to occurwhenever the difference between the true position and theindicated position exceeds the applicable alert limit

False detection A false detection is defined as the detectionof a positioning failure when a positioning failure has notoccurred

Missed detection A missed detection is defined to occurwhen a positioning failure is not detected

Failed exclusion A failed exclusion is defined to occur whentrue positioning failure is detected and the detection conditioncannot be eliminated within the time-to-alert A failedexclusion would cause an alert

Wrong exclusion A wrong exclusion is defined to occurwhen detection occurs and a positioning failure exists but isundetected after exclusion resulting in a missed alert

False alert A false alert is defined as the indication of apositioning failure when a positioning failure has notoccurred A false alert is the result of a false detection

Missed alert A missed alert is defined to be a positioningfailure which is not enunciated as an alert within the time-to-alert Both missed detection and wrong exclusion can causemissed alerts

Fig 23 FDE Events [36]

As discussed above GNSS satisfies the horizontal and verticalintegrity requirements for the intended operation when HPL andVPL are below the specified HAL and VAL This situation isdepicted in Fig 24

VAL

VPL

HAL

HPL

Fig 24 Protection levels and alert limits

The horizontal plane in Fig 24 is locally tangent to the navigationsystem geodetic reference (eg WGS84 ellipsoid in GPS) Thevertical axis is locally perpendicular to the same referenceWhenever HPL or VPL exceed HAL or VAL the integrity requiredto support the intended operation is not provided and an alert mustbe issued by the GNSS equipment within the specified TTA Insome unfavourable occasions the NSE exceeds the HPLVPLvalues In these cases it is said that an integrity event has occurredand that the system is providing unreliable information classifiedas Misleading Information (MI) or Hazardously MisleadingInformation (HMI) The difference between MI and HMI ishighlighted in Fig 25

As discussed availability is the probability that the navigationsystem is operational during a specific flight phase (ie theaccuracy and integrity provided by the system meet therequirements for the desired operation) Therefore the navigation

system is considered available for use in a specific flight operationif the PLs it is providing are inferior to the corresponding specifiedALs for that same operation

The circumferences shown in Fig 25 have their centres at theestimated aircraft position and their radii are the system PLs(green) and the operation ALs (red) The aircraft shape representsthe actual position so the navigation system error is the distancefrom the centre of the circumferences to this shape According tothe previous definitions situations B C and F represent integrityevents In particular case B is a MI event and cases CF are HMIevents The desirable situation is represented by case A Particularattention should be given to situations B and especially C which isthe most feared situation as the system does not alert the user forthe unavailability of the system and depending on the on-goingflight operational task this may lead to a SoL risk

Alert Limit

Protection Level

A B C

D E F


461 Space Based Augmentation Systems

SBAS is a form of WAD that augments core satellite constellationsby providing ranging integrity and correction information viageostationary satellites An SBAS typically comprises of [112]

a network of ground reference stations that monitor satellitesignals

master stations that collect and process reference station dataand generate SBAS messages

uplink stations that send the messages to geostationarysatellites

transponders on these satellites that broadcast the SBASmessages

By providing differential corrections extra ranging signals viageostationary satellites and integrity information for eachnavigation satellite SBAS delivers much higher levels of servicethan the core satellite constellations In certain configurationsSBAS can support approach procedures with vertical guidance(APV) There are two levels of APV APV I and APV II Bothuse the same lateral obstacle surfaces as localizers however APVII may have lower minima due to better vertical performanceThere will nonetheless be only one APV approach to a runway endbased on the level of service that SBAS can support at anaerodrome The two APV approach types are identical from the

perspective of avionics and pilot procedures In many cases SBASwill support lower minima than that associated with non-precisionapproaches resulting in higher airport usability Almost all SBASapproaches will feature vertical guidance resulting in a significantincrease in safety APV minima (down to a Decision Height (DH)of 75 m (250 ft) approximately) will be higher than Category Iminima but APV approaches would not require the same groundinfrastructure so this increase in safety will be affordable at mostairports SBAS availability levels will allow operators to takeadvantage of SBAS instrument approach minima when designatingan alternate airport Notably SBAS approach does not require anySBAS infrastructure at an airport SBAS can support all en-routeand terminal RNAV operations Significantly SBAS offersaffordable RNAV capability for a wide cross section of users Thiswill allow a reorganization of the airspace for maximum efficiencyand capacity allowing aircraft to follow the most efficient flightpath between airports High availability of service will permit todecommission traditional NAVAIDs resulting in lower costs

There are four SBASs now in service including

the North American Wide Area Augmentation System(WAAS)

the European Geostationary Navigation Overlay Service(EGNOS)

the Indian GPS and Geostationary Earth Orbit (GEO)Augmented Navigation (GAGAN) System

the Japanese Multi-functional Transport Satellite (MTSAT)Satellite-based Augmentation System (MSAS)

Other SBAS currently under study or developments include theRussian System for Differential Correction and Monitoring(SDCM) the SouthCentral American and Caribbean SACCSA(Soluciόn de Aumentaciόn para Caribe Centro y Sudameacuterica) the Chinese Satellite Navigation Augmentation System (SNAS) theMalaysian Augmentation System (MAS) and various programsin the African and Indian Ocean (AFI) region The approximatecoverage areas of the various SBAS are shown in Fig 26

Although Australia Indonesia New Zealand and various othernations in the southern portion of the Asia-Pacific region have notannounced SBAS development programs the extension of systemssuch as MSAS GAGAN and SNAS could provide SBAS coveragein these areas Within the coverage area of SBAS ICAO memberstates may establish service areas where SBAS supports approvedoperations Other States can take advantage of the signals availablein the coverage area by fielding SBAS components integrated withan existing SBAS or by authorizing the use of SBAS signals Thefirst option offers some degree of control and improvedperformance The second option lacks any degree of control andthe degree of improved performance depends on the proximity ofthe host SBAS to the service area In either case the State whichhas established an SBAS service area should assume responsibilityfor the SBAS signals within that service area This requires theprovision of NOTAM information services

If ABAS-only operations are approved within the coverage area ofSBAS SBAS avionics will also support ABAS operationsAlthough the architectures of the various existing SBASs aredifferent they broadcast the standard message format on the samefrequency (GPS L1) and so are interoperable from the userrsquosperspective

It is anticipated that these SBAS networks will expand beyondtheir initial service areas Other SBAS networks may also bedeveloped and become operational When SBAS coverage areasoverlap it is possible for an SBAS operator to monitor and sendintegrity and correction messages for the geostationary satellites ofanother SBAS thus improving availability by adding rangingsources

AFI

SNAS

MAS

ExistingLikely FuturePotential Expansion

Fig 26 Current and possible future SBAS coverage Adapted from [113]

As the American WAAS has been developed in line with ICAOSARPs and RTCA MOPS the GBAS technology considered is thispaper is based on the RTCA WAAS standard [41] which is alsoaligned with the ICAO SARPs for SBAS [114]

The aim of WAAS is to provide augmentation signals to correctsome of the main GNSS errors and providing the followingservices

Position correction (ECEF coordinates)

Ionospheric grid correction

Long term ephemeris error correction

Short term and long term satellite clock error correction

Integrity information

WAAS consists of a ground space and user segment (Fig 27) Aground segment is composed by a network of ground referencestations and uplink stations The reference stations which arecalled Ranging and Integrity Monitoring Station (RIMS) areresponsible for the analysis of GNSS signals and for producingranging corrections and integrity signals The uplink stations areresponsible for sending regular correctionsintegrity signal updatesto the space segment The space segment is made by differentsatellites in geostationary orbits and broadcast the rangingcorrections and integrity signals to the WAAS users The usersegment (ie users equipped with WAAS enabled GNSSreceivers) uses the information broadcast from GNSS satellites tocompute PVT and WAAS signals broadcast from the spacesegment to improve position accuracy (applying ionosphericcorrections) and integrity of the navigation solution

This correction evaluation together with the correction of otherparameters such as ephemeris error and clock error allow WAASto provide to the user a position accuracy of about 76 meters orbetter both for lateral and vertical measurements [41] This permitsWAAS to achieve under certain conditions accuracy levelscompatible with CAT-I precision approach requirements

As the CAT-I capability required significant efforts forcertification a new Precision Approach sub-mode was definedcalled Approach Operations with Vertical Guidance (APV) givingan intermediate precision approach between NPA (Non- PrecisionApproach) and CAT-I This is further divided in APV-I and APV-II

Fig 27 WAAS Architecture and Operational Environment [63]

Ionospheric delay is one of the major error sources of pseudorangeThe WAAS ionospheric delay corrections are broadcast as verticaldelay estimates at specified ionospheric grid points (IGPs)applicable to a signal on L1 The WAAS Reference Stations(WRSs) measure the slant ionospheric delays to all satellites inview These measurements must be translated into a form that canbe applied by the user because the user will have a different line ofsight to the satellite than the WRSs WAAS uses a two-dimensional grid model to represent the vertical ionospheric delay

distribution [47] Ten different bands are used to allow a regularspacing of IGPs The 1808 possible IGP locations in bands 0-8 areillustrated in Fig 28 (there are 384 additional IGP locations inbands 9-10 not shown) In the bands 0-8 the IGPs are spaced 5apart from each other both in longitude and latitude for latitudes upto N55 and S55 Above 55 and up to 75 in latitude the IGPs arespaced 10 from each other both in longitude and in latitude AtS85 and N85 (around the poles) the IGPs are spaced 90 In thebands 9-10 the IGP grid at 60 has 5 longitudinal spacingincreasing to 10 spacing at 65 70 and 75 and finally becoming30 at N85 and S85 round the poles To accommodate an evendistribution of bands IGPs at 85 are offset by 40 in the 0-8 bandsand 10 in the 9-10 bands The IGPs error data are transmitted inMessage 26 and denoted in terms of GIVEI (Grid IonosphericVertical Error Indicator) which corresponds to specific values ofGrid Ionospheric Vertical Error (GIVE) and GIVE varianceଶǡߪ) ூா) The GIVEIi GIVEi and theߪଶǡ ூா are listed in Table15

Fig 28 WAAS IGPs for bands 0-8 [41]

The GIVE is used to calculate the User Ionospheric Vertical Error(UIVE) and the User Ionospheric Range Error (UIRE) The UIVEand UIRE are respectively the confidence bounds on the uservertical and range errors due to the ionosphere Both the UIVE andUIRE are referred to the Ionospheric Pierce Point (IPP) locationThe IPP is defined as the intersection of the line segment from thereceiver to the satellite and an ellipsoid with constant height of 350km above the WGS-84 ellipsoid Fig 29 shows the relationshipbetween user location and IPP location [41]

Table 15 Evaluation of GIVEIi [41]

GIVEIi GIVEi [m] [m2]

0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826

15 Not Monitored Not Monitored

Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp

Fig 29 Ionospheric Pierce Point Geometry [41]

The latitude of the IPP is given by

= sinଵ൫௨ ௨൯ሾሿ(119)ܣ

where ௨ is the user location latitude ܣ is the azimuth angle ofthe satellite from the userrsquos location (௨ǡߣ௨) measured clockwisefrom north and is the Earthrsquos central angle between the user

position and the projection of the pierce point

If ௨gt 70deg and ݐ ܣݏ ݐ ʹȀߨ) െ ௨) or ௨lt minus70deg

and ݐ ܣሺݏ ሻߨ ݐ ʹȀߨ) ௨) the longitude of the

IPP is given by

ߣ = λ௨ ଵ൬ݏୱ୧୬ట

ୡ୭ୱథ൰ሾሿܣ (120)

Otherwise



ψ୮୮ is given by

=గ

ଶെ ܧ െ ଵቀݏ

ோ

ோାቁሾሿܧ (122)

where ܧ is the elevation angle of the satellite form the userrsquoslocation measured with respected to the local tangent plane isthe approximate Earth radius (assumed to be 6378163 km) and ℎூis the height of the maximum electron density (assumed to be 350km) Fig 30 shows the principles adopted for interpolation of theIPPs The variance of UIVE can be calculated using one of thefollowing formulas

σூாଶ = sum ሺݔǡݕሻήߪǡௗ

ଶସୀଵ (123)


ଶଷୀଵ (124)

where ǡௗߪଶ is the model variance of inospheric vertical

delays at an IGP As indicated in the WAAS MOPS a dedicatedmodel can be used to calculate both fast and long-term correctiondegradation components (for inclusion in Message Types 7and 10)

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ (ܘܘǡܘܘሺܘܘ

Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP

Fig 30 Principle of Interpolation of the IPPs [41]

If the degradation model is not implemented the basic WAASionospheric model is used by taking ௗߪ

ଶ = ߪ ூாଶ For the

ith satellite the variance of UIRE is then calculated as follows

σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)

where ܨ is the obliquity factor given by

ܨ = 1 minus ቀோୡ୭ୱா

ோାቁଶ

൨భ

మ

(126)

Real-time data from can be obtained from the FAA website forWAAS and from the ESA website for EGNOS [113] The FAAalso created a comprehensive portal containing real-time data onother GBAS systems including not only WAAS and EGNOS butalso MSAS and GAGAN [115] The airborne receiver error isdenoted as σ୧ୟ୧ This error is defined in the WAAS MOPS basedon the equipment operation classes There are four operationclasses defined in the WAAS MOPS [41] A description of theseclasses is provided in Table 16

The fast corrections and long term corrections are two importantmessages transmitted by SBAS The long term corrections containinformation on the slowly varying satellite orbit and clock errorsThe fast corrections provide additional information on the fastvarying clock errors Long term corrections consist of position andclock offset values only (EGNOS) or they also contain velocity andclock drift corrections (WAAS)

The User Differential Range Error (UDRE) message providesinformation that allows the user to derive a bound on the projectionof the satellite orbit and satellite clock errors onto the line of sight

of the worst case user The UDRE is transmitted as an indicator(UDREI)

Table 16 SBAS Operational Classes [41]

Class Description

Class 1

Equipment that supports oceanic and domestic en routeterminal approach (LANV) and departure operation

When in oceanic and domestic en route terminalLNAV and departure operations this class of equipment

can apply the long-term and fast SBAS differentialcorrections when they are available

Class 2

Equipment that supports oceanic and domestic en routeterminal approach (LANV LNAVVNAV) and

departure operation When in LNAVVNAV this classof equipment applies the long-term fast and ionospheric

corrections When in oceanic and domestic en routeterminal approach (LNAV) and departure operations

this class of equipment can apply the long-term and fastSBAS differential corrections when they are available

Class 3

Equipment that supports oceanic and domestic en routeterminal approach (LANV LNAVVNAV LP LPV)

and departure operation When in LPV LP orLNAVVNAV this class of equipment applies the long-term fast and ionospheric corrections When in oceanicand domestic en route terminal approach (LNAV) anddeparture operations this class of equipment can apply

the long-term and fast SBAS differential correctionswhen they are available

Class 4

Equipment that supports only the final approach segmentoperation This class of equipment is intended to serve as

an ILS alternative that supports LP and LPV operationwith degradation (fail-down) from LPC to lateral only

(LNAV) Class 4 equipment is only applicable tofunctional Class Delta and equipment that meets ClassDelta-4 is also likely to meet the requirements for Class

Beta-1 2 or -3

In terms of WAAS integrity features Message Types 27 and 28 areparticularly important Type 27 Messages may be transmitted tocorrect the σUDRE in selected areas Each Type 27 Message specifies δUDRE correction factors to be applied to integritymonitoring algorithms of users when inside or outside of a set ofgeographic regions defined in that message δUDRE indicators areassociated with the δUDRE values listed in Table 17 that multiplythe model standard deviation defined using the UDREI parametersin the WASS Types 2-6 and Type 24 Messages

As an alternative to Message 27 a service provider might broadcastMessage Type 28 (not both) to update the correction confidence asa function of user location Message Type 28 provides increasedavailability inside the service volume and increased integrityoutside The covariance matrix is a function of satellite locationreference station observational geometry and reference stationmeasurement confidence Consequently it is a slowly changingfunction of time Each covariance matrix only needs to be updatedon the same order as the long-term corrections Each message iscapable of containing relative covariance matrices for twosatellites This maintains the real-time six-second updates ofintegrity and scales the matrix to keep it within a reasonabledynamic range

Assuming a Message Type 28 data is used and that fast and longterm corrections are applied to the satellites without the correctiondegradation model (ie an active type 7 or 10 message data is notavailable) then the residual fast and long term error is defined as[41]

௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)

The residual tropospheric error is denoted as σ୧୲୭୮୭ It is modelled

as a random parameter with a standard deviation of σ୧୲୭୮୭ as

specified in the MOPS [41]

Table 17 δUDRE Indicators and values in Message Type 27

Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100

Cholesky factorization is used to reliably compress the informationin the covariance matrix (ܥ) This factorization produces 4x4 anupper triangular matrix () which can be used to reconstruct therelative covariance matrix as follows

ܥ = (127)

Cholesky factorization guarantees that the received covariancematrix remains positive-definite despite quantization errorsBecause R is upper triangular it contains only 10 non-zeroelements for each satellite These 10 elements are divided by ascale factor to determine the matrix E which is broadcast inMessage Type 28

ܧ =ோ

ట=

⎣⎢⎢⎡ଵଵܧ ଵଶܧ ଵଷܧ ଵସܧ

0 ଶଶܧ ଶଷܧ ଶସܧ

0 0 ଷଷܧ ଷସܧ

0 0 0 ⎦ସସܧ⎥⎥⎤

(128)

where y = 2(௦௫௧ ହ) The covariance matrix is thenreconstructed and used to modify the broadcast σUDRE values as a function of user position The location-specific modifier is givenby

δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)

where isܫ the 4D line of sight vector from the user to the satellitein the WGS-84 coordinate frame whose first three components arethe unit vector from the user to the satellite and the fourthcomponent is a one The additional term ߝ is to compensate forthe errors introduced by quantization If degradation data isavailable the ߝ value is derived from the covariance databroadcast in a Type 10 message (௩ܥ) as follows

ߝ ௩ܥ= ∙ y (130)

If ௩ܥ from Message Type 10 is not available ߝ is set tozero but there is an 8 meter degradation applied as defined in theWAAS MOPS [41] The WAAS fast corrections and long-termcorrections are designed to provide the most recent information tothe user [41] However it is always possible that the user fails toreceive one of the messages In order to guarantee integrity evenwhen some messages are not received the user performingapproach operations (eg LNAVVNAV LP or LPV) must apply

models of the degradation of this information In other flightphases the use of these models is optional and a global degradationfactor can be used instead as specified in the WAAS MOPS [41]The residual error associated with the fast and long-termcorrections is characterized by the variance ௧ߪ)

ଶ ) of a model

distribution This term is computed as

௧ߪଶ =

൜(σୈ ∙ δUDRE) + εୡ+ εୡ+ ε୪୲ୡ+ ε if RSSୈ = 0

(σୈ ∙ δUDRE)ଶ+ εୡଶ + εୡ

ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where

RSSୈis the root-sum-square flag in Message Type 10

σୈ is the model parameter from Message Types 2-6 24

δUDRE is the user location factor (from Message Types 28 or 27otherwise δUDRE = 1)

εୡ is the degradation parameter for fast correction data

εୡ is the degradation parameter for range rate correction data

ε୪୲ୡ is the degradation parameter for long term correction or GEOnav-message data

ε is the degradation parameter for en route through NPAoperations

The total error σ୧ଶ is given by [41]

ߪଶ = ௧ߪ

ଶ + ூோாߪଶ + ߪ

ଶ + ௧ߪଶ (132)

For Class 1 equipment

ߪଶ = 25mଶ (133)

For Class 2 3 and 4 equipment

ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)

The projection matrix (S) is defined as [41]

S = ൦

௦௧ଶݏ௦௧ଵݏ ௦௧ேݏ⋯

s௧ଵ s௧ଶ ௧ேݏhellip

s ଵ s ଶ ⋯ s ே

௧ଶݏ௧ଵݏ ௧ேݏhellip

൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)

where ܩ is the observation matrix is the weighted matrix௦௧ݏ is the partial derivative of position error in the east direction

with respect to the pseudorange error on the ith satellite ௧ݏ isthe partial derivative of position error in the north direction withrespect to the pseudorange error on the ith satellite ݏ is thepartial derivative of position error in the vertical direction withrespect to the pseudorange error on the ith satellite and s ୧is thepartial derivative of time error with respect to pseudorange error onthe ith satellite The weighted matrix W is defined as

= ൦

ଵݓ 0 ⋯ 00 wଶ hellip 0⋮ ⋮ ⋱ ⋮0 0 ேݓhellip

൪ (136)

=ݓ 1 ߪଶfrasl (137)

and the observation matrix G consists of N rows of LOS vectorsfrom each satellite augmented by a ldquo1rdquo for the clock Thus the ithrow corresponds to the ith satellites in view and can be written interms of the azimuth angle ݖܣ and elevation angle ߠ The ith rowof the G matrix is

G୧= [minuscosߠsinݖܣ minus cosߠcosݖܣ minus sinߠ 1] (138)

The SBAS Vertical Protection Level (VPLSBAS) is calculatedusing the equation

ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)

The value of K used for computing VPL is K=533 The SBASHorizontal Protection Level (ௌௌܮܪ) is calculated using theequations

ௌௌܮܪ =

ቊுǡேܭ ή for en route through LNAV

ுǡܭ ή for LNAV VNAVfrasl LP LPV approach(141)

where

equiv ඨௗೞమ ାௗ

మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)

௦௧ଶ = sum ௦௧ǡݏ

ଶ ߪଶ

୧ୀ ݒ (143)

௧ଶ = sum ௧ǡݏ

ଶ ߪଶ

୧ୀ (144)

ாேଶ = sum ߪ௧ǡݏ௦௧ǡݏ

ଶ୧ୀ (145)

The values Kୌǡ is 618 for en route through LNAV and 60 forLNAVVNAV LP LPV More detailed information about WAAScan be found in the applicable MOPS standard [41]

462 Ground Based Augmentation Systems

The current GNSS constellations are unable to provide accuracyavailability continuity and integrity to achieve the stringentaccuracy and integrity requirements set by ICAO for precisionapproach GBAS employs LADGNSS techniques to augmentaccuracy and ad-hoc features to augment integrity beyond thelevels that can be achieved with SBAS Employing all provisionsincluded in the current RTCA standards [36 40] GBAS couldprovide augmentation to the core constellations to supportprecision approach up to Category IIIb However to date ICAOhas only issued Standards and Recommended Practices (SARPs)for GBAS operating over single frequency and single constellationup to CAT I operations [38] SARPs for CAT IIIII have beenalready developed by the ICAO Navigation System Panel (NSP)but not yet included in Annex 10 waiting for further developmentsto take place in the aviation industry As shown in Fig 31 GBASutilises three segments satellites constellation ground stations andaircraft receiver The GBAS ground station is formed by referencereceivers with their antennas installed in precisely surveyedlocations The information generated in the receiver is sent to aprocessor that computes the corrections for each navigationsatellite in view and broadcasts these differential correctionsbesides integrity parameters and precision approach pathpointsdata using a VHF Data Broacast (VDB) The informationbroadcast is received by aircraft in VHF coverage that also receiveinformation from the navigation satellites Then it uses thedifferential corrections on the information received directly fromthe navigation satellites to calculate the precise position Theprecise position is used along with pathpoints data to supplydeviation signals to drive appropriate aircraft systems supportingprecision approach operations

Fig 31 GBAS architecture [115]

Although the operating principle Signal-in-Space andperformance characteristics of GBAS are completely differentfrom ILS the GBAS approach guidance inidications provided tothe pilot are similar to the localizer and glide path indicationsprovided by an ILS However compared to ILS precisionapproach systems GBAS presents several distinct benefits Theseinclude

Reduction of critical and sensitive areas typical of ILS

Possibility to perform curved approaches

Positioning service for RNAV operations in the TerminalManoeuvring Area (TMA)

Provision of service in several runways in the same airport

Provision of several approach glide angles and displacedthreshold

Guided missed approach service

Adjacent airports served by a single GBAS (within VDBcoverage)

According to [115] GBAS is intended to support all types ofapproach landing departure and surface operations and maysupport en-route and terminal operations The SARPs weredeveloped to date to support Category I precision approachapproach with vertical guidance and GBAS positioning serviceThe GBAS ground station performs the following functions

Provide locally relevant pseudo-range corrections

Provide GBAS-related data

Provide final approach segment data when supportingprecision approach

Provide ranging source availability data

Provide integrity monitoring for GNSS ranging sources

VDB radio frequencies used in GBAS are selected in the band of108 to 117975 (just below the ATM band) The lowest assignablefrequency is 108025 MHz and the highest assignable frequency is117950 MHz with a channel spacing of 25 kHz A Time DivisionMultiple Access (TDMA) technique is used with a fixed framestructure The data broadcast is assigned one to eight slots GBASdata is transmitted as 3-bit symbols modulating the data broadcastcarrier by Differential 8 Phase Shift Keying (D8PSK) at a rate of10 500 symbols per second GBAS can provide a VHF databroadcast with either horizontal (GBASH) or elliptical (GBASE)polarization The navigation data transmitted by GBAS includesthe following information

Pseudo-range corrections reference time and integrity data

GBAS-related data

Final approach segment data when supporting precision

approach

Predicted ranging source availability data

LAAS (US) is a system capable to provide local augmentation forthe GNSS signals and it is the first candidate to support all types ofapproach and landing procedures up to Category III as well assurface operations All existing GBAS systems refer to the sameLAAS standards developed by RTCA [36 40] The typical LAASfacility consists of three elements the first is the ground segmentusually installed on the airport field the second is the airbornesegment represented by the data link receiver as well as a systemcapable of applying the augmentation parameters for landingguidance the third is the space segment which is actually made bythe GPSGLONASS constellations and will also include the futureGALILEOBEIDOU constellations when the required levels ofmaturity will be achieved WAAS essentially provides twodifferent services the first is the precision approach service bygiving deviation guidance both lateral and vertical for the FinalApproach Segment (FAS) to the runway the second is thedifferentially-corrected positioning service transmitting to theairborne systems the correction message for augmented GNSSaccuracy The specific data link to be used for communicationsbetween aircraft and ground stations is not completely specified bythe current standards while there are constraints in terms ofbandwidth link budget and data rate [65] For approach andlanding services the LAAS performance is classified in terms ofGBAS Service Level (GSL) A GSL defines a specific level ofrequired accuracy integrity and continuity The GSL classificationand the GSL performance requirements are listed in Tables 18 and19 Currently GBASLAAS installations around the world havebeen certified for GSL-C only However several research anddevelopment efforts are on-going towards demonstrating andproducing adequate evidence of compliance for GLS-DEFinstallations LAAS can also support airport surface operations by

enabling several functions associated with the specific aircraftequipment such as an electronic moving map and database

Enhanced pilot situational awareness of aircraft position theposition information will allow the pilot to identify the correct taxiroute and to monitor his position along the route this situationalawareness is improved in all visibility conditions particularly forcomplex airports Nowadays to support the low visibility surfacemovement operations is a very costly task with LAAS ADS-B andemerging cockpit displays technologies these operations could beconducted in the same way of those supported with lightsmarkings and follow-me operators

Traffic surveillance this function can support air traffic control andcrew with traffic surveillance of other aircraft both in good and lowvisibility condition

Runway incursion and conflict detection alerting the availabilityof accurate LAAS aircraft position information enables automatedsystems to detect runway incursions and other conflicts providingsuitable alerts Various error sources affect the system accuracyintegrity and continuity and these are nowadays an active area ofresearch Some of these errors are

Hardwaresoftware faults in ground equipment or satellitessuch as the clock error

Multipath effects occurring on aircraft or ground receiverantennas

Errors in the ephemeris information

Residual ionospheric and tropospheric errors

Degradation of the satellite signal at the source

Interferencejamming issues

Table 18 GBAS Service Level Performance and Service Levels (adapted from [36])

GSL Accuracy Integrity Continuity Operations Supported

95LatNSE

95VertNSE

Prob (Loss ofIntegrity)

Timeto

Alert

LAL VAL Prob (Loss ofContinuity)

A 16 m 20 m 1-2times10-7150 sec 10 sec 40 m 50 m 1-8times10-615 sec Approach operations with verticalguidance (performance of APV-I

designation)

B 16 m 8 m 1-2times10-7150 sec 6 sec 40 m 20 m 1-8times10-615 s Approach operations with verticalguidance (performance of APV-II

designation)

C 16 m 4 m 1-2times10-7150 sec 6 sec 40 m 10 m 1-8times10-615 s Precision approach to lowest CAT Iminima

D 5 m 29 m 10-915 s (vert)30 s (lat)

2 sec 17 m 10 m 1-8times10-615 s Precision approach to lowest CATIIIb minima when augmented with

other airborne equipment

E 5 m 29 m 10-915 s (vert)30 s (lat)

2 sec 17 m 10 m 1-4times10-615 s Precision approach to lowest CATIIIIIa minima

F 5 m 29 m 10-915 s (vert)30 s (lat)

2 sec 17 m 10 m 1-2times10-615 s (vert) 30s (lat)

Precision approach to lowest CATIIIb minima

The LAAS service volume (Fig 32) is defined as the region wherethe system is required to meet the accuracy integrity and continuityrequirements for a specific GSL class

For each runway supported by the system the minimum servicevolume to support Category I Category II or APV (verticalguidance) approaches is defined as follow

Laterally beginning at 450 feet each side of the Landing ThresholdPointFictitious Threshold Point (LTPFTP) and projecting out

plusmn35deg either side of the final approach path to a distance of 20 NMfrom the LTPFTP

Vertically within the lateral region up to the maximum of 7deg or175 times the Glide Path Angle (GPA) above the horizon with theorigin at the Glide Path Intercept Point (GPIP) up to a maximumof 10000 feet AGL and down to 09deg above the horizon with theorigin in the GPIP to a minimum height of one half the DH

LTPFTP LandingFictitious Threshold Point

GPIP Glide Path Intersection Point

FPAP Flight PathAlignment Point

Plan view

LTPFTP

plusmn 450 ftplusmn 35ordm

15 NM plusmn10ordm

20 NM

10000 ftProfile view

GPIP

Greater than 7ordmor 175

FPAP

03-045

FPAP

Fig 32 Minimum category I II and APV service volume(adapted from [65])

Table 19 GBAS Service Levels (adapted from [36])

GSL Operations Supported by GSL

A Approach operations with vertical guidance (performanceof APV-I designation)

B Approach operations with vertical guidance (performanceof APV-II designation)

C Precision approach to lowest CAT I minima

D Precision approach to lowest CAT IIIb minima whenaugmented wih other airborne equipment

E Precision approach to lowest CAT IIIIIa minima

F Precision approach to lowest CAT IIIb minima

The minimum service volume to support Category III precisionapproach or autoland with any minima is the same as the minimumCategory II service volume with the addition of the volume withinplusmn450 feet from the runway centreline extending from the thresholdto the runway end from 8 feet above the surface up to 100 feetThere are different metrics for the GBAS performance one of theseis the SIS performance This is defined in terms of accuracyintegrity continuity and availability of the service [65] thisperformance refers to the output of the ldquofault-freerdquo airborne userequipment The interaction between airborne and ground systemsis defined by a separation of responsibilities

The ground system is responsible for monitoring the satellitessignal quality and availability computing the differentialcorrections and detecting and mitigating the faults originated in theground station or in the space segment

The airborne equipment computes the pseudorange values andevaluates the performance level monitoring detecting andmitigating any fault conditions due to the other avionics equipmentFor a precision approach the avionics GBAS receiver only usessatellites for which corrections are available

Avionics GBAS receivers have to comply with the requirementsoutlined in ICAO Annex 10 vol 1 [38] and the specifications ofRTCADO-253C [36] GBAS avionics receivers must have thecapability to receive navigation satellites signal and the VDBinformation with respective antennas and a way to select theapproach and an indication of course and glide path Like ILS andMicrowave Landing System (MLS) GBAS has to provide lateraland vertical guidance relative to the defined final approach courseand glide path The GBAS receiver employs a channelling schemethat selects the VDB frequency Approach procedure data areuplinked via the VDB and each separate procedure requires adifferent channel assignment In terms of aircraft systemintegration GBAS avionics standards have been developed to

mimic the ILS in order to minimize the impact of installing GBASon the existing avionics Typically display scaling and deviationoutputs are the same utilized for ILS so that maximuminteroperability is achieve at the Human-Machine Interface (HMI)level allowing the avionics landing systems to provide finalapproach course and glide path guidance both at airports equippedwith ILS and GLS For TMA area navigation including segmentedand curved approaches the GBAS avionics receiver providesaccurate position velocity and time data that can be used as aninput to an on-board navigation computer In line with ICAOSARPs and the strategy for the introduction and application of non-visual aids to approach and landing which permit a mix of systemsproviding precision approach service the avation industry hasdeveloped multi-mode receivers that support precision approachoperations based on ILS MLS and GNSS (GBAS and SBAS) Alsofor GBAS integrity monitoring is accomplished by the avionicscontinually comparing HorizontalLateral and Vertical ProtectionLevels (HPLLPL and VPL) derived from the augmentation signaland satellite pseudorange measurements against the alert limit forthe current phase of flight When either the vertical or thehorizontal limit is exceeded an alert is given to the pilot [116]Additionally the LAAS MOPS [36] also contemplate thepossibility of introducing avionics-based augmentationfunctionalities by defining the continuity of protection levels interms of Predicted Lateral and Vertical Protection Levels (PLPLand PVPL) The standard states that on-board avionics systemscould support PLPL and PVPL calculations to generate appropriatecaution flags However it does not recommend any specific formof ABAS and does not indicate the required performance of suchon-board equipment to supplement LAAS operations Research inthis field has concentrated on possible RAIM aiding rather thanproper ABAS developments Some techniques have beendeveloped that include the possible aiding of barometric altimeterwith a special focus on vertical guidance integrity monitoring andaugmentation [117-121] and more recently the possible inclusionof predictive features has also been studied especially formissionroute planning applications However the mainlimitations of such techniques is in the inability to model GNSSerrors due to aircraft dynamics including antenna obscurationDoppler shift and multipath contributions due to the aircraftstructure and the surrounding environment (the latter beingimportant when the aircraft flies at low altitudes) This is why anew form of ABAS specifically tailored for real-time integritymonitoring and augmentation in mission-critical and safety-criticalaviation applications is needed [53 54] and is discussed later inthis section

There are two conditions in the protection level calculations Oneis the H0 hypothesis the other is H1 hypothesis The H0 hypothesisrefers to no faults are present in the range measurements (includingboth the signal and the receiver measurements) used in the groundstation to compute the differential corrections The H1 hypothesisrefers to the presence of a fault in one or more range measurementsthat is caused by one of the reference receivers used in the groundstation The H0 Hypothesis total error model is

ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)

where σୟ୧୧ଶ is the total aircraft contribution to the corrected

pseudorange error for the ith satellite This is given by

ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)

The residual tropospheric and ionospheric errors are due to theposition difference of reference receiver and aircraft According tothe LAAS MASPS the tropospheric error is defined as [40]

(ߠ)௧ߪ = ேℎߪଵషల

ඥଶା௦మ(ఏ)(1 minus

೩

బ) (148)

where σ =troposphere refractivity uncertainty transmitted in theGBAS Message Type 2 θ is the elevation angle for the ith rangingsource It is expressed in the ENU frame Δh is the difference inaltitude between airborne and ground subsystems (referencereceivers) in meters and h is the tropospheric scale height(transmitted in GBAS Message Type 2)The residual ionosphericerror is defined as [40]

ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)

where F୮୮ is the obliquity defined in equation (25) The reference

receiver error model is used to generate the total error whichcontributing the corrected pseudorange for a GPS satellite causedby the reference receiver noise The standard deviation of thereference receiver error is [40]

(ߠ)_ௌߪ = ට (బାభషഇ ഇబfrasl )మ

ெ+ ( ଶ)ଶ (150)

where M is the number of ground reference receiver subsystemsand θ୧is the elevation angle for the ith ranging source Theairborne receiver error is a function of the satellite elevation angleabove the local level plane It is defined as [40]

(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)

where θ୧ is the elevation angle for the ith ranging source and theparameters a aଵ and θ are defined in [40] for various AirborneAccuracy Designators (AAD) It is to be noted that also the aircraftmultipath error is a function of the satellite elevation angle TheAirframe Multipath Designator (AMD) is a letter that indicates theairframe multipath error contribution to the corrected pseudorangefor a GPS satellite There are two types of AMD in the LAASMASPS denoted as A and B [40] The aircraft multipath error forAMD type A is

ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =

ଵଷାହଷ൫షഇ భబfrasl ൯

ଶ[m] (153)

The multipath model for AMD type A ߪ) ௨௧௧ ) was obtained

during an FAA sponsored research program which was aimed atinvestigating and quantifying the total effect of multipath from theairframe and from ground multipath during approach and landingoperations [55] The FAA sponsored program included thedevelopment of an electromagnetic modelling capability to predictamplitude time delay and phase characteristic of airframemultipath The final empirical model is the result of extensiveflight test data analysis conducted with large commercial airlinerplatforms (ie B777-300ER and B737-NG) as described in [122]As stated in the LAAS MASPS [40] the multipath model for AMDtype B ߪ) ௨௧௧

) is still under development [40] Sinceߪ ௨௧௧

is expected to produce conservative multipath error estimations itis acceptable to use ߪ ௨௧௧

in all cases until more reliable

ߪ ௨௧௧ models are developed The H1 hypothesis total error

model is given by

ுଵߪଶ =

ܯ

minusܯ 1௦௨ௗߪଶ + ௧௦ߪ

ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)

where ܯ is the number of reference receivers used to compute thepseudorange corrections for the ith satellite SBASGBASprojection matrix (S) matrix is obtained from the observationmatrix (G) and weighted matrix (W) and its elements determinethe protection levels of GBAS The S matrix for GBAS has thesame formats already defined for SBAS The fault-free verticalprotection level (ுܮ) can be calculated using the equation [24]

ுܮ = ܭ ௗටsum ߪଶ_ೡݏଶே

ୀଵ (155)

where s୮_౬౨౪୧is the projection of the vertical component and

translation of the along track errors into the vertical for the ithsatellite This is given by

=_ೡݏ +௩ݏ lowast௫ݏ tan ߠ ௌ (156)

where ߠ ௌ is the glide path angle for the final approach path and is the number of ranging sources used in the position solution TheH1 hypothesis vertical protection level (VPLୌଵ) can be calculatedusing the equations

ுଵܮ = ܮܣܯ (157)

ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)

where j is the ground reference receiver index K୫ is found inTable 7-9 and the other terms are

B௩௧ = sum ܤ௩௧ݏேୀଵ (159)

௩௧ுଵߪଶ = sum ௩௧ݏ

ଶ ுଵߪଶே

ୀଵ (160)

The fault-free lateral protection level (LPLୌ) is calculated usingthe equation (RTCA 2004)

ܮ ுܮ = ܭ ௗටsum ଶ_ݏ ߪଶே

ୀଵ (161)

where s୮_ ౪୧is the projection of the vertical component and

translation of the along track errors into the vertical for ith satellite(also denoted s୪ୟ୲୧) The H1 hypothesis lateral protection level(LPLH1) can be calculated using the following equations from theLAAS MASPS [40]

ܮ ுଵܮ = ܮܣܯ ܮ (162)

ܮ ܮ = หܤ௧ห+ ܭ ௗߪ௧ுଵ (163)

where

௧ܤ = sum ܤ௧ݏேୀଵ (164)

௧ுଵߪଶ = sum ௧ݏ

ଶ ுଵߪଶே

ୀଵ (165)

The subscript is the ground subsystem reference receiver indexand the multiplier K୫ can be found in [40] If the GBAS providesGSL E or F services then the predicted protection level must becalculated to enable continuity of the GBAS SIS The PredictedVertical Protection Level (PVPL) and Predicted Lateral ProtectionLevel (PLPL) are defined in MASPS as [40]

=ܮ ுଵܮுܮܣܯ (166)

ܮ =ܮ ܮܣܯ ுܮ PLPLୌଵ (167)

ுܮ = ܭ ௗටsum ߪଶ௩௧ݏଶே

ୀଵ (168)

ுଵܮ = +௩௧ߪௗܭ ܭ ௗߪ௩௧ுଵ (169)

ܮ ுܮ = ܭ ௗටsum ߪଶ௧ݏଶே

ୀଵ (170)

ܮ ுଵܮ = +௧ߪௗܭ ܭ ௗߪ௧ுଵ (171)

where ௗܭ is the multiplier which determines the probability of

fault-free detection given M reference receivers

௩௧ߪଶ = sum ௩௧ݏ

ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)

௧ߪଶ = sum ௧ݏ

ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)

The VAL defines the threshold values of VPL and PVPL (ie theGBAS signal is not to be used to navigate the aircraft when theVPL exceeds the VALPVAL)

463 Receiver Autonomous Integrity Monitoring

Various methods have been proposed and developed for stand-alone GNSS integrity monitoring One of the popularimplementations for aviation application is the RAIM techniqueRAIM has its foundations in statistical detection theory whereinredundant GNSS measurements are used to form a test-statisticfrom which a fault can be inferred RAIM is based on the reasoningthat the quality of a userrsquos position solution can be evaluated at thereceiver This supports detection of system-level faults RAIM wasintroduced in the latter part of the 1980s when autonomous meansof GNSS failure detection started to be investigated [42] A fault isidentified based on a self-consistency check among the availablemeasurements Traditionally RAIM and its performance havemostly been associated with the integrity-monitoring tasks inaviation and other safety-critical applications where relativelygood line-of-sight signal reception conditions prevail and there areoften strict rules of well-defined integrity modes The goal in thesetraditional RAIM operating environments was to eliminate largemeasurement errors due to for example satellite clock orephemeris failures which can be caused by failures in the satelliteor in the control segment These errors are very rare with a typicalrate of one error per 18 to 24 months in the GPS system [121]

Fault Detection-based RAIM (FD-RAIM) techniques provide thefollowing basic information the presence of a failure and whichsatellite(s) have failed FD-RAIM algorithms rely on users beingable to access more satellites than the minimum number requiredfor a navigation solution in order to estimate the integrity of thesignal from these redundant measurements Typically RAIMrequires 5 satellites for performing fault detection (sometimes 4satellites when baro-aiding is used) However in order to performfault detection and exclusion 6 satellites are needed Consideringfor example the GPS constellation providing only a singlefrequency catering to SPS RAIM cannot meet Category Irequirements for precision approach applications although RAIM-enabled receivers can be used as a navigation aid for lessdemanding phases of flight Hence the aim is to evaluate the likelyperformance of RAIM algorithms in a future multi-GNSSenvironment in which users have access to signals from more thanone system simultaneously This over-determination of thenavigation position solution from the large number of receivedranging measurements potentially allows users to apply RAIM to alevel appropriate for precision approach tasks Hence the detectionprobability will increase dramatically due to both the increasedsize of the available satellites and the improved accuracy of thesignals compared with traditional GPS-only signals

Fault Detection and Exclusion-based RAIM (FDE-RAIM) FDErequires six satellites and like FD-RAIM may use barometricaiding as an additional information source With six or more visiblesatellites FDE-RAIM detects a faulty satellite removes it from thenavigational solution and continues to provide FDEFD with theremaining visible satellites FDE is required for oceanic RNAVapprovals and is being mandated in aviation standards (TSO-C145aand C146a)

Another concept often used within the RAIM context is a ldquoRAIMholerdquo which refers to the period of time when there are insufficientvisible GNSS satellites to provide an integrity check at any givenlocation RAIM holes can be predicted using a number oftechniques The most common are

spatial (grid-based) and temporal sampling intervals basedtechniques when available computation capability is low

precise computation techniques for estimating satellite

coverage boundaries the intersection points and analysis ofthe topology of the regions of intersection when availablecomputation capability is high

While the adoption of RAIM techniques can significantly improvethe situation the inherent reactive nature of traditional RAIMtechniques do not allow an immediate implementation of predictivefeatures beyond the extrapolations that can be made from GNSSsignals and ephemeris data The introduction of ABAS SBAS andGBAS systems has allowed for an extended range of integritymonitoring and augmentation features (also providing substantialaccuracy and in some cases availability improvements) whichcan be exploited synergically in the various aircraft flight phasesHowever all these integrity augmentation systems have not beensuccessful so far in introducing predictive integrity monitoring andaugmentation features suitable for the most demanding flight tasks(ie precision approach in CAT-III and autoland certification)

Conventionally pseudorange-based and carrier-phase RAIM(PRAIM and CRAIM) are employed in the standard positioningalgorithms to ensure that a level of trust can be placed on thesolution PRAIM consists of two processes namely detection (of apotential failure) and derivation of the required protection levelThe detection process requires the construction of a test-statisticusing the measurement residuals followed by the determination ofa threshold value that provides an indication of the presence of afailure The derivation of the protection level is based on anestimate of the upper bound of the positioning error that mightresult from an undetected error Both HPL and VPL are employedin order to confirm if an intended operation can be supported bythe available GNSS PRAIM has achieved a level of success in civilaviation applications and is being applied at various flight phases(eg steady flight) But when performing high dynamicsmanoeuvres integer ambiguity resolution process has to beperformed and in this case the ambiguity residuals also contributeto the measurement residuals Hence to verify if the positionestimates can be trusted a high confidence in the resolution of theambiguities is required This necessitates the development ofreliable and efficient carrier phase integer ambiguity validationtechniques as an integral part of CRAIM

In addition to the conventional RAIM techniques (PRAIM andCRAIM) extended RAIM (e-RAIM) procedures support detectionof faults in the dynamic model and isolate them from themeasurement model and vice versa Most e-RAIM algorithms arederived from the Least Square (LS) estimators of the stateparameters in a Gauss-Markov KF

Recently Advanced RAIM (A-RAIM) and Relative RAIM(R-RAIM ) were proposed as two parallel candidates for futuregeneration integrity monitoring architectures to test the serviceavailability of LPV-200 for worldwide coverage with modernizedGNSS and augmentation systems [123 124] With double civilianfrequencies being transmitted the ionospheric error can bemeasured and removed thus improving the overall systemperformance The major difference between these two techniques isin the positioning method Code-only measurements are used in A-RAIM while both code and time-differenced carrier phasemeasurements are used in R-RAIM to ensure higher precisionwithout the necessity of an integer ambiguity resolution algorithm[125-127]

R-RAIM can be further divided into range domain R-RAIM and theposition domain R-RAIM based on the location where observationsfrom two time epochs are combined together This distinctionresults in in different error and projection matrices With advantagesin R-RAIM the trade-off is more complicated errors and projectionmatrices and therefore a more complicated process to transfer theseerrors with given risks in RAIM

The efficiency of RAIM is closely dependent on the receiver-satellite geometry and this implies that RAIM may not always beavailable Many preliminary investigations on RAIM have beenperformed [128-131] and the inference is that the stand aloneGNSS constellation does not provide the required RAIMavailability and GNSS must be augmented if it is to be used as aprimary navigation means for en route to non-precision phases offlight The non GNSS measurements which are helpful to improvethe RAIM availability include barometric altitude receiver clockcoasting geostationary satellite range etc

The integrity performance (in terms of detection and protectionlimit) provided by RAIM is a complex function of

the number of visible satellites that can be accessed at anygiven time

the receiver-satellite geometry

the probability density function of the error distribution in thereceived pseudorange signals from each satellite

the availability of each broadcast signal which refers to thepercentage of time that each satellite broadcasts a rangingsignal

integration with other sensorsaids (VORDME baroinertial)

RAIM performance for receivers using a GPS-only constellationhas been thoroughly analysed and some recommendations havebeen provided in the RTCA MOPS [36] Also some work has beenperformed to characterise RAIM performance against theidentified factors [132 133]

RAIM does not impose extensive hardware modifications to thereceiver and it is a feasible and effective way to detect and mitigatesingle spoofing signals Some recent studies have been performedto explore the potential of RAIM to deal with radiofrequencyinterference A recursive RAIM technique is being employed fordetecting and mitigating more than one spoofing signal withoutother independent information [1344]

Until September 27 2009 a RAIM prediction was not expected tobe performed for an RNAV route conducted where Air TrafficControl (ATC) provides RADAR monitoring or RNAVdeparturearrival procedure that has an associated RADARrequired note charted After this date operators filing RNAV 2routes (Q and T) RNAV 1 STARs and RNAV 1 DPrsquos will need toperform a RAIM prediction as part of their pre-flight planningICAO Annex 10 and ICAO PBN manual require the ANSPs toprovide timely warnings of GNSS RAIM outages A pre-flightGNSS RAIM prediction analysis is required by the FAA for flightsintending to use RNAVRNP routes as well as departure and arrivalprocedures while using GPS as the sole navigation sourceTherefore RAIM prediction results are dispatched to pilots flightdispatchers Air Traffic Controllers (ATCo) and airspace plannersThe use of appropriate RAIM prediction services is considered asa prerequisite for these GNSS approvals Pilots and ATCo needsuch information to ensure proper flight planning during possibleservice unavailability Since RAIM not only aims at detectingfaults but also at evaluating the integrity risk both the detectorand the estimator influence the RAIM performance

In a multi-constellation environment RAIM can exploit redundantmeasurements to achieve self-contained FDFDE at the userreceiver With the modernisation of GPS the full deployment ofGLONASS and the emergence of GALILEO BDS QZSS andIRNSS an increased number of redundant ranging signals becomeavailable which has recently drawn a renewed interest in RAIMIn particular RAIM can help alleviating the requirements onground monitoring For example recent research has been

focussing on A-RAIM employing multi-GNSS for verticalguidance of an aircraft [135]

RAIM Methods

A number of different RAIM algorithms have been developed overthe years Some are primarily design tools that predict whether ornot RAIM will be available for a given position at a given timewhilst others are implemented within receivers to perform FDFDEprocedures

Some techniques use a filtering or averaging technique such as theposition comparison method However the majority of RAIMtechniques use a so-called ldquosnapshotrdquo approach in which onlymeasurement data from a single epoch is used to check theconsistency of the solution Such techniques include the rangecomparison method the residual analysis method and the paritymethod [136-139] With these methods only current redundantmeasurements are used in the self-consistency check On the otherhand both past and present measurements can also be used alongwith a priori assumptions with regard to vehicle motion to providea decision

The snapshot approach has gained more acceptance than the otherin recent times because it has the advantage of not having to makeany questionable assumptions about how the system got to itspresent state It matters only that the system is in a particular stateand the RAIM decision as to failure or no-failure is based oncurrent observations only [140] These RAIM methods provide thesame level of integrity ie fundamentally these methods areidentical although conceptually they appear quite different andoften represented by single Least Squares Residuals (LSR) [139]

Some RAIM techniques have also been designed to use datacollected and filtered over multiple epochs This generatespredicted measurements (receiver-satellite ranges) with which tocompare each new measurement Although such techniquespromise very high performance especially when combined withadditional sensors such as inertial navigation system they aredifficult to model and analyse in the general case

The basic measurement relationship for RAIM is described by anover-determined system of linear equations of the form and is givenby

=ݕ ௧௨ݔܩ + Є (174)

where ݕ is the difference between the actual measured range (orpseudorange) and the predicted range based on the nominal userposition and the clock bias ݕ) is an ntimes1 vector) n is the number ofredundant measurements ௧௨ݔ are three components of trueposition deviation from the nominal position plus the user clockbias deviation ௧௨ݔ) is a 4times1 vector) Є is the measurement errorvector caused by the usual receiver noise vagaries in propagationimprecise knowledge of satellite position and satellite clock errorSA (if present) and possibly unexpected errors caused by asatellite malfunction (Є is an ntimes1 vector) and ܩ is the usual linearconnection matrix obtained by linearizing about the nominal userposition and clock bias ܩ) is an ntimes4 matrix)

Both the RAIM detector and the estimator have been investigatedin the literature With regard to fault detection two RAIMalgorithms have been widely implemented over the past 25 yearschi-squared (χ2) RAIM (also called parity-based or residual- based RAIM) and Solution Separation (SS) RAIM [132 133]Fundamental differences between the two algorithms have beenpointed out in [141] but it remains unclear whether SS or χ2 RAIM provides the lowest integrity risk In parallel with regard toestimation researchers have explored the potential of replacing theconventional Least-Squares (LS) process with a Non-Least-Squares (NLS) estimator to lower the integrity risk in exchange fora slight increase in nominal positioning error The resulting

methods show promising reductions in integrity risk but they arecomputationally expensive for real-time aviation implementations

The LS residual method uses all the measurements ොtoݕ calculate aLS estimate of the n-component GNSS position and clock offset orother companion quantityݔ using

=ොݔ ොݕܪଵ(ܪܪ) (175)

where the subscript ( ) denotes an estimate ܪ is the meaurmeentmatrix The least-squares solution is then used to predict the sixrange measurements

=ොݕ ොݔܪ (176)

The residual between the prediction and the measurementsindicates any inconsistency that may arise due to the mentionedmeasurement errors and is given by

ݓ = minusݕ =ොݕ minusܫ] ݕ[ܪଵ(ܪܪ)ܪ (177)

The observable in this integrity monitoring method is the sum ofthe squares of the residuals which is always a positive scalar andis given by

ܧ = ݓ ݓ (178)

If all elements of are zero-mean Gaussian distributions then theSquare Sum Error ( (ܧ has a non-normalized chi-squaredistribution with (minus 4 ) degrees of freedom In order to have alinear relationship between a satellite error and the induced test-

statistic an assumption is to assess ඥ ܧ (minus 4)frasl Apart from the ܧ technique an alternative method that employs a lineartransformation to the measurement ݕ is given by

ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)

The parity vector is the result of multiplying ݕ by an (minus 4) timesmatrix which is derived from a singular value decompositionor a factorization of the observation matrix ܪ which makes therows of mutually orthogonal and unity in magnitude If themeasurement error vector has independent random elements thatare zero-mean and normally distributed then the followingequations hold true

= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)

It implies that the magnitudes of and ݓ are the same inspite oftheir different dimensionalities Integrity alerts can therefore be setusing either ܧ or as a test statistic Under the assumption thatthe measurement noise is Gaussian with zero-mean and standarddeviation ఢߪ the quantity ଶݓ ఢߪ

ଶfrasl is a chi-square distributedrandom variable with (minus 4) degrees of freedom (a minimum offour satellites are required and the degrees of freedom are equal tothe number of redundant measurements) This is representedmathematically as

௪ మ

ఙചమ ~ ଶ(minus 4) (183)

The threshold value is set for the test-statistic to achieve anydesired probability of False Alarm (FA) under Normal Conditions(NC) and is given by

(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ

ଶ(షర) మfrasl (షర

మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ

ோమ ఙചమfrasl

(184)

where the integral is the incomplete gamma function Given thenumber of visible satellites and (ܥ|ܣܨ) the threshold canbe solved for A protection radius or HAL is set based on theRNP

By the number of alternative hypotheses there are two types ofRAIM algorithms for both A-RAIM and R-RAIM the classicRAIM method with single alternative hypothesis and the MultiHypothesis Solution Separation (MHSS) RAIM method [142] Theclassic RAIM method is typically used in Range Domain R-RAIM(RD-RAIM) while MHSS is used in A-RAIM Typically A-RAIM is adopted as the preferential method and Position DomainR-RAIM (PD-RAIM) is employed in case A-RAIM is not available[125]

464 Aircraft Based Augmentation Systems

In addition to the existing SBAS GBAS and RAIM techniquesGNSS augmentation may take the form of additional informationbeing provided by other on-board avionics systems As thesesystems normally operate via separate principles than the GNSSthey are not subject to the same sources of error or interference Asystem such as this is referred to as an Aircraft BasedAugmentation System or ABAS ABAS is different from RAIMin which the aircraft characteristics (flight dynamics body shapeantenna location EMCEMI etc) are typically not considered andvarious kinds of consistency check are accomplished using theGNSS signals to detect and exclude faultyunreliable satellites

The additional sensors used in ABAS may include InertialNavigation Systems (INS) VOR-DMETACAN Radar VisionBased Sensors etc Unlike SBAS and GBAS technologypublished research on ABAS is limited and mainly concentrates onadditional information being blended into the position calculationto increase accuracy andor continuity of the integrated navigationsolutions In recent years significant efforts were made fordeveloping ABAS architectures capable of generating integritysignals suitable for safety-critical GNSS applications (eg aircraftprecision approach and landing) which led to the development ofan Avionics Based Integrity Augmentation (ABIA) systemImplementing a Flight Path Guidance (FPG) module an ABIAsystem can provide steering information to the pilot andadditionally electronic commands to the aircraftUAS FlightControl System (FCS) allowing for real-time and continuousintegrity monitoring avoidance of safetymission-critical flightconditions and rapid recovery of the RNP in case of GNSS datadegradation or loss The architecture of an advanced ABIA systemis presented in Fig 33

Fig 33 ABIA system architecture

This system addresses both the predictive and reactive nature ofGNSS integrity augmentation To comprehend this concept somekey definitions of alerts and TTArsquos applicable to the ABIA systemare presented below [53]

Caution Integrity Flag (CIF) a predictive annunciation that theGNSS data delivered to the avionics system is going to exceedthe Required Navigation Performance (RNP) thresholdsspecified for the current and planned flight operational tasks(GNSS alert status)

Warning Integrity Flag (WIF) a reactive annunciation that theGNSS data delivered to the avionics system has exceeded theRequired Navigation Performance (RNP) thresholds specifiedfor the current flight operational task (GNSS fault status)

ABIA Time-to-Caution (TTC) the minimum time allowed forthe caution flag to be provided to the user before the onset of aGNSS fault resulting in an unsafe condition

ABIA Time-to-Warning (TTW) the maximum time allowedfrom the moment a GNSS fault resulting in an unsafe conditionis detected to the moment that the ABIA system provides awarning flag to the user

Based on the above definitions two separate models for the timeresponses associated to the Prediction-Avoidance (PA) andReaction-Correction (RC) functions performed by the ABIAsystem are defined (Fig 39) The PA time response is given by

∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where

∆T ୧ୡ୲=Time required to predict a critical condition

∆Tେ ୮୭୲=Time required to communicate the predicted failure to

the FPG module

∆T୴୭୧ =Time required to perform the avoidance manoeuvre

In this case ∆T୴୭୧ le TTC

If the available avoidance time ∆T୴୭୧ is not sufficient to performan adequate avoidance manoeuvre (ie ∆T୴୭୧ gt TTC) theaircraft will inevitably encroach on critical conditions causingGNSS data losses or unacceptable degradations In this case theRC time response applies

∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where

∆Tୈ ୲ ୡ୲=Time required to detect a critical condition

∆T ୮୭୲=Time required to communicate the failure to the FPG

module

∆Tେ୭ ୡ୲=Time required to perform the correction manoeuvre

In general the condition to be satisfied is expressed as

∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)

The RC time response is substantially equivalent to what currentGBAS and SBAS systems are capable of achieving A comparisonbetween Fig 34 (a) and Fig 34 (b) allows to immediately visualisethe benefits introduced by the ABIA PA function Further progressis possible adopting a suitable algorithm in an Integrity FlagModule (IFG) module capable of initiating an early correctionmanoeuvre as soon as the condition ∆T୴୭୧ le TTC is violated In this case the direct Prediction-Correction (PC) time responsewould be

∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)

This concept is illustrated in Fig 35 By comparing with Fig 34 itis evident that the ABIA system would be able to reduce the timerequired to recover from critical conditions if the followinginequality is verified

∆Tୟ୪୷େ୭ ୡ୲lt TTC + ∆Tୈ ୲ ୡ୲+ ∆Tେ ୮୭୲+ ∆Tେ୭ ୡ୲ (189)

(a) (b)

Fig 34 ABIA PA and RC functions

Fig 35 ABIA PC function

Targeting an ABIA implementation a dedicated analysis isrequired in order to determine the flight envelope limitationsassociated with the use of GNSS In particular the followingmodels have to be introduced [53 54]

The Antenna Obscuration Matrixes (AOM) in azimuth andelevation constructed as a function of attitude (Euler) anglesin all relevant aircraft configurations

The GNSS Carrier-to-Noise and Jamming-to-Signal Models(CJM) accounting for the relevant transmitterreceivercharacteristics propagation losses and RF interference

The Multipath Signal Model (MSM) including fuselagewing and ground path fading components and the associatedrange errors

The Doppler Shift Model (DSM) and associated criticalconditions causing GNSS tracking issues

Using appropriate aircraft dynamics models the manoeuvringenvelope of the aircraft can be determined in all required flightconditions Using the AOM CJM MSM and DSM modelstogether with the GNSS receiver tracking models and themanoeuvring requirements of specific flight tasks (egtesttraining missions or standard airport approach procedures) itis possible to identify the conditions that are potentially critical forthe on-board GNSS system and set appropriate thresholds for theABIA CIFs and WIFs thereby generating timely alerts when theaircraft is performing critical manoeuvres prone to induce GNSSsignal degradations or losses

5 Towards a Space-Ground-Aircraft AugmentationNetwork

Current SBAS and GBAS technologies are not able to meet thestringent GNSS data integrity requirements imposed byairworthiness regulations in some of the most demandingoperational tasks (eg UAS sense-and-avoid) GBAS providesprecision position services limited to use in the approach phaseonly SBAS provides a precision position service in all flightphases but GBAS provides better accuracy in the approach phaseOn the other hand the ABASABIA system approach isparticularly well suited to distinctively increase the levels ofintegrity and accuracy (as well as continuity in multi-sensor datafusion architectures) of GNSS in a variety of mission- and safety-critical applications Synergies between these three GNSSaugmentation systems (Fig 36) can be studied to develop a Space-Ground-Aircraft Augmentation Network (SGAAN) that can beused for a number of safety-critical aviation applications(Fig 37)

Space Based Augmentation Systems (SBAS)

Ground Based Augmentation Systems (GBAS)

Avionics Based Augmentation Systems (ABAS)

ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY

Fig 36 Synergies between SBAS GBAS and ABAS

Fig 37 Space-ground-aircraft augmentation network

Once the reliability of the mathematical algorithms forABASSBASGBAS is established dedicated IFG modules can beimplemented for alerting the pilotUAS remote pilot when thecritical conditions for GNSS signal losses are likely to occur(Fig38)

The ABAS IFG is designed to provide caution and warning alertsin real-time (ie in accordance with the specified TTC and TTWrequirements in all relevant flight phases) IFG module inputs arefrom the GNSS Receiver and aircraft flight dynamics A GNSSConstellation Simulator (GCS) can suppors the GNSS satellitevisibility signal and geometry analysis while an AircraftDynamics Simulator (ADS) can be used to generate the nominalflight path trajectory and attitude (Euler) angles Additionally anAircraft 3-Dimensional Model (A3DM) in CATIA (ComputerAided Three-dimensional Interactive Application) and a Terrainand Objects Database (TOD) are also required to run the MPSUsing a Digital Terrain Elevation Database (DTED) it is possible

to obtain a detailed map of the terrain beneath the aircraftProviding the aircraft trajectory inputs from the ADS moduleterrain elevation data can be automatically extracted and fed to theTOM module where they are integrated with the database of man-made objects (eg buildings) The Doppler Analysis Module(DAM) calculates the Doppler shift by processing ADS and GCSinputs The Multipath Analysis Module (MAM) processes theA3DM TEM GCS and ADS inputs to determine multipathcontributions from the aircraft (wingsfuselage) and from theterrainobjects close to the aircraft The Obscuration MatrixModule (OMM) receives inputs from the A3DM GCS and ADSand computes the GNSS antenna(e) obscuration matrixes for allaircraft manoeuvres The CN0 and JS Analysis Module (SAM)calculates the nominal link budget of the direct GNSS signalsreceived by the aircraft in the presence of atmospheric propagationdisturbances as well as the applicable RF interference signallevels The definition of suitable ABAS integrity thresholds isheavily dependent on the aircraft dynamics and geometriccharacteristics Further details can be found in the references [5354 148-150]

The IFGs for SBAS and GBAS introduce the system functionalitiesrequired to compute the VPL and HPL and to compare them withthe designated VAL and HAL (Fig 38) As discussed only theLAAS MOPS introduces the concept of predictive integrity flags(PVPL and PLPL) However the standard does not providedetailed guidance on how these features can be implemented inpractice to exploit potential synergies with ABAS AdditionallyPVALPLPL features are not present in the WAAS MOPS [41]VAL and HAL defined in the WAAS MOPS and are listed in Table20 The SBAS VAL is the threshold used to generate integrity flags

based on the SBAS VPL Similarly the SBAS HAL is thethreshold used to generate integrity flags based on the SBAS HPLFor oceanic en route terminal or Lateral NavigationVerticalNavigation (LNAVVNAV) approaches the VAL is not definedby the WAAS MOPS and ICAO SARPs [38 39] LNAVVNAVapproaches use lateral guidance (556 m lateral limit) from GNSSandor GBAS and vertical guidance provided by either barometricaltimeter or GBAS Aircraft that do not use GBAS for the verticalguidance portion must have VNAV-capable altimeters which aretypically integrated with modern flight directors andor FlightManagement Systems (FMS)

Table 20 SBAS vertical and horizontal alert limits [41]

Navigation ModeVertical AlertLimit (VAL)

Horizontal AlertLimit (HAL)

OceanicRemote NA 7408 m

En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m

LNAVVNAVApproach (after

FAWP)50 m 556 m

LPV or LP Approach 50 m 40 m

LPV II 35 m 40 m

Fig 38 SGAAN integrity Augmentation architecture

Localizer Performance with Vertical Guidance (LPV) enables theaircraft descent to 200-250 feet above the runway and can only beflown with a Wide Area Augmentation System (WAAS) andEuropean Geostationary Navigation Overlay Service (EGNOS)receiver LPV approaches are operationally equivalent to thelegacy Instrument Landing System (ILS) but are more economicalbecause no navigation infrastructure has to be installed inproximity of the runway Localizer Performance (LP) is a Non-Precision Approach (NPA) procedure that uses the high precisionof LPV for lateral guidance and barometric altimeter for verticalguidance LP approaches can only be flown by aircraft equippedwith WAASEGNOS receivers The minimum descent altitude forthe LP approach is expected to be approximately 300 feet abovethe runway The VAL values are listed in Table 21

Table 21 Vertical Alert Limit [40]

IntendedGSL

Height aboveLTPFTP (feet)

Alert Limit (meters)

A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

Similarly the Lateral Alert Limit (LAL) defines the thresholdvalues of LPL and PLPL The LAL values are listed in Table 22The Final Approach Segment Vertical and Lateral Alert Limits(FASVAL and FASLAL) are listed in Table 23

Table 22 Lateral Alert Limit [40]

IntendedGSL

Distance fromLTPFTP (meters)


AB --- FASLAL

C Along the runway andfor Dle873

FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915

DEF Along the runway andfor Dle291

FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215

Table 23 FASVAL and FASLAL

GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m

ABCDEF le10 m le17 m

Based on these alert limits and limitations the criteria forproducing SBASGBAS CIFs and WIFs can be set and are listedbelow

When VPLSBAS exceeds VAL or HPLSBAS exceeds HAL theWIF is generated

When PVPLGBAS exceeds VAL or PLPLGBAS exceeds LALthe CIF is generated

When VPLGBAS exceeds VAL or HPLGBAS exceeds HAL theWIF is generated

The performance of SBAS and GBAS can be enhanced by addingABIA models to the existing standards [36 40 41] As both SBASand GBAS use redundant GNSS satellite observations to supportFDE within the GNSS receiver (ie implementing a form ofRAIM) some additional integrity flag criteria can be introducedIn a WAASRAIM integration scheme the minimum number ofsatellites required for FDE is 6 At present no information isavailable regarding the provision of RAIM features within LAAS-enabled GNSS receivers Therefore the inclusion of a basic formof RAIM within such receiver (ie at least 5 satellites are requiredfor FDE) can be assumed Based on these assumptions the numberof satellites in view can be used to set additional integritythresholds for SBAS and GBAS [143 144] Additionally newaugmentation strategies including Ground-based RegionalAugmentation System (GRAS) which is a combination of SBASand GBAS concepts to enhance GNSS performance can be usedwithin the SGAAN network Such network could improve thenewly introduced APV procedures (supported by GNSS andorbaro-VNAV) and provide continuous lateralvertical guidancewithout the need for a terrestrial radio navigation aid Recentstudies have shown that ABAS systems would work synergicallywith SBAS and GBAS enhancing integrity levels in all flightphases from initial climb to final approach [144] Therefore theintegration of ABASABIA with SBAS and GBAS is a clearopportunity for future research towards the development ofSGAAN suitable for manned and unmanned aircraft applicationsand for a variety of mission-critical and safety-critical aviationapplications including flight test precision approach andautomatic landing

6 GNSS for Trusted Autonomous Operations

Current UAS technologies are perceived to have a lack of trustrelative to the human-machine teaming aspects The trust inhuman-machine teaming becomes even more important in GNSSdeniedchallenging environments and in providing effectivedecision-making in such safety-critical tasks

In modern UAS applications GNSS supports the development oflow-cost and high performance (and relatively low cost and low-volumeweight) navigation and guidance systems Additionallywhen used in conjunction with suitable data link technologiesGNSS-based navigation systems facilitates the provision ofAutomated Dependent Surveillance (ADS) functionalities forcooperative UAS SAA In non-cooperative SAA the adoption ofGNSS can also provide the key positioning and in some casesattitude data (using multiple antennas) required for automatedcollision avoidance A key limitation of GNSS for both cooperative(ADS) and non-cooperative applications is represented by theachievable levels of integrity Therefore the implementation ofintegrity augmentation functionalities could support thedevelopment of the IAS suitable for both cooperative and non-cooperative scenarios

61 GNSS Augmentation for UAS SAA

One of the key challenges encountered by the aviation communityfor integration of UAS into non-segregated airspace is theprovision of a Sense-and-Avoid (SAA) capability meeting thestringent integrity requirements set by international standards andnational certification authorities Cooperative and non-cooperativeSAA are implemented to address UAS safe integration into the

non-segregated airspace The SAA capability can be defined as theautomatic detection of possible conflicts (ie collision threats) bythe UAV platform and the implementation of avoidancemanoeuvres to prevent the identified collision threats As part ofour research the possible synergies attainable with the adoption ofdifferent detection tracking and trajectory generation algorithmswere studied Additionally the error propagation from differentsources and the impacts of host and intruders dynamics on theultimate SAA solution were investigated The system detectionrange and Filed-of-ViewField-of-Regard (FOVFOR) have to beadequate to ensure separation from the intruder to prevent aprobable near mid-air collision A number of cooperative and non-cooperative sensorssystems have been studied recentlyCooperative systems typically include Traffic Collision AvoidanceSystem (TCAS)Airborne Collision Avoidance System (ACAS)and Automatic Dependent Surveillance Broadcast (ADS-B) Theinclusion of ADS-B in association with GNSS-based navigationsystems redefines the paradigm of Cooperative SAA (C-SAA) inthe CNSATM context by allowing the share of accurate GNSStrajectory information Optical thermal LIDAR MMW Radar andacoustic sensors can be used as part of Non-Cooperative SAA (NC-SAA) architectures As an example a combined C-SAANC-SAA architecture is depicted in Fig 39 with anidentification of primary (solid line) and auxiliary sensors (dashedline) for cooperative and non-cooperative SAA tasks AdditionallyATM primary surveillance radar and Air Traffic Controller(ATCo) digital instructions using Controller to Pilot Data LinkCommunications (CPDLC) are considered The sequential stepsinvolved in the SAA process for executing an efficient TrackingDeciding and Avoiding (TDA) loop are also illustrated in Fig 39Criticality analysis is carried out to prioritize (ie to determine ifa collision risk threshold is exceeded for all tracked intruders) andto determine the action commands If an avoidance action isrequired the SAA system generates an optimal avoidancetrajectory using a fast-converging guidance algorithm such asdifferential geometry [145-147]

PMO techniques would have the benefit of providing amathematical optimum However they can be used instead of

DCO only if the SAA time horizon allows (ie only if the time toconflict is much greater than the computational time required toobtain an optimal trajectory) This could be the case for examplein properly developed air traffic separation maintenance systemsError analysis is performed to determine the overall uncertaintyvolume in the airspace surrounding the intruder tracks based on thecooperativenon-cooperative unified method described in [146]This is accomplished by considering both the navigation and thetracking errors affecting the measurements and translating them tounified range and bearing uncertainty descriptors As discussed inthe previous section the SGAAN research demonstrated thepotential of this new technology to enhance GNSS integrityperformance in a variety of mission- and safety-criticalapplications including experimental flight testflight inspectionprecision approach and automatic landing (also in synergy withGBAS and SBAS) [148] Therefore an ABIA system concept wasdeveloped for UAS applications (Fig 40)

Fig 39 SAA system architecture Adapted from [146]

Fig 40 ABIA system architecture for UAS applications [148]

As in a manned aircraft version this system performs a continuousmonitoring of GNSS integrity levels in flight by analysing therelationships between aircraft manoeuvres and GNSS accuracydegradations or signal losses (Doppler shift multipath antennaobscuration signal-to-noise ratio jamming etc) In case of anydetected or predicted integrity threshold violation the ABIAsystem provides suitable warning or caution signals to the UAVAFCS and to the remote Ground Control Station (GCS) therebyallowing timely correction manoeuvres to be performed Thisincreased level of integrity could provide a pathway to supportunrestricted access of UAS to all classes of airspace A possibleABIASAA integration architecture is illustrated in Fig 41Position Velocity and AttitudeRates (PVA) measurements areobtained by using the various navigation sensorssystems on-boardthe aircraft (ie implementing multi-sensor data fusiontechniques)

The key advantage is that the safe avoidance is determined byevaluating the risk-of-collision and then a safe manoeuvring pointis identified from where the host UAV can manoeuvre safely (ieany manoeuvre can be performed within the UAV operationalflight envelope) The risk of collision is evaluated by setting athreshold on the probability density function of a near mid-aircollision event over the separation volume The risk-of-collision iszero at the safe manoeuvring point If both the safe-separationthresholds are violated a mid-air collision threat is detected and theSAA WIF is generated To prevent any WIF the flight pathoptimization process starts when the first CIF is generated PMOand DCO techniques are used to generate a new optimisedtrajectory free of any integrity degradations Depending on therelationship between the available time-to-collision and thecomputation time required to generate the optimal trajectory PMOor DCO solutions are applied The optimised trajectory data aresent to the AFCS (and to the ground pilot) for execution of theavoidance manoeuvres In the trajectory optimisation process theaircraft 3DOF6DOF model defines the dynamics constraintswhile the satellite elevations and the aircraft heading rates are usedas path constraints Results from simulation case studies confirmedthat the Integrity-Augmented SAA (IAS) solution is capable ofperforming high-integrity conflict detection and resolution whenGNSS is used as the primary source of navigation data [148-150]

ABIASAA integrated architecture [148]

61 Resilience in GNSS Challenged Environments

In GNSS challenged environments measurement models ofdistributed sensors and GNSS jammer location estimation modelscan support the design of a model-predictive approach Thedeveloped models address uncertainty in platform navigation andjammer localization methods

In the aviation context complex cyber-physical systems are beingused on board aircraft (avionicsmission systems) and on theground (CNSATM systems Airline Operational Centres MilitaryCommand and Control etc) These cyber-physical systems haveintegrated computational and physical elements including CNSsensorssystems control systems data networks and externalcommunications The complexity of these ever moreinterconnected and interleaved systems can create multipleopportunities for a number of cyber-physical threats to materialise

Signals from commercial high power transmitters ultra widebandradar television VHF mobile satellite services and personalelectronic devices can interfere with the GNSS signals There arethree distinct forms of deliberate interference with GNSS signalsincluding jamming spoofing and meaconing There have beennumerous documented examples of intentional and unintentionalGPS jamming and spoofing For example employing AutomaticDependent SurveillancendashBroadcast (ADS-B) systems based onGNSS are subject to a number of cyber-attacks Three types ofthreats ADS-B message have been identified message corruptionmessage denial and message delay ADS-B using GNSS isinherently vulnerable to hacking jamming spoofing andmeaconing because of its open architecture and unencryptedsignals and because equipment is easy to obtain Several anti-spoofing techniques have been proposed in the open literature andcan generally be classified into two main categories spoofingdetection and spoofing mitigation Jamming is likely to produce themost significant impact on aviation GNSS operations Jammingcan be split into 4 broad areas accidental criminal red teamdeliberate and blue team deliberate

Earlier attempts on assessing vulnerability of civil GPS receiversto jamming were made by the UK Defence Research Agency(DRA) which was later incorporated into the Defence Evaluationand Research Agency (DERA) and successively into QinetiQThe effects of a low-power jammer were demonstrated by flighttests using a BAC-111 conducted at UKrsquos Farnborough facilityAccording to [151] a jammer radiating 1 W of FM noise in GPS16 GHZ frequency band was able to jam a civil GPS receiver at upto 22 km The differential signals in a DGNSS receiver are alsovulnerable to various types of jamming including terrorist attacksFor example the DGNSS facility can be outfitted with an antennadesigned to null out a jamming signal Because of the effectivejamming range double every 6 dB increase in transmitter power itis possible to build a small jammer capable of interfering with civilGPS receivers at ranges in excess of 50 km

To minimize the susceptibility to GNSS jamming combat aircraftare outfitted with a Controlled-Reception Pattern Antennas(CRPA) which are designed to detect a jamming signal anddesensitize the antenna in the direction of the jammer When theGNSS receiver is integrated with an INS the INS can take over asthe principal navigation system until the aircraft tis flown beyondthe range of the jammer Furthermore GNSS signals can bedegraded by natural and artificial obstacles in difficult scenarios(eg urban canyons and mountainous areas) requiring the need foreffective augmentation strategies to be implemented [152]

7 Conclusions and Future Research

A detailed review of Global Navigation Satellite Systems (GNSS)aviation applications was presented In recent years variousaugmentation strategies have been proposed and developed to

increase the levels of GNSS accuracy and integrity in aviationmission-essential and safety-critical applications The reviewcovered all existing approaches including Satellite BasedAugmentation Systems (SBAS) Ground Based AugmentationSystems (GBAS) Aircraft Based Augmentation Systems (ABAS)Receiver-Autonomous Integrity Monitoring (RAIM) and multi-sensor data fusion Suitable mathematical models were presentedaddressing the main sources of GNSS data degradation or loss inflight including antenna obscuration geometric accuracydegradation fading multipath and Doppler shift Some casestudies were also presented investigating the synergies attainablefrom the online integration of ABAS with SBAS and GBAS witha special focus on integrity augmentation features Finally thepotential of integrating SBAS-GBAS-ABAS with existing UAScooperative and non-cooperative SAA architectures wasinvestigated It was concluded that this integration leads to anIntegrity Augmented SAA (IAS) solution that is well suited for avariety of mission-essential and safety-critical aviationapplications Therefore the integration of SBASGBASABAS isa clear opportunity for future research towards the development ofa Space-Ground-Avionics Augmentation Network (SGAAN)suitable for manned and unmanned aircraft applications and for avariety of mission-essential and safety-critical GNSS operationaltasks including flight test precision approach and automaticlanding

Future GNSS research in the aviation context will concentrate onthe following main areas

Evaluate the potential of GNSS integrity augmentationtechniques to enhance the performance of next generationCommunication Navigation and SurveillanceAir TrafficManagement (CNSATM) decision support tools forPerformanceIntent Based Operations (PBOIBO) and 4DTmanagement

Investigate the potential of GNSS integrity augmentationtechniques to enhance the performance of Next GenerationFlight Management Systems (NG-FMSs) for manned andunmanned aircraft This will require an evolution of currentFMS architectures introducing suitable integrity monitoringand augmentation functionalities for 4-DimensionalTrajectory (4DT) planning and update throughout all flightphases

Evaluate the potential of introducing ionospheric scintillationmodels in the GNSS integrity augmentation systems Inparticular future research should focus on possible missionplanning implementations useful when flying over regionsaffected by intense scintillation andor in times of predictedhigh scintillation

Further investigate the potential of GNSS integrityaugmentation techniques to support trusted autonomoussystem applications by addressing other navigationcommunication and surveillance systems in the CNS+Acontext

Investigate the potential of integrity augmentation techniquesto enhance GNSS performance in aircraft surface operations

Investigate the potential of GNSS augmentation concepts tosupport aviation forensic applications (ie accident andincident investigation)

Investigate the potential synergies attainable by theemployment of GNSS integrity augmentation systems inurban canyons as well as to provide persistent navigation insparse and denied environments

References

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[2] P Daly GLONASS Approaches Full Operational Capability (FOC)Proceedings of the 8th International Technical Meeting of the SatelliteDivision of The Institute of Navigation (ION GPS 1995) Palm SpringsCA September 1995 pp 1021-1030

[3] D M Thomis ldquoGlobal Positioning System ndash A Modification to theBaseline Satellite Constellation for Improved Geometric PerformancerdquoUS Air Force Institute of Technology 1984

[4] G M Siouris ldquoAerospace Avionics Systemsrdquo Academic Press SanDiego CA (USA) 1993

[5] A Leick ldquoGPS Satellite Surveyingrdquo Third Edition John Wiley and SonsNew York 2003

[6] V Ashkenazi ldquoPrinciples of GPS and Observablesrdquo Lecture NotesIESSG University of Nottingham 1995

[7] G Seeber ldquoSatellite Geodesyrdquo Second Edition Walter de Gruyter EditorBerlin (Germany) New York (USA) 2003

[8] S Gleason and D Gebre-Egziabher (Editors) ldquoGNSS Applications andMethodsrdquo GNSS Technology and Application Series Artech HouseNorwood MA (USA) 2009

[9] V Ashkenazi T Moore and JM Westrop ldquoCombining Pseudo-rangeand Phase for Dynamic GPSrdquo Paper presented at the InternationalSymposium on Kinematic Systems in Geodesy Surveying and RemoteSensing London (UK) 1990

[10] V Ashkenazi T Moore G Ffoulkes-Jones S Whalley and M AquinoldquoHigh Precision GPS Positioning by Fiducial Techniqueslrdquo GlobalPositioning System An Overview Bock Y Leppard N EdsInternational Association of Geodesy Symposia Vol 102 Springer NewYork (USA) 1990

[11] T Moore ldquoGPS Orbit Determination and Fiducial Networksrdquo LectureNotes IESSG University of Nottingham (UK) 1996

[12] JFG Monico V Ashkenazi and T Moore ldquoHigh Precision GPSNetwork with Precise Ephemerides and Earth Body Tide Modelrdquo RevistaBrasileira de Geofisica Vol 15 N 2 pp 155-160 1997

[13] A H Dodson ldquoPropagation Effects on GPS Measurementsrdquo LectureNotes IESSG University of Nottingham (UK) 1997

[14] R Giffard ldquoEstimation of GPS Ionospheric Delay Using Ll Code andCarrier Phase Observablesrdquo In Proceedings of the 31st Annual PreciseTime and Time Interval (PTTI) Meeting Dana Point CA (USA) 1999

[15] J A Klobuchar ldquoDesign and Characteristics of the GPS IonosphericTime Delay Algorithm for Single Frequency Usersrdquo In Proceedings ofthe IEEE Position Location and Navigation Symposium Las Vegas NV(USA) 1986

[16] J Saastamoinen ldquoAtmospheric correction for the troposphere andstratosphere in radio ranging satellitesrdquo The Use of Artificial Satellitesfor Geodesy Henriksen S Mancini A Chovitz B Eds AmericanGeophysical Union Washington WA USA 1972

[17] J Saastamoinen ldquoContribution of the theory of atmospheric refractionrdquoBulletin Geacuteodesique Vol 107 pp 13ndash34 1973

[18] H Hopfield ldquoTwo-quartic Tropospheric Refractivity Profile forCorrecting Satellite Datardquo Journal of Geophysical Research Vol 74Oceans and Atmospheres pp 4487ndash4499 1969

[19] H Hopfield ldquoTropospheric effect on electro-magnetically measuredrange prediction from surface weather datardquo Radio Science Vol 6 Issue3 pp 357ndash367 1971

[20] R Leandro M Santos and R Langley ldquoUNB neutral atmosphere modelsDevelopment and performancerdquo In Proceedings of the Institute ofNavigation National Technical Meeting Monterrey CA USA January2006

[21] C Chao ldquoA model for Tropospheric Calibration from Daily Surface andRadiosonde Balloon Measurementsrdquo Technical Memorandum JetPropulsion Laboratory (JPL) Pasadena CA USA pp 350ndash391 1972

[22] I Ifadis ldquoThe Atmospheric Delay of Radio Waves Modeling theElevation Dependence on a Global Scalerdquo Technical Report No 38LSchool of Electrical and Computer Engineering Chalmers University ofTechnology Gothenburg (Sweden) 1986

[23] T Herring ldquoModeling atmospheric delays in the analysis of spacegeodetic datardquo In Proceedings of Refraction of Transatmospheric Signalsin Geodesy De Munck J Spoelstra T Eds Netherlands GeodeticCommission Publications on Geodesy The Hague Netherlands Volume36 pp 157ndash164 1992

[24] A Niell ldquoGlobal mapping functions for the atmosphere delay at radiowavelengthsrdquo Journal of Geophysical Research Vol 101 pp 3227ndash3246 1996

[25] J Boehm B Werl and H Schuh ldquoTroposphere Mapping Functions forGPS and Very Long Baseline Interferometry from European Centre forMedium-Range Weather Forecasts Operational Analysis Datardquo Journalof Geophysical Research Solid Earth Vol 111 Issue B2 2006


[27] JS Subirana JM Zornoza and M Hernaacutendez-Pajares ldquoMultipathrdquoEuropean Space Agency (ESA) Navipedia ndash GNSS Measurements andData Processing 2011 Available online athttpwwwnavipedianetindexphpMultipath cite_ref-1 Accessed on20042017

[28] A J Van Dierendonck P Fenton and T Ford ldquoTheory and Performanceof Narrow Correlator Spacing in GPS Receiverrdquo NAVIGATIONJournal of the Institute of Navigation vol 39 no 3 pp 265-284 1992

[29] GA McGraw and MS Braasch ldquoGNSS Multipath Mitigation UsingGated and High Resolution Correlator Conceptsrdquo In Proceedings of the1999 National Technical Meeting of the Institute of Navigation SanDiego CA (USA) 1999

[30] PC Fenton and J Jones ldquoThe Theory and Performance of NovAtel IncrsquosVision Correlatorrdquo In Proceedings of the 2005 ION GNSS ConferenceLong Beach CA (USA) 2005

[31] UD DOD ldquoGlobal Positioning System Standard Positioning ServicePerformance Standardrdquo Fourth Edition Department of DefencePositioning Navigation and Timing Executive Committee DocumentGPS SPS PS 2008

[32] AH Phillips ldquoThe Determination of PDOP in GPSrdquo NATO AdvisoryGroup for Aerospace Research and Development (AGARD) DocumentAGARD-AG-314 1990

[33] ICAO ldquoReport of the Special CommunicationsOperations DivisionalMeetingrdquo ICAO Doc 9650 1995

[34] ICAO ldquoPerformance Based Operations Manualrdquo Document No 9613AN937 Third Edition 2008

[35] US DoTDoD ldquoUS Federal Radionavigation Planrdquo United StatesDepartment of Defence Department of Transport Doc DoT-VNTSC-RITA-08-02DoD-46505 2008

[36] RTCA ldquoMinimum Operational Performance Standards for GPSGBASAirborne Equipmentrdquo Radio Technical Commission for Aeronautics(RTCA) Inc Special Committee No 159 Document RTCA DO-253CWashington DC (USA) 2008

[37] CAA ldquoGPS Integrity and Potential Impact on Aviation Safetyrdquo CAASafety Regulation Group Paper 200309 2003

[38] ICAO ldquoStandards and Recommended Practices (SAPRs) Volume 1 ndashAnnex 10 (Including Amendments 1-81)rdquo Issue 6 2006

[39] ICAO ldquoGBAS CAT IIIII Development Baseline SARPsrdquo Draftproposed changes to Annex 10 Volume I as agreed at the 17 ndash 28 May2010 meeting of the ICAO Navigation Systems Panel (NSP) 2010Available online at httpwwwicaointsafetyairnavigationdocumentsgnss_cat_ii_iiipdf

[40] RTCA ldquoMinimum Aviation System Performance Standards (MASPS) forthe Local Area Augmentation System (LAAS)rdquo Radio TechnicalCommission for Aeronautics (RTCA) Inc Special Committee No 159Document RTCA DO-245A Washington DC (USA) 2004

[41] RTCA ldquoMinimum Operational Performance Standards for GlobalPositioning SystemWide Area Augmentation Systems AirborneEquipmentrdquo Radio Technical Commission for Aeronautics (RTCA) IncSpecial Committee No 159 Document RTCA DO-229D WashingtonDC (USA) 2006

[42] B W Parkinson and J J Spilker Jr Editors ldquoGlobal Positiong SystemTheory and Applications ndash Volume Irdquo Progress in Astronautics andAeronautics vol 163 Published by the American Institute of Aeronauticsand Astronautics 1996

[43] P M Kintner B M Ledvina and E R de Paula ldquoGPS and IonosphericScintillationsrdquo Space Weather vol 5 issue S09003 pp 1-23 2007

[44] R Sabatini ldquoExperimental Investigation of Differential GPS for FlightTest of High Performance Aircraftrdquo University of Rome ndash ldquoLa SapienzardquoSchool of Aerospace Engineering Thesis submitted in partial fulfilmentfor the degree of Doctor of Engineering in Atronautics 2005

[45] R Sabatini and GB Palmerini ldquoDifferential Global Positioning System(DGPS) for Flight Testingrdquo NATO Research and TechnologyOrganization (RTO) Systems Concepts and Integration Panel (SCI)AGARDograph Series RTO-AG-160 Vol 21 2008

[46] L Boithias ldquoRadio Wave Propagationrdquo McGraw Hill (New York) 1982[47] ITU ldquoIonospheric Propagation Data and Prediction Methods Required for

the Design of Satellite Services and Systemsrdquo InternationalTelecommunication Union (ITU) Recommendation ITU-R P531-12 (PSeries ndash Radiowave propagation) 2013

[48] W B Davenport and W L Root ldquoAn Introduction to the Theory of

Random Signals and Noiserdquo Wiley-IEEE Press 1987 ISBN 978-0-

87942-235-6

[49] P W Ward ldquoGPS Receiver RF Interference Monitoring Mitigation andAnalysis Techniquesrdquo Navigation Journal of the Institute of Navigation(USA) vol 41 pp 367-391 1994

[50] A Steingass ldquoThe High Resolution Aeronautical Multipath NavigationChannelrdquo German Aerospace Center DLR (Germany) 2004httpwwwkn-sdlrdesatnav Accessed 14 May 2012

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[52] M S Braasch ldquoOn the characterization of multipath errors in satellite-based precision approach and landing systemsrdquo PhD Thesis College ofEngineering and Technology Ohio University (USA) 1992httpetdohiolinkeduviewcgiBraasch20Michaelpdfohiou1173748635 Accessed 10 May 2012

[53] R Sabatini T Moore and C Hill ldquoA New Avionics Based GNSSIntegrity Augmentation System Part 1 ndash Fundamentalsrdquo Journal ofNavigation Vol 66 No 3 pp 363-383 2013

[54] R Sabatini T Moore and C Hill ldquoA New Avionics Based GNSSIntegrity Augmentation System Part 2 ndash Integrity Flagsrdquo Journal ofNavigation Vol 66 No 4 pp 511-522 2013

[55] T Murphy R Friedman J Booth P Geren N Molloy B Clark andJ Burns ldquoProgram for the Investigation of Airborne Multipath ErrorsrdquoProceeding of the ION National Technical Meeting (NTM) 2004 SanDiego CA (USA) 2004

[56] J Booth T Murphy F Liu ldquoValidation of the Airframe Multipath ErrorAllocation for Local Area Differential GPSrdquo Proceedings of the IAINWorld Congress in association with the ION 2000 Annual Meeting SanDiego CA (USA) 2000

[57] OM Mubarak and AG Dempster ldquoStatistical Analysis of Early LatePhase for Multipath Detectionrdquo IGNSS Symposium 2009 Gold CoastAustralia 2009

[58] PW Ward ldquoUsing a GPS Receiver Monte Carlo Simulator to Predict RFInterference Performancerdquo Proceedings of the 10th InternationalTechnical Meeting of the Satellite Division of the Institute of NavigationKansas City MO (USA) 1997

[59] RTCM ldquoRTCM Recommended Standards for Differential NAVSTARGPS Servicerdquo Radio Technical Committee for Maritime Services SpecialCommittee No 104 Paper 134-89SC104-68Washington DC (USA)1990

[60] RTCM ldquoRTCM Recommended Standards for Differential NAVSTARGPS Servicerdquo Radio Technical Committee for Maritime Services SpecialCommittee No 104 Paper 194-93SC104-STD Washington DC (USA)1990

[61] RTCM ldquoRTCM Recommended Standards for Differential GNSSServicerdquo Radio Technical Committee for Maritime Services SpecialCommittee No 104 Paper 136-2001SC104-STD Version 23Washington DC (USA) 2011

[62] RTCA ldquoMinimum Aviation System Performance Standards DGNSSInstrument Approach System Special Category 1 (scat-1)rdquo RadioTechnical Commission for Aeronautics (RTCA) Inc Special CommitteeNo 159 Document RTCA DO-217 Washington DC (USA) 1993

[63] US DoDFAA ldquoGlobal Positioning System Wide Area AugmentationSystems (WAAS) Performance Standardrdquo First Edition United StatesDepartment of Defence and Federal Aviation Administration WashingtonDC (USA) 2008

[64] J Rife S Pullen B Pervan and P Enge ldquoCore Overbounding and itsImplications for LAAS Integrityrdquo In Proceedings of ION GNSS (pp2810-2821 2004

[65] RTCA ldquoGNSS-Based Precision Approach Local Area AugmentationSystem (LAAS) Signal-in-Space Interface Control Document (ICD)rdquoRadio Technical Commission for Aeronautics (RTCA) Inc SpecialCommittee No 159 Document RTCA DO-246D Washington DC(USA) 2008

[66] RR Hatch ldquoAmbiguity Resolution While Moving ExperimentalResultsrdquo In Proceedings of ION GPS-91 the 4th International TechnicalMeeting of the Satellite Division of the US Institute of NavigationAlbuquerque (NM) 1991

[67] H J Euler and H Landau ldquoFast GPS Ambiguity Resolution On-The-Flyfor Real-time Applicationsrdquo Paper presented at the 6th InternationalGeodetic Symposium on Satellite Positioning Columbus Ohio (USA)1992

[68] P Hansen ldquoReal-time GPS Carrier Phase Navigationrdquo The University ofNottingham IESSG Paper presented at the DSNS-94 ConferenceLondon (UK) 1994

[69] H J Euler ldquoAchieving High-accuracy Relative Positioning in Real-timeSystem Design Performance and Real-time Resultsrdquo In Proceedings ofthe 4th IEEE Plans Conference Las Vegas NV (USA) 1994

[70] D Walsh ldquoKinematic GPS Ambiguity Resolutionrdquo PhD Thesis IESSGUniversity of Nottingham (UK) 1994

[71] C C Tiberius and P J De Jonge ldquoFast Positioning using the LAMBDAMethodrdquo Proceedings of DSNS95 Bergen Norway 1995

[72] P J Teunissen ldquoInteger Aperture GNSS Ambiguity ResolutionrdquoArtificial Satellites vol 38 issue 3 pp 79-88 2003

[73] P J Teunissen ldquoTowards a Unified Theory of GNSS AmbiguityResolutionrdquo Journal of Global Positioning Systems vol 2 no 1 pp 1-12 2003

[74] H Shaowei ldquoAmbiguity Recovery for Long‐Range GPS KinematicPositioningrdquo Navigation vol 44 no 2 pp 257-266 1997

[75] P J Teunissen ldquoGNSS Ambiguity Resolution with Optimally ControlledFailure-raterdquo Artificial Satellites vol 40 issue 4 pp 219-227 2005

[76] S Verhagen ldquoImproved performance of Multi-Carrier AmbiguityResolution based on the LAMBDA methodrdquo In Proceedings of Navitec2006 ESA-ESTEC Noordwijk (The Netherlands) 2006

[77] H Liu Z Chen W Ye and H Wang ldquoGNSS Carrier Phase AmbiguityResolution based on Integrity Restriction in Ambiguity DomainrdquoAdvances in Space Research vol 53 issue 8 pp 1207ndash1218 2014

[78] S Nassar A Noureldin and N El-Sheimy ldquoImproving PositioningAccuracy during Kinematic DGPS Outage Periods using SINSDGPSIntegration and SINS Data De-noisingrdquo Survey Review vol 37issue 292 pp426-438 2004

[79] A Keith ldquoUsing Wide Area Differential GPS to Improve Total SystemError for Precision Flight Operationsrdquo PhD Thesis Stanford University(USA) 2000

[80] G W A Offermans A W S Helwig and D Van Willigen ldquoEurofixTest Results of a Cost-Effective DGNSS Augmentation Systemrdquo Journalof Navigation vol 50 no 2 pp 209-223 1997

[81] T Moore ldquoOther Satellite Navigation Systemsrdquo Lecture Notes IESSGUniversity of Nottingham (UK) 1996

[82] T Moore ldquoAn Introduction to Differential GPSrdquo Lecture Notes IESSGUniversity of Nottingham (UK) 1996


[84] K Zhang F Wu S Wu C Rizos C Roberts L Ge T Yan C GordiniA Kealy M Hale P Ramm H Asmussen D Kinlyside and PHarcombe ldquoSparse or dense Challenges of Australian Network RTKrdquoProceedings of International Global Navigation Satellite Systems SocietySymposium (IGNSS2006) Surfers Paradise (Australia) July 2006

[85] V Janssen and J Haasdyk ldquoAssessment of Network RTK performanceusing CORSnet-NSWrdquo Proceeedings of the IGNSS 2011 Symposium15-17 November 2011 Sydney (Australia) 2011

[86] JM Juan A Rius M Hernaacutendez-Pajares and J Sanz ldquoA Two-layerModel of the Ionosphere using Global Positioning System DatardquoGeophys Research Letters Vol 24 pp 393ndash396 1997

[87] S Bisnath and Y Gao ldquoPrecise Point Positioning ndash A Powerful Techniqewith a Promising Futurerdquo GPS World (Algorithms and Methods ndashInnovation) pp 43-50 2009

[88] AS Jokinen ldquoEnhanced Ambiguity Resolution and Integrity MonitoringMethods for Precise Point Positioningrdquo PhD Thesis Centre for TransportStudies Department of Civil and Environmental Engineering ImperialCollege London (UK) 2014

[89] National Coordination Office for Space-Based Positioning Navigationand Timing GPS Washington DC (USA) URL httpwwwgpsgovAccessed 19 July 2017

[90] European Global Navigation Satellite System Agency Prague (CzechRepublic) and Saint-Germain-en-Laye (France) URLhttpswwwgsaeuropaeueuropean-gnssgalileogalileo-european-global-satellite-based-navigation-system Accessed 19 July 2017

[91] Information and Analysis Center for Positioning Navigation and TimingKorolyov (Russia) URL httpswwwglonass-iacruenGLONASSindexphp Accessed 19 July 2017

[92] China National Space Administration BeiDou Navigation SatelliteSystem Haidian District Beijing (China) URL httpenbeidougovcnAccessed 19 July 2017

[93] Indian Space Research Organisation Bengaluru (India) URLhttpwwwisrogovinspacecraftsatellite-navigation Accessed 19 July2017

[94] GW Hein JA Rodriguez S Wallner et al ldquoEnvisioning a FutureGNSS System of Systemsrdquo Part 1Inside GNSS vol 2 issue 1 pp 58-672007

[95] Y Urlichich V Subbotin G Stupak et al ldquoGLONASS ModernizationrdquoProceedings of ION GNSS+ 2011 pp 3125ndash3128 Portland Oregon(US) 2011

[96] Cabinet Office Office of National Space Policy Government of JapanTokyo (Japan)URL httpqzssgojpen Accessed 19 July 2017

[97] O Montenbruck P Steigenberger L Prange Z Deng Q Zhao FPerosanz et al ldquoThe Multi-GNSS Experiment (MGEX) of theInternational GNSS Service (IGS) ndash Achievements Prospects andChallengesrdquo Advances in Space Research vol 59 pp 1671-1697 2017

[98] International Committee on Global Navigation Satellite Systems TheWay Forward International Committee on Global Navigation SatelliteSystems STSPACE67 United Nations Office for Outer Space AffairsVienna (Austria) 2016

[99] GM Siouris ldquoAerospace Avionics Systemsrdquo Academic Press SanDiego California (USA) 1993

[100]GW Hein and MM Ertel ldquoHigh-precision Aircraft Navigation usingDGPSINS integrationrdquo Institute of Astronomical and Physical Geodesy(IAPG) University FAF Munich Neubiberg (Germany) 1993

[101]F Cappello S Ramasamy and R Sabatini ldquoA Low-Cost and HighPerformance Navigation System for Small RPAS Applicationsrdquo

Aerospace Science and Technology vol 58 pp 529ndash545 2016 DOI101016jast201609002

[102]R Kapoor S Ramasamy A Gardi and R Sabatini ldquoUAV NavigationUsing Signals of Opportunity in Urban Environments An Overview ofExisting Methodsrdquo Energy Procedia vol 110 pp 377-383 2017 DOI101016jegypro201703156

[103]A Gelb ldquoApplied Optimal Estimationrdquo The MIT Press Cambridge(Massachusetts) and London (England) 1992

[104]E Waltz and J Linas ldquoMultisensor Data Fusionrdquo Artech House London(England) and New York (US) Second Edition pp 159-211 1994

[105]R Van de Leijgraaf J Breeman G Moek and SS Van Leeuwen SSldquoA Position Reference System for Fokker 70rdquo NLR TechnicalPublication TP 93084L 1993

[106]M Napier ldquoThe Integration of Satellite and Inertial Positioning SystemsrdquoProceedings of the NAV-89 Symposium The Royal Institute ofNavigation London (UK) 1989

[107]T Jacob and G Schanzer ldquoIntegrated Flight Guidance System UsingDifferential GPS for Landing Approach Guidancerdquo AGARD-CP-455NATO Advisory Group for Aerospace Research and DevelopmentNeuilly-sur-Seine (France) 1989

[108]A Noureldin A El-Shafie and M Bayoumi ldquoGPSINS Integrationutilizing Dynamic Neural Networks for Vehicular NavigationrdquoInformation Fusion vol 12 pp 48-57 2011

[109]ESA (2011a) ldquoIntegrityrdquo European Space Agency Navipedia websitehttpwwwnavipedianetindexphpIntegrity Year of Publication 2011(Edited by GMV) Visited on 18th January 2017

[110]US DoDDoTDoHS ldquoFederal Radionavigation Plan ndash 2012rdquo UnitedStates Department of Defence Department of Transport and Departmentof Homeland Security - National Technical Information ServicesSpringfield VA (USA) 22181 Doc DOT-VNTSC-RITA-08-02DoD-465005 2012

[111]G N Skillicorn ldquoThe Past Present and Future of LAASrdquo IntegratedCNS Technologies Conference and Workshop Annapolis MD (USA)2003

[112]ICAO ldquoGlobal Navigation Satellite Systems (GNSS) ManualrdquoInternational Civil Aviation Organization Document No 9849 AN457First Edition 2005

[113]ESA ldquoSBAS Systemsrdquo European Space Agency Navipedia websitehttpwwwnavipedianetindexphpSBAS_Systems 2011 (Edited byGMV) Accessed on 20th March 2016

[114]ICAO ldquoInternational Standards and Recommended Practices Annex 10to the Convention on International Civil Aviationrdquo AeronauticalTelecommunications Volume I Radio Navigation Aids Sixth Edition(Including Amendments 1-81) 2006

[115]FAA ldquoSatellite Navigation - Ground Based Augmentation System(GBAS)rdquo US Federal Aviation Administration Website SectionDedicated to Navigation ProgramsGNSShttpwwwfaagovaboutoffice_orgheadquarters_officesatoservice_unitstechopsnavservicesgnsslaas Vested on 24th March 2016

[116]ICAO ldquoGuide for Ground Based Augmentation SystemsImplementationrdquo International Civil Aviation Organisation 2013

[117]J E Angus ldquoRAIM with Multiple Faultsrdquo NAVIGATION Journal ofthe Institute of Navigation vol 53 no 4 2006

[118]T Walter P Enge J Blanch and B Pervan ldquoWorldwide VerticalGuidance of Aircraft Based on Modernized GPS and New IntegrityAugmentationsrdquo Proceedings of the IEEE Vol 96 No 12 2008

[119]A Ene J Blanch and J D Powell ldquoFault Detection and Elimination forGALILEO-GPS Vertical Guidancerdquo Proceedings of the Institute ofNavigation National Technical Meeting San Diego CA (USA) 2007

[120]J Blanch A Ene T Walter and P Enge ldquoAn Optimized MultipleHypothesis RAIM Algorithm for Vertical Guidancerdquo In Proceedings ofION GNSS 2007 2007

[121]H Kuusniemi and T Jokitalo ldquoIndoor and Week Signal NavigationrdquoChapter 12 in ldquoGNSS Applications and Methodsrdquo S Gleason and DGebre-Egziabher Artech House pp 306-324 2009

[122]T Murphy R Friedman J Booth P Geren N Molloy B Clark andJ Burns ldquoProgram for the Investigation of Airborne Multipath ErrorsrdquoProceeding of the ION National Technical Meeting (NTM) 2004 SanDiego CA (USA) 2004

[123]FAA ldquoGEAS - GNSS Evolutionary Architecture Studyrdquo GEAS Phase Indash Panel Report 2008

[124]FAA ldquoGEAS - GNSS Evolutionary Architecture Studyrdquo GEAS Phase IIndash Panel Report 2010

[125]Y Jiang and J Wang ldquoA-RAIM and R-RAIM Performance using theClassic and MHSS Methodsrdquo The Journal of Navigation vol 67 pp 49-61 2014 DOI 101017S0373463313000507

[126]F Van Graas and A Soloviev ldquoPrecise Velocity Estimation Using aStand-Alone GPS Receiverrdquo Navigation vol 51 issue 4 pp 283ndash2922004

[127]W Ding and J Wang Precise velocity estimation with a stand-alone GPSreceiverrdquo Journal of Navigation vol 64 issue 2 pp 311ndash325 2011

[128]K L Van Dyke ldquoRAIM Availability for Supplemental GPS NavigationrdquoNavigation Journal of The Institute of Navigation vol 39 no4 pp 429-443 1992

[129]Y C Lee ldquoRAIM Availability for GPS Augmented with BarometricAltimeter Aiding and Clock Coastingrdquo Navigation Journal of theInstitute of Navigation vol 40 no2 pp 179-198 1993

[130]P Misra E Bayliss R LaFrey M Pratt and J F Mclellan ldquoReceiverAutonomous Integrity Monitoring (RAIM) of GPS and GLONASSrdquoNavigation Journal of The Institute of Navigation vol 40 no1 pp 87-104 1993

[131]J Sang K Kubik and Y Feng ldquoReceiver Autonomous IntegrityMonitoring (RAIM) in Civil Aviation Use of GPS as a Sole Means ofNavigationrdquo In Proceedings of Satellite Navigation Technology 1995 andBeyond Brisbane June 1995

[132]T Walter and P Enge ldquoWeighted RAIM for Precision Approachrdquo InProceedings of the 8th International Technical Meeting of the SatelliteDivision of the Institute of Navigation Palm Springs CA (USA) 1995

[133]R G Brown ldquoA Baseline GPS RAIM Scheme and a Note on theEquivalence of Three RAIM Methodsrdquo Journal of the Institute ofNavigation vol 39 no 3 1992

[134]T Huiqi H Li W Zhang and M Lu ldquoA Recursive ReceiverAutonomous Integrity Monitoring (Recursive-RAIM) Technique forGNSS Anti-Spoofingrdquo In Proceedings of the 2015 InternationalTechnical Meeting of The Institute of Navigation California (USA) pp738 ndash 744 January 2015

[135]EU-US Cooperation on Satellite Navigation Working Group C-ARAIMTechnical Subgroup ARAIM Technical Subgroup Milestone 1 Report2012 httpeceuropaeuenterprisenewsroomcf_getdocumentcfmdoc_id=7793

[136]Y C Lee ldquoAnalysis of Range and Position Comparison Methods as aMeans to Provide GPS Integrity in the User Receiverrdquo In Proceedings ofthe Annual Meeting of the Institute of Navigation pp 1-4 Seattle WA(USA) June 1986

[137]B W Parkinson and P Axelrad ldquoAutonomous GPS Integrity Monitoringusing the Pseudorange Residualrdquo Navigation (Washington) vol 35 pp255-274 1988 httpdxdoiorg101002j2161-42961988tb00955x

[138]M A Sturza and A K Brown ldquoComparison of Fixed and VariableThreshold RAIM Algorithmsrdquo Proceedings of the 3rd InternationalTechnical Meeting of the Institute of Navigation Satellite Division IONGPS-90 (Colorado Springs CO) pp 437-443 September 1990

[139]R G Brown and P Y C Hwang ldquoGPS Failure Detection byAutonomous Means within the Cockpitrdquo In Proceedings of the AnnualMeeting of the Institute of Navigation Seattle pp 5-12 June 1986httpdxdoiorg101002j2161-42961986tb01485x

[140]R G Brown ldquoReceiver Autonomous Integrity Monitoringrdquo In B WParkinson and J J Spilker (Eds) Chapter 5 in Global Positioning SystemTheory and Applications Volume 2 AIAA Inc Washington DC (USA)pp 143-165 1996

[141]M Joerger F C Chan and B Pervan ldquoSolution Separation versusResidual-Based RAIMrdquo NAVIGATION vol 61 issue 4 pp 273ndash2912014

[142]J Blanch A Ene T Walter and P Enge ldquoAn Optimized MultipleHypothesis RAIM Algorithm for Vertical Guidancerdquo ION GNSS 2007Fort Worth TX 2007

[143]R Sabatini T Moore C Hill A Gardi S Ramasamy and M GilgienldquoTrajectory Optimisation for Avionics-Based GNSS IntegrityAugmentation Systemsrdquo Proceedings of the 35th AIAAIEEE DigitalAvionics Systems Conference (DASC2016) Sacramento CA (USA)September 2016

[144]R Sabatini T Moore and C Hill ldquoAvionics-Based GNSS IntegrityAugmentation Synergies with SBAS and GBAS for Unmanned AircraftApplicationsrdquo Proceedings of the 35th AIAAIEEE Digital AvionicsSystems Conference (DASC2016) Sacramento CA (USA) September2016

[145]L Rodriguez R Sabatini A Gardi and S Ramasamy ldquoA Novel Systemfor Non-Cooperative UAV Sense-and-Avoidrdquo In Proceedings ofEuropean Navigation Conference 2013 Vienna (Austria) 2013

[146]S Ramasamy R Sabatini and A Gardi ldquoLIDAR Obstacle Warning andAvoidance System for Unmanned Aerial Vehicle Sense-and-AvoidrdquoAerospace Science and Technology Elsevier vol 55 pp 344ndash358 2016DOI 101016jast201605020

[147]S Ramasamy R Sabatini and A Gardi ldquoA Unified Approach toSeparation Assurance and Collision Avoidance for Flight ManagementSystemsrdquo Proceedings of the 35th AIAAIEEE Digital Avionics SystemsConference (DASC2016) Sacramento CA (USA) September 2016

[148]R Sabatini T Moore and C Hill ldquoAvionics Based GNSS IntegrityAugmentation for Mission- and Safety-Critical Applicationsrdquo Inproceedings of the 25th International Technical Meeting of the SatelliteDivision of the Institute of Navigation ION GNSS-2012 NashvilleTennessee (USA) September 2012 URLhttpwwwionorgpublicationsabstractcfmarticleID=10288

[149]R Sabatini T Moore C Hill and S Ramasamy ldquoInvestigation of GNSSIntegrity Augmentation Synergies with Unmanned Aircraft SystemsSense-and-Avoidrdquo In Proceedings of SAE AeroTech Congress 2015Technical Paper 2015-01-2456 Seattle WA (USA) September 2015DOI 1042712015-01-2456

[150]R Sabatini T Moore and C Hill ldquoAvionics-Based GNSS IntegrityAugmentation for Unmanned Aerial Systems Sense-and-Avoidrdquo InProceedings of the 27th International Technical Meeting of the SatelliteDivision of the Institute of Navigation ION GNSS+ 2014 Tampa Florida(USA) September 2014 URLhttpmionorgabstractcfmpaperID=1811

[151]J Owen ldquoA Review of the Interference Resistance of SPS GPS Receiversfor Aviationrdquo Journal of Navigation PB - Blackwell Publishing LtdDOI 101002j2161-42961993tb02307x 1993

[152] JR Rufa and EM Atkins ldquoUnmanned Aircraft System Navigation inthe Urban Environment A Systems Analysisrdquo Journal of AerospaceInformation Systems 2016

Potential elimination of some ground-based navigationaids (VOR ILS etc) with cost saving to Air NavigationService Providers (ANSPs)

This paper is organised as follows Section 2 provides a detaileddiscussion on GNSS aviation applications followed by adescription of models for GNSS performance threats in Section 3Section 4 presents the different augmentation strategies and theidentification of a pathway to a future GNSS Space-Ground-Avionics Augmentation Network (SGAAN) is discussed in Section5 an investigation of the potential of GNSS augmentationtechniques to support trusted autonomous Unmanned AircraftSystem (UAS) applications is presented in Section 6 Theconclusions of this article are summarised in Section 7 andrecommendations for future research are highlighted in Section 8

2 GNSS Aviation Applications

Although different GNSS systems employ diversified hardwareand software features all systems are composed by a spacesegment a control segment and a user segment (Fig 1) The spacesegment includes the satellites required for global coverage Thesesatellites are predominantly in Intermediate Circular Orbit (ICO)

at nominal altitudes of 19100 km (GLONASS) 20184 km (GPS)and 23222 km (GALILEO) from the Earthrsquos surface

BDS also employs satellites in Geostationary Orbit (GEO) andInclined Geosynchronous Orbit (IGSO) The user segment includesthe large variety of GNSS receivers developed for air ground andmarine navigation positioning applications The control segmentincludes one or more Control and Processing Stations (CPSs)connected to a number of Ground Monitoring Stations (GMSs) andantennae located around the globe for Telemetry Tracking andCommand (TTampC) signals downuplink and navigationintegritysignals uplink to the satellites The GMS antennae passively trackall GNSS satellites in view collecting ranging signals from eachsatellite This information is passed on to the CPS where thesatellite ephemeris and clock parameters are estimated andpredicted Additionally satellite integrity data are analysed andappropriate integrity flags are generated for faultyunreliablesatellites The ephemerisclock and integrity data are then up-linked to the satellite for retransmission in the navigation messageThe satellite clock drift is corrected so that all transmitted data aresynchronised with GNSS time

SpaceSegment

ControlSegment

UserSegment

Satellite TTampC Data

NavigationIntegrity Data

Satellite Navigation Signals

Constellation Monitoring Data

Ground Monitoring Station

Satellite TTampC Link

NavigationIntegrity Uplink

ControlProcessing Station

Legend

Fig 1 GNSS segments

The fundamental equation is the following

ݐ ேௌௌ minus௦ݐ= ௦ݐ߂ (1)

where ݐ ேௌௌ is the GNSS time ௦ݐ is the satellite time and ௦ݐ߂ is thedifference between satellite and GNSS time The corrections areapplied to the last term of equation (1) typically using polynomialcoefficients and a relativistic correction term The correctionequation can be written as

௦ݐ߂ = + ଵ(ݐ ேௌௌminusݐ) + ଶ(ݐ ேௌௌminusݐ)ଶ + ݐ߂ (2)

where ଵ and ଶ are the polynomial coefficients for phasefrequency and age offset ݐ߂ is the relativistic correction term andݐ is the time of transmission of the corrections

Typically the ephemeris corrections are obtained through anestimation of the Cartesian co-ordinates of the satellites along theorbits by integrating the equations of motion For integritypurposes suitable Fault Detection Isolation and Recovery (FDIR)techniques are employed In particular the health status of thesatellite subsystems is continuously monitored (satellite payloadbus solar arrays battery power and the level of propellant used formaneuvers) and any anomaly must be promptly detected andresolved When needed spare satellites can be activated The

Signal-in-Space (SIS) is also constantly monitored to guarantee therequired performance standards Despite the significanttechnological enhancements recently introduced in controlsegment integrity features current GNSS systems have limitedFDIR capability In most cases several minutes or even hours arerequired to provide the required integrity information (ie usedonot use signals) to GNSS users Obviously this is not acceptablefor mission-essential and safety-critical aviation applications

21 GNSS Observables

There are basically three types of GNSS observables that can beused in aviation GNSS receivers pseudorange carrier phase andDoppler observable Pseudoranges are commonly used in real-time aircraft navigation and can provide an accuracy ranging fromabout 20 m (single frequency receivers) to about 2 m in DifferentialGNSS (DGNSS) positioning The carrier phases are traditionallyused in high precision trajectory determination applications (egTSPI systems for flight test and flight inspection) and can achievesub-centimetre accuracy However it is also quite common to usecombinations of pseudoranges and carrier phase measurementsboth in real-time and post mission applications Moreover it hasbecome common practice to take advantage of various




(ݐ) = ݐ) ݐminus

) times (3)



ݐ=ݐ + ݐ (4)

ݐ ݐ= + ݐ (5)




(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (6)

Therefore

(ݐ) = ߩ


(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (7)

where ܫ(ݐ) and k











⎩⎪⎨

⎪⎧





(9)


O

hRe

(xk yk zk)

(x2 y2 z2)

(x3 y3 z3)

XE YE

ZE

(x4 y4 z4)

(x1 y1 z1)

GreenwitchMeridian

Equator

North Pole





(i = 1 2 3 4)


ቀ௨௨

ቁ∆ݑ + ቀ

௩௩

ቁ∆ݒ + ቀ

௪௪

ቁ∆ݓ + ∆ = ∆ (11)

(i = 1 2 3 4)





ߔ


+ ఃܫ (ݐ) minus

(ݐ)

+ ః (ݐ) + ః (ݐ) +

(ݐ) + ఃߝ (12)


is the







ߔ( ) = (ݐ)ߔ minus )ߔ ) (13)





(14)

Therefore


൰ (15)


ௗ௧ถ

timesఘಲ(௧)

+⋯ (16)


+⋯ (17)

and finally

ߔ( ) = )ߔ ) minus


(18)


emitted signal







=

ଵାᇲ

(19)


=ᇱݎ minusೖ

ೖ∙ (20)



௧భ(21)





Resolution



Delays


Delay and Multipath











RAD

XTK

ATK

Rs

Ru

LOS




∆= 4031ா

మ(23)


∆= 0162ி∙ாೡ

(24)


ܨ = 1 + 274 ∙ 10(96 minus ଷ(ܧ (25)



ቃ( (ݕ (26)

ܦܫ = )ܥܦ ℎݐ) (27)



ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)



ಽమቁଶ

minus 1൨ଵ

(29)

where


మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)




90 23 02

30 46 04

10 130 12

5 260 23


ܦ = ܦܪ + ܦ (31)






DirectSignal

MultipathSignal

GNSS Antenna





23 UERE Vector




20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6













































































































(ݐ) = ݐ) ݐminus

) times (3)



ݐ=ݐ + ݐ (4)

ݐ ݐ= + ݐ (5)




(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (6)

Therefore

(ݐ) = ߩ


(ݐ) + (ݐ) +

(ݐ) + (ݐ) ߝ+ (7)

where ܫ(ݐ) and k











⎩⎪⎨

⎪⎧





(9)


O

hRe

(xk yk zk)

(x2 y2 z2)

(x3 y3 z3)

XE YE

ZE

(x4 y4 z4)

(x1 y1 z1)

GreenwitchMeridian

Equator

North Pole





(i = 1 2 3 4)


ቀ௨௨

ቁ∆ݑ + ቀ

௩௩

ቁ∆ݒ + ቀ

௪௪

ቁ∆ݓ + ∆ = ∆ (11)

(i = 1 2 3 4)





ߔ


+ ఃܫ (ݐ) minus

(ݐ)

+ ః (ݐ) + ః (ݐ) +

(ݐ) + ఃߝ (12)


is the







ߔ( ) = (ݐ)ߔ minus )ߔ ) (13)





(14)

Therefore


൰ (15)


ௗ௧ถ

timesఘಲ(௧)

+⋯ (16)


+⋯ (17)

and finally

ߔ( ) = )ߔ ) minus


(18)


emitted signal







=

ଵାᇲ

(19)


=ᇱݎ minusೖ

ೖ∙ (20)



௧భ(21)





Resolution



Delays


Delay and Multipath











RAD

XTK

ATK

Rs

Ru

LOS




∆= 4031ா

మ(23)


∆= 0162ி∙ாೡ

(24)


ܨ = 1 + 274 ∙ 10(96 minus ଷ(ܧ (25)



ቃ( (ݕ (26)

ܦܫ = )ܥܦ ℎݐ) (27)



ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)



ಽమቁଶ

minus 1൨ଵ

(29)

where


మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)




90 23 02

30 46 04

10 130 12

5 260 23


ܦ = ܦܪ + ܦ (31)






DirectSignal

MultipathSignal

GNSS Antenna





23 UERE Vector




20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6













































































































ߔ


+ ఃܫ (ݐ) minus

(ݐ)

+ ః (ݐ) + ః (ݐ) +

(ݐ) + ఃߝ (12)


is the







ߔ( ) = (ݐ)ߔ minus )ߔ ) (13)





(14)

Therefore


൰ (15)


ௗ௧ถ

timesఘಲ(௧)

+⋯ (16)


+⋯ (17)

and finally

ߔ( ) = )ߔ ) minus


(18)


emitted signal







=

ଵାᇲ

(19)


=ᇱݎ minusೖ

ೖ∙ (20)



௧భ(21)





Resolution



Delays


Delay and Multipath











RAD

XTK

ATK

Rs

Ru

LOS




∆= 4031ா

మ(23)


∆= 0162ி∙ாೡ

(24)


ܨ = 1 + 274 ∙ 10(96 minus ଷ(ܧ (25)



ቃ( (ݕ (26)

ܦܫ = )ܥܦ ℎݐ) (27)



ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)



ಽమቁଶ

minus 1൨ଵ

(29)

where


మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)




90 23 02

30 46 04

10 130 12

5 260 23


ܦ = ܦܪ + ܦ (31)






DirectSignal

MultipathSignal

GNSS Antenna





23 UERE Vector




20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6















































































































RAD

XTK

ATK

Rs

Ru

LOS




∆= 4031ா

మ(23)


∆= 0162ி∙ாೡ

(24)


ܨ = 1 + 274 ∙ 10(96 minus ଷ(ܧ (25)



ቃ( (ݕ (26)

ܦܫ = )ܥܦ ℎݐ) (27)



ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)



ಽమቁଶ

minus 1൨ଵ

(29)

where


మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)




90 23 02

30 46 04

10 130 12

5 260 23


ܦ = ܦܪ + ܦ (31)






DirectSignal

MultipathSignal

GNSS Antenna





23 UERE Vector




20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6











































































































ܦܫ = [1 + 16(053 minus ܦܫ[)ଷܧ (28)



ಽమቁଶ

minus 1൨ଵ

(29)

where


మቀଵ

ಽమమ minus

ଵ

ಽభమ ቁ (30)




90 23 02

30 46 04

10 130 12

5 260 23


ܦ = ܦܪ + ܦ (31)






DirectSignal

MultipathSignal

GNSS Antenna





23 UERE Vector




20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6












































































































20 4 6 8 10 12 14 16 18

Not to scale

100

200

300

400

Extended Operations

Normal Operations

UE

RE

(95

)m



24 DOP Factors



൦

߂ ଵ

߂ ଶ

߂ ଷ

߂ ସ

൪= ൦


൪൦

ݑ߂ݒ߂ݓ߂߂

൪+൦


൪ (33)






ZeroAOD

MaxAOD in

NOP

145Day

AOD

Space

Clock Stability





00

31

00

00

10

89

31

00

20

10

257

31

00

204

10

Control







20

00

08

98-196

45

10

20

67

08

98-196

45

10

20

206

12

98-196

45

10

User




Multipath


NA

39

29

24

10

NA

39

29

24

10

NA

39

29

24

10


170-241

388



Freq Rr

ImprovedSpecSingle

Freq Rr

ModernSingle

Freq Rr

ModernDualFreqRr

IonosphericDelay


TroposphericDelay



29 20 20 04



UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6










































































































UEE [m] 95 55 46 45 16

















Operations








volume


than 6 hours each






=ݎ +ҧݔܤ Є (34)






= ߪଶܥ (36)



௫ܥ = ܤ)] ܤଵ(ܤ ܥ[ ܤ)] ܤଵ(ܤ ] (37)


ଵ(38)



ܥ = ଶߪܫ (39)



ଶ (40)



ܦ = ൦


൪ (41)


ܦ ௗ = ඥݎ ௗܦ ( = 1 2 3 4) (42)


௫ܥ =

⎣⎢⎢⎢⎡௨ߪ

ଶ ௨௩ߪ ௨௪ߪ ௨ߪ௩௨ߪ ௩ߪ

ଶ ௩௪ߪ ௩ߪ௪௨ߪ ௪௩ߪ ௪ߪ

ଶ ௪ߪߪ ௨ ߪ ௩ ߪ ௪ ߪ ଶ⎦

⎥⎥⎥⎤

(43)


തതതതܥ =

⎣⎢⎢⎡ேߪ




⎥⎥⎤

(44)





ଷܧܧ = ߪ ߪ= ܦ (47)


ܧܧ = ߪ ߪ= ܦ (49)






ܦܩ

=1

ߪඥߪே


ଶ + ߪ ଶ


ߪඥߪே


ଶ


ߪඥߪே

ଶ + ாߪଶ


ߪඥ ுߪ

ଶ =ுߪ

ߪ


ߪඥ ߪ ଶ =

ߪ

ߪ



1

2

3

4

5

6

7

8

9

lt 25

25-50

50-75

75-100

100-200

200-500

500-1000

1000-5000

gt 5000

lt 1ns

1ns-10ns

10ns-100ns

100ns-1ms

1ms-10ms

10ms-100ms

100ms-1ms

1ms-10ms

gt10ms


Unit Sphere

Tetrahedron

Antenna

A

B D

C



ܦ = ටଵ

ಲమ +

ଵ

ಳమ +

ଵ

మ +

ଵ

ವమ (50)


D

A

B

C

A

S1

S2

S3

ܦ ൌS1+S2+S3+S4





=

ସ( ସ)(51)












FTE

TSENSE











TYPE OFOPERATION

HORVERTACCURACY




En RouteContinental






App10 s 40m50 m


App6 s 40m20m


App6 s 40m10m





099 to 099999



1 s 155m53m
















Antenna Gain (dB)

Elevation



ா =


ே (52)





32 GNSS Signal



where











SV Block


Signal Power

L1 -1615 dBW -1585 dBW

L2 -1615 dBW -1600 dBW

C











=ܬ 10 ቂଵ


ଵ



=ఒೕ

ସగ൬10


మబ ൰ (57)

















langூrangమ(58)


(ܫ) =

Γ( )ܫ ଵ ( ூ) (59)


=ଵ

ௌరమ (60)



=

Γ( ூ)

Γ( )(61)


approximated by

௨ = 275 times ସଵଶ (62)




Weak 01 15

02 35

Moderate 03 6

04 85

05 11

06 14

Strong 07 17

08 20

09 24

10 275






(ܧ)ܣ cong


(ܧ)ܣ congଷହ

௦ா(dB)ܧݎ gt 10 (64)



ߪ = 0025ହ( ݏ ହ(ܧ (dB) (65)



= 10 ቀ1 +ೞೞ

బቁ (dB) (66)




35 Doppler Shift



ቁ ݏ (67)




Tݒ

χnrsquo

ݒ0ݒ

En

χ n

0deg

ݒ

N

90deg

180deg

270deg

S

EW

ݒ

0ݒ




ቁୡ୭ୱఞᇱ

ୱ୧୬ா(69)


χrsquo0deg

180deg

225deg

270deg

45deg

90deg

135deg

ܦͲݒ

ݒ

െݒͲܦ

315deg

ݒ

ݏݒ

ܯݒ ܦ

െܯݒ ܦ





ࢼ



= ܣଶ = ௗܣ

ଶ + ܣଶ + ܣௗܣ2 ߚݏ (70)


ା ௦ఉ(71)


=

+

-






( ) = ቐ

0 lt 2ܤminusଵ

minus 2ܤ lt lt 2ܤ

0gt 2ܤ

(73)




R

T

Reference

Reflecting SurfaceV

Sn

R image







= +timestimes







మ

మమ൰ (78)



బ(79)






మ

మమ൰ (81)



బ(82)






ܧ

10ቁ

(84)




ߪ3 = +ߪ3 ߠ le 45deg (85)




ଶ + ߠଶ +

ఏ

ଷle 15deg (86)




௧ߪ =ଷ

ଶగට

బ(1 +

ଵ





జߪ =ଷಽ

ଶగට జ

ଶ( )( )

మ

(degrees) (88)


జߪ =ଷಽௌഔ

ଶగට

( )

మ

(degrees) (89)



(rad) (90)



(rad) (91)



ఠబయ =

ௗయோௗ௧య

ቀಳ


యೃ

య

య (degrees) (92)


ிߪ3 = ௧ிߪ3 + le 14(Hz) (93)


௧ிߪ =ଵ

ଶగටସி

ேబቂ1 +

ଵ

బቃ (Hz) (94)


=ௗ

ௗ௧ቀ

ଵ

ଷఠబ

ௗோ

ௗ௧ቁ=

ଵ

ଷఠబ

ௗశభோ

ௗ௧శభ(Hz) (95)


ߪ3 = ௧ߪ3 + le (chips) (96)



మ

బቂ2(1 minus ) +

ସிమௗ

బቃ (Hz) (97)



=ೃ

ఠబ (chips) (98)



௦ௗ(ܥ) = (ܥ)]ݔ ி(ܥ) ](99)(ܥ)


4 GNSS Augmentation




Corrections

DataLink

DGNSS Reference

Receiver


Data link

GNSS


Receiver








minus

= ߩ

minus ߩ


+ minus

+ Δߝ (104)

where



code delays





1

2

3

4




minus

minus

minus

= ߩ

minus ߩ

minus ߩ

minus ߩ

+

(105)

where




ߪ = ඥߪଶ + ߪ

ଶ + ߪଶ + ߪ

ଶ = ߪ2 (106)





Φ ( ) = Φ

( ) minusΦ( ) (107)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(108)


- and

ߩ (ݐ) = ߩ

(ݐ) - ߩ(ݐ)


Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(109)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(110)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(111)

Φ ( ) = ቀ

ቁ∙ ߩ

(ݐ) +Φ ( ) minus

(112)


Φ ( ) = Φ

( ) minusΦ ( ) (113)

which simplifies to

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(114)

where

=





and

Φ ( ) = ቀ

ቁߩ

(ݐ) minus

(115)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (116)

Φ ( ) = ቀ

ቁߩ

(ݐ) minus (117)


Φ

+Φ

+Φ

+Φ

+

Φ

+Φ

+Φ

ଵଵ +

Φ

ଶଶ +

Φ

ଷଷ +

Φ

ܥ⋯+ܥ =








[sec]

LF (30 - 300 kHz) gt 700 lt 20


HF ( 3 MHz - 25 MHz) lt 200 5


lt 100 lt 5




421 DGNSS Accuracy




Ephemeris Error





Multipath




GPS CA code)1 - 5 m


P code)01 - 1 m



resolvedlt 2 cm







Troposphere 3 - 4 1

Satellite Clock 3 0

Multipath 2 2

Receiver Noise 2 2




1000 NM

Space Segment


Control Segment


0 03 15 3

Propagation Errors

Ionosphere (ft)

Troposphere (ft)

0

0

72

6

16

6

21

6

TOTAL (RMS) 0 94 17 22

User Segment

Receiver Noise (ft)

Multipath (ft)

3

0

3

0

3

0

3

0

UERE (ft RMS) 3 98 174 222






































Regional)

Block andOrbit

Satellites Signals

GPS


IIR-M(MEO)







GLONASS

MEO Out ofservice

L1L2 SF and L1OF







BeiDou-1MEO 4


B1

BeiDou-2

MEO 6 B1-2 B2 B3

IGSO 8 B1-2 B2 B3

GEO 6 B1-2 B2 B3

BeiDou-3



QZSSI (GEO andIGSO)







applications) [99]









The accuracy limits
















(a) (b) (c)










ାФାଵ + (121)




ାଵା = ାଵ


















SBAS

GBAS














VAL

VPL

HAL

HPL






Alert Limit

Protection Level

A B C

D E F



















AFI

SNAS

MAS




















0 03 00084

1 06 00333

2 09 00749

3 120 01331

4 15 02079

5 18 02994

6 21 04075

7 24 05322

8 27 06735

9 30 08315

10 36 11974

11 45 18709

12 60 33260

13 150 207870

14 450 1870826


Local TangentPlane

EarthEllipsoid

Pierce Pointpp pp

Directionto SV

Re

hl

Useru u

E

IonosphereEarth

Centre

pp



= sinଵ൫௨ ௨൯ሾሿ(119)ܣ





IPP is given by



Otherwise




=గ


ோ




ଶସୀଵ (123)


ଶଷୀଵ (124)



ઢܘܘ ൌ ܘܘെ

ઢܘܘ =


Userrsquos IPP

ઢܘܘ ൌ ܘܘെ

ઢܘܘ =

െܘܘ

(ܘܘǡܘܘሺܘܘ

Userrsquos IPP





σூோாଶ = ܨ

ଶ ∙ σூாଶ (125)



ோାቁଶ

൨భ

మ

(126)






Class Description

Class 1




Class 2





Class 3




Class 4




Beta-1 2 or -3




௧ߪଶ = [൫ߪோா൯∙ ߜ) (ܧܦ + 8]ଶ [m] (132)





Indicator

0 1

1 11

2 125

3 15

4 2

5 3

6 4

7 5

8 6

9 8

10 10

11 20

12 30

13 40

14 50

15 100


ܥ = (127)


ܧ =ோ

ట=




0 0 0 ⎦ସସܧ⎥⎥⎤

(128)


δUDRE = ඥ(ܫ ∙ ܥ ∙ (ܫ + ߝ (129)


ߝ ௩ܥ= ∙ y (130)



ଶ ) of a model


௧ߪଶ =



ଶ + ε୪୲ୡଶ + ε

ଶ if RSSୈ = 1(131)

where









ߪଶ = ௧ߪ


ଶ + ௧ߪଶ (132)


ߪଶ = 25mଶ (133)


ߪ = ௦ேௌௌߪ)ଶ [ ] + ߪ ௨௧௧

ଶ [ ] + ௗ௩ߪଶ [ ])ଵ ଶfrasl (134)


S = ൦





൪

= ܩ) ∙ ∙ ଵ(ܩ ∙ ܩ ∙ (135)



= ൦


൪ (136)





ௌௌܮ ൌ ܭ (139)

where

ଶ = sum ǡݏ

ଶ ߪଶ

୧ୀ (140)


ௌௌܮܪ =



where


మ

ଶ+ ට(

ௗೞమ ௗ

మ

ଶ)ଶ ாே

ଶ (142)


ଶ ߪଶ

୧ୀ ݒ (143)


ଶ ߪଶ

୧ୀ (144)


ଶ୧ୀ (145)





















GBAS-related data


approach















95LatNSE

95VertNSE


Timeto

Alert



designation)


designation)


D 5 m 29 m 10-915 s (vert)30 s (lat)



E 5 m 29 m 10-915 s (vert)30 s (lat)


F 5 m 29 m 10-915 s (vert)30 s (lat)











Plan view

LTPFTP


15 NM plusmn10ordm

20 NM


GPIP


FPAP

03-045

FPAP
















ߪଶ = ߪ

ଶ + ௧ߪଶ + ߪ

ଶ + ߪଶ (146)



ߪଶ = ௩ߪ

ଶ (ߠ) + ߪ ௨௧௧ଶ (ߠ) (147)




೩

బ) (148)


ߪ = ݔ)௩௧__ௗ௧ߪܨ + 2 (ݒ (149)




ெ+ ( ଶ)ଶ (150)


(ߠ)௩ߪ = + ଵ(ఏ ఏబfrasl ) (151)


ߪ ௨௧௧ [i] = ൫013 + 053(ఏ ଵfrasl )൯[m] (152)

For AMD type B

ߪ ௨௧௧ [i] =


ଶ[m] (153)







model is given by

ுଵߪଶ =

ܯ


ଶ

ߪ+ଶ + ௦ߪ

ଶ (154)



ୀଵ (155)






ܮ = หܤ௩௧ห+ ܭ ௗߪ௩௧ுଵ (158)


B௩௧ = sum ܤ௩௧ݏேୀଵ (159)


ଶ ுଵߪଶே

ୀଵ (160)



ୀଵ (161)





where



ଶ ுଵߪଶே

ୀଵ (165)





ୀଵ (168)



ୀଵ (170)





ଶఙ_మ

(ெ ଵ)

ேୀଵ (172)


ଶఙ_మ

(ெ ଵ)

ேୀଵ (173)



























RAIM Methods






=ݕ ௧௨ݔܩ + Є (174)







=ොݕ ොݔܪ (176)




ܧ = ݓ ݓ (178)



ොݔ⋯൩=

ܪଵ(ܪܪ)

⋯

൩[ݕ] (179)


= ݓ (180)

= (181)

= ݓ ݓ = ܧ (182)



௪ మ



(ܥ|ܣܨ) = ݓ) gt (ܥ| =

ଵ


మ)int )ݏ

షర

మଵ)

షೞ

మݏஶ


(184)













∆T = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆T୴୭୧ (185)

where



the FPG module




∆Tେ = ∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲+ ∆Tେ୭ ୡ୲ (186)

where



module



∆Tୈ ୲ ୡ୲+ ∆T ୮୭୲le TTW (187)


∆Tେ = ∆T ୧ୡ୲+ ∆Tେ ୮୭୲+ ∆Tୟ୪୷େ୭ ୡ୲ (188)



(a) (b)














ACCURACY

INTEGRITY

AVAILABILTY

CONTINUITY












En Route NA 3704 m

Terminal NA 1852 m

LNAV orLNAVVNAV

ApproachNA 556 m


FAWP)50 m 556 m


LPV II 35 m 40 m




IntendedGSL



A --- FASVAL

B --- FASVAL

C Hle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335

DEF Hle100 FASVAL

100ltHle200 FASVAL

200ltHle1340 002925H(ft)+ FASVAL-585

Hgt1340 FASVAL+3335



IntendedGSL



AB --- FASLAL


FASLAL

873ltDle7500 00044D(m)+ FASLAL-385

Dgt7500 FASLAL+2915


FASLAL

291ltDle873 003952D(m)+ FASLAL-115

873ltDle7500 00044D(m)+ FASLAL+1915

Dgt7500 FASLAL+5215


GSL FASVAL FASLAL

ABC le10 m le40 m

ABCD le10 m le17 m

ABCDE le10 m le17 m





































References


















































87942-235-6










































































































Documents

Global navigation satellite systems performance analysis