IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

Enhanced Precise Point Positioning for GNSS UsersJ. M. Juan, M. Hernández-Pajares, J. Sanz, P. Ramos-Bosch, A. Aragón-Àngel, R. Orús,

W. Ochieng, S. Feng, M. Jofre, P. Coutinho, J. Samson, and M. Tossaint

Abstract—This paper summarizes the main results obtainedduring the development of an Enhanced Precise Point Positioning(EPPP) Global Navigation Satellite Systems multifrequency useralgorithm. The main innovations include the application of preciseionospheric corrections to facilitate the resolution of undifferencedcarrier phase ambiguities, ambiguity validation, and integritymonitoring. The performance of the EPPP algorithm in terms ofaccuracy, convergence time, and integrity is demonstrated withactual GPS and simulated Galileo data. This can be achieved withvery limited bandwidth requirements for EPPP users (less than300 b/s for dual-frequency GPS data).

Index Terms—Global Navigation Satellite Systems (GNSS), highprecise positioning, integrity monitoring, Precise Point Positioning(PPP), real-time ionospheric corrections.

I. INTRODUCTION

PRECISE point Positioning is typically considered as thetechnique that allows a dual-frequency GPS user to deter-

mine a position at the decimeter error level (kinematic mode)and centimeter error level (static mode) with a single receiver.This is based on the real-time availability of satellite products(GPS orbits and clocks) that, by using data from a network ofpermanent GPS receivers and better modeling, are significantlymore precise than those computed by the GPS control segment.Another important characteristic of the classical PPP user al-gorithm is the usage of the ionospheric-free combinations ofobservables to remove more than 99.9% of the slant ionosphericdelay. These main observables, ionospheric-free carrier phases,and code observations for all of the satellites in view must bemodeled by the user in a precise way by correcting the depen-dencies that are relevant at the centimeter level and estimating,

Manuscript received May 16, 2011; revised October 21, 2011 and December12, 2011; accepted February 12, 2012. This work has been performed inthe context of EPPP- and PRTODTS ESA-funded projects, and it has beenpartially supported by the Spanish Ministry of Science and Innovation underthe CTM2010-21312-C03-02 project.

J. M. Juan, M. Hernández-Pajares, J. Sanz, P. Ramos-Bosch, A. Aragón-Àngel, and R. Orús were part of the Research Group of Astronomy and Geo-matics at the Technical University of Catalonia (gAGE/UPC) while the projectdevelopment, 08034 Barcelona, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

W. Ochieng and S. Feng are with the Engineering Geomatics Group(ICEGG) at Imperial College London, South Kensington, SW7 2AZ London,U.K. (e-mail: [email protected]; [email protected]).

M. Jofre and P. Coutinho are with the Aerospace Technological Centerin Catalonia (CTAE), 08840 Viladecans, Spain (e-mail: [email protected];[email protected]).

J. Samson and M. Tossaint are with the European Space Agency (ESTEC/ESA), 2200 AG Noordwijk, The Netherlands (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2012.2189888

in a navigation filter, the remaining relevant unknowns (such asthe phase ambiguities and zenith tropospheric delay, togetherwith the 3-D position and receiver clock error).

In this context, recent related developments in the researchfields of GPS precise positioning and the modernization ofGlobal Navigation Satellite Systems (GNSS) open the possi-bility of significantly improving the PPP technique. This paperexploits these developments to propose an Enhanced PrecisePoint Positioning (EPPP) concept including a user algorithm.Specifically, the paper considers 1) the resolution of undiffer-enced ambiguities by explicitly accounting for UncalibratedHardware Delays, thereby enabling ambiguity fixing [1]–[4];2) the feasibility and impact of providing accurate ionosphericdelay values as an additional product of the wide area networkof permanent receivers, such as the Ranging and IntegrityMonitoring Stations (RIMS) of the European EGNOS system,to support High Precise Positioning Services (in a similar wayas that in [5], [6]); and 3) the use of the modernized GPS and up-coming Galileo, to not only augment the number of transmitterswith the associated redundancy and geometry improvementsbut also improve the measurement/observable precision, dueto the new kind of signals provided over a larger number offrequencies. These new signals have a potentially positive effectof improving the convergence time, position accuracy, integrity,continuity, and availability. Note that recent results ([7]) suggestthat it may be feasible to provide reliable integrity monitoringin high-precision GNSS positioning.

The following sections briefly describe the implementationof the suggested improvements, from algorithm specificationsto the associated user performance evaluations using actualGPS and simulated Galileo user data.

II. WAYS OF IMPROVING PPP

A. Basic PPP Algorithms

For a given moving receiver “k,” the basic PPP user algo-rithm consists of the accurate estimation of its position �rk andclock error dtk from the accurate predicted GNSS position ofeach transmitter (satellite) �ri and real-time clock corrections dti

for i = 1 . . . Ns, where Ns is the number of satellites in view.This can be performed by means of dual-frequency mea-

surements that allow the removal of the first-order ionosphericdelay through the ionospheric-free carrier phase Lc and codePc observables, defined as:

Lc =f21L1 − f2

2L2

f21 − f2

2

Pc =f21P1 − f2

2P2

f21 − f2

2

. (1)

0196-2892/$31.00 © 2012 IEEE


2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

In this way, given the moving receiver k, the correspondingsystem of observation equations can be solved for the set oftransmitters in view i = 1 . . . Ns:

(Lc)ik + cdti − (ρ0)

ik = − (ρ̂0)

ik · [�rk − �r0,k] + cdtk +M i

k

· δTk + (Bc)ik + λnwk + ε (2)

(Pc)ik + cdti − (ρ0)

ik = − (ρ̂0)

ik · [�rk − �r0,k] + cdtk

+M ik · δTk + ε′ (3)

where t is the time of reception, c is the speed of light invacuum, ρ0 is the modeled range considering an initial ap-proximate position �r0,k of the receiver k, ρ̂0 is the corre-sponding unit length vector along the direction pointing theGNSS transmitter i from its approximate position, M andδT are, respectively, the tropospheric mapping and residualvertical tropospheric delay (remaining after accounting for thea priori hydrostatic value included in ρ0), and w is the un-modeled user wind-up (due to the relative transmitter-receiverrotation taken into account in ρ0), where λn = c/(f1 + f2).Finally, Bc is the ionospheric-free carrier phase ambiguity inlength units, and ε and ε′ represent, respectively, the phaseand pseudorange measurement errors associated with thermalnoise and multipath. The transmitter’s wind-up can be eas-ily modeled, and subtracted from the measurements, and thereceiver’s windup (wk) can also be corrected for receiverswith a known attitude (for instance, a fixed site, such as thesamples presented in this paper),1 which can thus be eliminatedas unknowns.

At each epoch t, with Ns satellites in view, the system of 2 ∗Ns equations (for both the ionospheric-free carrier phase andcode measurements) with Ns+ 5 unknowns (Ns ambiguities+ 3 coordinates + 1 receiver clock bias + residual troposphere)can be solved by applying a Kalman filter and the following.

i) The user position and clock (�rk, dtk) can be treated aswhite noise.

ii) The residual (“wet”) tropospheric delay can be treated asa random walk process.

iii) The ionospheric free carrier phase ambiguity Bc is esti-mated as a random variable (“constant parameter”), withthe exception of the occurrence of cycle-slip events. Insuch a case, Bc is treated as a white noise process.

The main advantage of the basic PPP approach is its sim-plicity and the associated low bandwidth message containingprecise predicted orbits such as those of IGS and real-timeclocks or satellite-clock models (similar to the clock model ofthe GPS navigation message). However, its main drawback isthe large convergence time needed by the user to get a goodestimation of Bc, which can last the greater part of 1 h or morebefore achieving a high accuracy performance at the level of1–2 decimeters of position accuracy.

1For rovers with an unknown attitude, it is possible to estimate the wind-up and, consequently, its attitude. This can be achieved by introducing theionospheric corrections in a similar way as that used in this paper; see, forinstance, [8].

To overcome these limitations of the basic PPP approach,the potential improvements of the following new techniques areaddressed in this paper.

1) The use of ionospheric corrections computed and broad-cast by a dedicated PPP Central Processing Facility(PPP-CPF). See Section II-B for further details.

2) The broadcast of the satellite fractional part of ambi-guities (computed at the CPF level), which allows theuser to fix the carrier phase ambiguities and improve thepositioning solution. See Section II-C for further details.

3) The use of future multiconstellation and multifrequency(more than 2) observables. See Section II-D for furtherdetails.

B. Improving the PPP Convergence Time: An AdditionalProduct, the Precise Real-Time Ionospheric Delays

When the convergence time of the basic PPP algorithmcould be improved with the availability of precise ionosphericcorrections provided by the CPF, in a similar manner as in theWARTK technique (see, for instance, [5] and [6]); this is thereason why this technique can be referred to as fast PPP. Indeed,for (1) and (2), for Lc and Pc, the user can add the followingequations from the Melbourne-Wübbena combination Lw −Pn and ionospheric phase LI , which are defined as follows:

Lw =f1L1 − f2L2

f1 − f2(4)

Pn =f1P1 + f2P2

f1 + f2

LI =L1 − L2 (5)

and can be modeled at the time of reception t for transmitteri and receiver k (using the same notation as in (1) and (2)) asfollows:

(Lw)ik − (Pn)

ik +

λwλn

λ1λ2Di =(Bw)

ik − λwλn

λ1λ2Dk (6)

(LI)ik − Si

k =λ1λ2

λwλn(Bw −Bc)

ik (7)

where S is the user slant ionospheric delay computed from theionospheric model provided by the PPP CPF together with thesatellite interfrequency delay code biases, subtracting them forboth frequency number 2 and frequency number 1: (D)ik ≡(D2)

ik − (D1)

ik.

The improvement to the classic PPP proposed in this paper-work consists of using (2) and (3) (classic PPP equations) with(6) and (7). In this way (from the last two equations, (6) and(7)), the Bc can be estimated along with the additional parame-ters Bw and receiver DCBs Dk, in a geometric and ionospheric-free way. This is possible due to the reduced noise of the Pn

observable, which is several times lower than the noise of Pc.Once we know Bw very precisely, and considering that the useris receiving precise values of the slant ionospheric delay Si

k

(at the level of a few centimeters), then the ionospheric-freeambiguity Bc can be determined very rapidly by means of (7).This strategy can be particularly useful to accelerate the high


JUAN et al.: ENHANCED PRECISE POINT POSITIONING FOR GNSS USERS 3

Fig. 1. Fractional part of ambiguities for GPS satellite PRN19. The wide laneis shown in blue and the L1 in red. The figure has been extracted from [9] usingthe CPF over a global network as mentioned below in Section III. The verticalaxis is in cycles and the horizontal axis in seconds in a day. The pattern in thefigure is due to the correlations with the other parameters in the filter, mainlythe satellite clocks.

accuracy positioning convergence time under the availabilityof a precise CPF ionospheric model (achievable in the well-covered midlatitude regions, such as Europe, and a networksuch as the RIMSs permanent GNSS receivers) and in theabsence of strong code multipath. Notice that there is no needfor ambiguity fixing, despite the fact that ambiguity fixing helpsto additionally improve performance.

C. Improving the PPP Accuracy: Fixing CarrierPhase Ambiguities

One of the important conditions for GNSS precise position-ing, in both postprocessing and real-time conditions, is the inte-ger nature of the double-differenced carrier phase ambiguities,(BX)i,jk,l, expressed in cycles:

(BX)i,jk,l = λX(NX)i,jk,l. (8)

The two pairs of GNSS transmitters and receivers, i, j, k, l,respectively, are involved in the double differences, and λX isthe wavelength for the corresponding carrier phase at frequency(or combination) X.

With a good enough knowledge of its floated estimation, itcan be fixed resulting in further improvement in performance.In this sense, it is easy to show that the condition of theinteger double-difference ambiguity is equivalent to express theundifferenced ambiguity in terms of an integer value ((NX)ik)and two “fractional parts,” depending on the GNSS transmitterand GNSS receiver ([1], [8]):

(BX)ik = λX(NX)ik + δBX,k + δBiX (9)

where δBX is the fractional part of the ambiguity, split into atransmitter (i) and receiver (k) term, which are typically stable,at least during times that are significantly larger than the typicalcorrection latencies for the user (see, for instance, Fig. 1 or[1]). The problem in their estimation process for the short

wavelength carrier phases (such as L1) is their correlation withthe estimation of the clocks.2 For this reason, some researchersinclude these fractional terms as parts of the clocks ([2]). How-ever, on the one hand, this redefinition of phase clocks makesthem incompatible with the pseudorange clocks, while, on theother hand, the inclusion of the fractional part of the ambiguityinto the phase clock impedes the comparison between differentcomputations among analysis centers (so it is still an open issuein the IGS Analysis Centers comparison). It can be shown (seean example in Fig. 1) that its estimation is stable enough insuch a way that the CPF can broadcast the fractional terms ofthe ambiguities, with a refresh time of up to several minutes anda corresponding saving in the CPF for user bandwidth. In sucha way, any user can apply the following relationship:

(BX)ik − δBiX = λX(NX)ik + δBX,k (10)

and consequently, from the single difference between satellites,the exact value of the single differences of NX can be known(it must be an integer). Introducing this value as a constraintimproves the positioning solution.

The feasibility and characterization of these approaches, interms of accuracy and integrity in particular, are shown in thefollowing section.

D. Improving Both Accuracy and Convergence:Multiconstellation and Multifrequency Scenario

One of the bases of the presented method is the fast res-olution of Bw by means of (6). However, although Pn isless noisy than other combinations and the wide lane combi-nation’s wavelength is quite large (approximately 86 cm forGPS frequencies), several minutes are required to achieve aconfident value of Bw that can fix it. The availability of triplefrequency carrier phase measurements offers the advantages ofan easier extra-wide lane and a wide lane ambiguity estimation(see, for instance, [5]), which in the case of the availability ofprecise ionospheric corrections, would contribute significantlyto the quick convergence of precise positioning (typically fromseveral minutes with two-frequency GNSS systems to a single-epoch three-frequency GNSS systems).

E. Integrity Monitoring for Precise Positioning

As described earlier, the proposed EPPP user algorithmincorporates the new approach for fixing the zero-differencedambiguities for increased accuracy and reduces convergencetime facilitated by the exploitation of precise ionosphericcorrections. Furthermore, an innovative approach to monitorthe quality and integrity of the PPP process has been devel-oped. This approach involves the incorporation of ambiguityvalidation3 (depending on the PPP mode) into the integrity

2If no ionospheric model is considered, i.e., not using Equation (7), the onlyway to distinguish the fractional part of Bc from clocks is by using equation Pc,which is quite noisy and consequently, its weight in the system equations willbe small.

3One has to take into account that one wrong ambiguity fixing will propagateforward by the Kalman filter, so it is important to detect this wrong fixing assoon as possible.



Fig. 2. Diagram showing the top-level design of the Enhanced PPP position-ing software.

monitoring process, which also includes Carrier phase ReceiverAutonomous Integrity Monitoring (CRAIM) (Fig. 2).

The ambiguity validation method uses the conventional teststatistic for ratio testing together with a doubly noncentral F dis-tribution to compute the level of confidence of the ambiguities([10]). Specifically, this is determined as a function of geometryand the ambiguity residuals from least-squares-based ambigu-ity resolution algorithms including Least-squares AMBiguityDecorrelation Adjustment (LAMBDA). The technique has theimportant benefit of facilitating early detection of any potentialthreat to the position solution originating in the ambiguity spacewhile giving overall protection in the position domain based onthe required navigation performance. This integrity monitoringprocess is particularly important (safety/commercial/liability)for critical mission applications.

III. DATA SETS AND COMPUTATIONS

In line with the main EPPP study goals, the approach adoptedto test the EPPP algorithms concentrates a significant part ofthe effort on the user side. Accordingly, the actual and signal-simulated data used mainly correspond to the user receiversby using different products. However, the different products(e.g., satellite clocks, orbits, and ionospheric corrections) havebeen generated either from additional permanent stations (in thecase of actual GPS data) or by assuming certain characteristicdistributions of errors from the true values (in the case ofsimulated data). A main requirement for the simulated datascenarios is to be as close as possible to the main scenarios withactual data.

A. Generation of Scenarios for Actual GPS Data

For actual GPS data, static receivers are treated as rovingusers. This constitutes the main test program due to its versatil-ity. Indeed, it has the advantages that 1) a very good referenceposition for each “rover” can be obtained in postprocess withmillimeter/centimeter level accuracy, and 2) there are plentyof such receivers distributed worldwide, for example, in theIGS network. These advantages enable tests to be conducted toquantify the influence of the distribution of satellites in view,

the performance with respect to the distance to the nearestCPF receiver, ionospheric conditions, among other potentialeffects.

Although the EPPP Central Processing Facility is not themain focus of this paper, it is vital for actual data scenariosin which the new EPPP approaches are to be studied (asopposed to the classical PPP strategy, in which available IGSPPP products can be used instead). The network of permanentstations for the EPPP CPF for actual data is composed oftwo distributions: a sparse one (∼30 worldwide distributedGNSS receivers) devoted to computing satellite orbit and clockcorrections; and another set of stations over Europe to computemore accurate ionospheric corrections. In the context of theESA-funded project PRTODTS, an assessment of the differentcomponents of the corrections/message has been determined inreal-time conditions.

The main conclusion of such an assessment, based on actualGNSS data, is that it is possible to achieve for a global service,in real time, satellite orbits, and clocks with an accuracy of fewcentimeters jointly with the stabilized satellite fractional part ofambiguities (see, for instance, Fig. 1) and, for a regional service,satellite DCBs and range. In this sense, the corrections to betransmitted to the user are as follows.

– Satellite clocks with an update time of few seconds,– Satellite orbit correction parameters with an update time

of few minutes,– Satellite fractional part of ambiguities with an update

time of few minutes,– Satellite DCBs also with an update time of few minutes,– and, ionospheric model parameters with an update time

of few minutes.

Considering these update times and the required resolution,it can be deduced that the bandwidth requirement is very low:less than 300 b/s for a single constellation GPS single user.

A first example of the feasibility of EPPP based on actualGPS data is shown in Fig. 3, which summarizes the resultsobtained for users MLVL, EUSK and EIJS (at 252, 170 and94 km far, respectively, from the nearest reference receiverBRUS). In this example, the full user state was reset every 2 hto better characterize the convergence process, and the positionerror RMS of the resulting 12 time windows is depicted.The horizontal and vertical errors are shown (left- and right-hand side, respectively) demonstrating the advantage of usingprecise, real-time ionospheric corrections to speed-up the PPPconvergence (Fast PPP). It can be seen that the convergencetime (to achieve, for instance, a 10-cm error level) is reducedfrom about 1 h (without ionospheric corrections) to a fewminutes.

B. Generation of Scenarios for Signal-Simulated GNSS Data

As stated earlier, the characterization of the potential im-provements in PPP, including a multiconstellation scenario, atthe user level is the main purpose of this paper. To do this,a set of signal-simulated scenarios were generated using thehardware setup indicated in Fig. 4. This requires significant



Fig. 3. RMS of the positioning error for the horizontal component (left) andvertical component (right). The classical PPP for the rovers MLVL (red), EUSK(green) and EIJS (blues) is compared with the fast PPP for MLVL (violet),EUSK (light blue) and EIJS (brown).

Fig. 4. Hardware setup at ESTEC GNSS laboratory.

resources particularly due to the fact that the measurementsmust be taken in “serial” mode (one user at a time) versus the“parallel” mode (all of the users gathering observations fromthe satellites in view simultaneously) in the actual scenarios.

As shown in Fig. 4, the hardware setup consists of thefollowing.

1) A GNSS signal simulator (SPIRENT), which, from usercoordinates and a GNSS constellation, generates a set ofGNSS signals able to be gathered by any actual GNSSreceiver.

2) A set of actual receivers, which gather in parallel theGNSS signal from the simulator (all corresponding to thesame user simulated in the signal simulator). In Fig. 4,the working frequencies of each receiver are depicted.In this way, data from a user but gathered from threedifferent receivers can be acquired.

A static user (NPLD, at 400 km from the nearest reference re-ceiver) has been treated as the roving one. A typical simulationtime of 3 h has been used for the rovers (three times the typicalconvergence time in standard PPP). As in previous simulationsperformed in the context of other studies (see, for instance,[6]), most of the different conditions (satellite clock and orbits

Fig. 5. Dual-frequency single constellation (GPS) 3-D RMS positioning errorfor user NPLD for a signal-simulated data set gathered from Septentrio PolarX receivers without resetting the user state but with adding realistic orbital,clock, and ionospheric corrections errors (the last being very high at the end)and a low multipath user error. The following are compared: no iono, no fixingambiguities (red); no iono and fixing (green); iono and fixing (blue); iono andiono fixing with the LAMBDA method (magenta); and iono and no iono fixingwith the LAMBDA method (light blue).

quality, ionospheric and tropospheric delay and multipath) weregenerated by software, except for thermal noise, which corre-sponds to the actual data (the observations have been gatheredfrom real receivers). Several scenarios have been simulated, butto focus on the main results, we are going to only present thestudy with nominal conditions. The nominal scenario consistsof adding to the receiver measurements (carrier phase andpseudorange) the following effects: 1) a pseudorange multipatherror of few decimeters in the zenith direction and at the meterlevel at a low elevation (based on actual data), 2) a satelliteclock correction with an error of 0.1 ns, 3) from the exactpositions of the GNSS satellites, a correction error of 0.05 m inRMS, 4) Ionospheric Correction Error (after ionospheric modelcorrection) from 0.1 to 0.6 TECU (0.016 m to 0.1 m in L1/P1).Most of these error levels were based on the CPF accuraciesobtained with real data (see Section III).

IV. EPPP ACCURACY, PROTECTION LEVELS,AND CONVERGENCE TIME

In the following subsections, an assessment of the user EPPPresults is presented in two scenarios: with and without resettingthe user navigation filter. The resetting of the navigation filterstates will provide us with a characterization of the positionconvergence time.

A. Navigation Filter Results Under theSignal-Simulated Scenario

This scenario has been run without resetting the user states(i.e., its navigation filter) and only for GPS data (Fig. 5).The positioning results show very good performance, con-firming the suitability of undifferenced PPP ambiguity fixing,in addition to the expected accuracy and convergence time



Fig. 6. Similar plot to the previous one but for multifrequency (three) anddual-constellation (GPS + Galileo) data.

results. In particular, it is worth mentioning that the funda-mental role of the accurate real-time ionospheric correctionis confirmed, which allows for a very fast convergence (oneorder of magnitude faster), with a final accuracy that is onlyslightly better than that from not using such corrections (at thecentimeter error level). The corresponding analysis of the dual-constellation and three-frequency measurements is presentedin Fig. 6.

Taking into account Figs. 5 and 6, the most relevant issue foraccuracy and convergence time is the availability of the iono-spheric corrections (this is reconfirmed in the next section).

i) Without ionospheric corrections when using only GPSdata, the convergence takes about 2000 s, but using bothconstellations, the convergence is shortened by up to900 s. These results are independent of whether the am-biguities are fixed.

ii) With ionospheric corrections, the convergence takes a fewminutes with only GPS data (300 s are needed to fix Bw),while when using three frequencies, the convergence isnearly instantaneous.

iii) Without taking into account the ionospheric corrections,the final accuracy of all of the cases is at the centimeterlevel, but this accuracy is achieved faster with multicon-stellation rather than single constellation data.

B. Real-Time Positioning Results Resetting the Whole UserState Each 900 S

To better characterize the convergence time, the user nav-igation states were reset (to simulate a receiver cold start)every 900 s. Moreover, the different variants considered inthe previous sections of this paper (multiconstellation GPS +Galileo versus single GPS constellation, dual-frequency versusthree-frequencies, simple ambiguity fixing versus LAMBDAambiguity fixing) were taken into account.

In Fig. 7, the detailed 3-D positioning error in terms of theactual time is shown, showing clearly the resetting and thatthe required convergence time under a single dual-frequencyconstellation is shorter with ionospheric corrections. Among

Fig. 7. Detailed 3-D error solution, resetting every 900 s, for the maincomputation modes in the GPS-only, dual-frequency mode.

other interesting features, it can be seen that the LAMBDAmethod fails to fix some ambiguities during some periods whenno ionospheric corrections are used. The worst LAMBDA re-sults obtained during some resetting periods when ionosphericcorrections were used are related to poorer geometry (higherDOP) when this technique was applied. This is directly relatedto the LAMBDA implementation in this paper, in which thistechnique has been applied outside of the navigation filter, forthe satellites in view with their wide lane ambiguities initiallyfixed.

Finally, to summarize the performance of each processingmode, the 11 time windows (resetting every 900 s for 3 h) areshown together through its 3-D positioning RMS (see Fig. 8).In this figure, the benefits of using the three PPP improvementsproposed in this paper (i.e., ambiguity fixing, multiconstellationand ionospheric corrections; see Section II) are clearly seen.The following conclusions can be extracted:

1) Better performance is achieved when the three improve-ments proposed in this paper are simultaneously used.

2) The main factor in the convergence time is the usage ofionospheric corrections. However, if the ambiguities arenot fixed, the ionospheric model error limits the accuracyat the end of the convergence period (yellow pointsin Fig. 8).

3) The use of the ionospheric correction allows achievingthe required accuracy to be able to fix the carrier phaseambiguities. Otherwise, without ionospheric corrections,the minimum accuracy needed to fix ambiguities in the900-s windows cannot be achieved.

C. EPPP Integrity: First Glance

Integrity is the ability of a positioning service to protectagainst hazardous anomalies. For instance, the positioning ser-vice must guarantee that the probability of positioning errorsgreater than a certain value (protection levels) is small andacceptable (i.e., 10−7). In this sense, the service provider musttransmit not only the corrections but also their confidencelevels. Using this information, the user receiver computes its



Fig. 8. Three-dimensional positioning error RMS for user NPLD consideringall of the 900 s resets of the user state under nominal conditions for differentEPPP user navigation modes: standard PPP for GPS only and GPS + Galileo(red and light blue, respectively); standard PPP + undifferenced carrier phaseambiguity fixing when possible, for GPS (green) and GPS + Galileo (brown);and standard PPP + precise ionospheric corrections + associated undifferencedcarrier phase ambiguity fixing, for GPS (purple) and GPS + Galileo (blue withtriangles) (. For completeness, the results for ionospheric correction withoutambiguity fixing are also shown for GPS only (blue with stars) and GPS +Galileo (yellow).

position and the corresponding protection levels. Accordingly,integrity is a critical part of positioning, and the improvementof any solution must take into account the achieved protectionlevel.

In this section, it is shown that the protection levels (com-puted from the message) always protect the positioning errors,and in the next section, the other user level other integrityalgorithms are presented.

The motivation of this point of study was to check whetherthe very first results of integrity in the positioning domaincould be obtained for EPPP from the simulated data sets. Todo this, the same protection levels used in the more extendedintegrity study recently performed for the WARTK high precisepositioning technique (MRS project; see, for instance, [7]) havebeen used. Indeed, the vertical protection level (VPL) and hori-zontal protection level (HPL) are defined as V PL = 5.33 ∗ k ∗V Sigma and HPL = 6.2 ∗ k ∗HSigma, respectively, whereVSigma and HSigma are the corresponding vertical and hori-zontal standard deviation estimated in the filter, and k is a factorto guarantee the proper overbounding of the protection levelswith respect to the actual errors. The nominal scenario adoptedin this point, to have some minimal statistics, was to reset (every900 s) the user navigation filter under a low multipath usingsingle constellation (GPS) data for the roving user NPLD (seeFig. 7 for the reference result).

It can be seen in Figs. 9 and 10 that the integrity is alwaysmaintained (actual errors lower than protection levels), evenduring the first steps of convergence, after each reset every900 s. In particular, it can be seen that the integrity margin (pro-tection levels minus actual errors) is high for dual constellation(Fig. 9) and even higher when the ambiguities are fixed thanksto the real-time ionospheric corrections (Fig. 10).

Fig. 9. Horizontal and vertical protection levels versus the correspondinghorizontal and vertical positioning errors for a NPLD rover in the reference casewith a low multipath, resetting every 900 s, dual (GPS + Galileo) constellation,three frequency measurements, and no ionospheric corrections and no fixingambiguities.

Fig. 10. Horizontal and vertical protection levels versus the correspondinghorizontal and vertical positioning errors for NPLD rover in reference casewith low multipath, resetting every 900 s, dual (GPS + Galileo) constellation,three frequency measurements, and ionospheric corrections with wide laneambiguity fixing.

V. EPPP INTEGRITY: SENSITIVITY

TO ERRORS AND FAILURES

For EPPP, there are two main sources of potential failures:the errors in the measurements of a PPP user and those inthe messages provided to the user. The scenarios simulatedto measure the performance of the EPPP integrity algorithmswere based on the manifestation of potential failures at the userside irrespective of source. In this case, the simulated scenariosreflect all known classes of failure modes both at system anduser levels (i.e., both measurement and message errors/failuresare included).

The approach to quality and integrity mentoring developedfor EPPP involves three stages. First, outlier detection is appliedat the ionospheric slant delay interpolation stage in order todetect anomalous values, second, ambiguity validation (i.e.,



Fig. 11. Sensitivity of HPL to ionosphere errors.

ambiguity domain integrity monitoring) is carried out using theproposed approach that employs a doubly noncentral F distribu-tion based test and finally, the CRAIM method is employed inthe position domain. The technique has the important benefit offacilitating early detection of any potential threat to the positionsolution, originating in the slant ionospheric delays and the am-biguity space, while at the same time giving overall protectionin the position domain based on the required navigation perfor-mance. Since the occurrence of failures (depending on source)should in fact affect the user’s computation of the slant delaysand resolution of ambiguities, the corresponding integrity mon-itoring algorithms are designed to offer maximum protectionfrom their effects before they propagate to the position domain.Therefore, the first two stages of integrity monitoring justify theassumption of single failure in the specification and testing ofthe position domain algorithm (i.e., CRAIM). Clearly, furtherwork is required to confirm the validity of this assumption forspecific PPP applications.

This study has analyzed the sensitivity of the approach tothe integrity monitoring proposed for EPPP, including thoseof HPL determination and ambiguity validation to ionosphereerrors. Although several types of failures were simulated andsuccessfully treated by the integrity algorithm, this paperfocuses on the integrity results related to the ionosphericcorrections.

The following abbreviations are used to represent variousscenarios: G denotes GPS data only; X denotes GPS andGalileo data; ni denotes Ionospheric corrections not considered;I denotes Ionospheric corrections applied and fw denotes Widelane ambiguities are constrained and N1 ambiguities fixed withLAMBDA.

A. Sensitivity of HPL to Ionosphere Errors

Figs. 11 and 12 show the sensitivity of HPL to the iono-spheric error corrections from the CPF. The absolute values ofionospheric correction error range from 0.01 to 6.7 cm with amean of 1.4 cm. It can be seen from Fig. 11 that the HPLs forthe two cases (with and without ionospheric error corrections)are always larger than the corresponding horizontal positionerrors (HPEs) during the positioning period. This shows that theHPLs overbound the HPEs. Furthermore, as expected, the HPLfor the case without ionospheric error corrections is consistently

Fig. 12. Sensitivity of HPL to ionosphere errors.

Fig. 13. Ambiguity validation for G_I_fw scenario. The scale of the right axisrefers to the curve in the same color.

higher than in the case with ionospheric corrections. Bothfindings provide a level of confidence in the algorithm for thecomputation of the HPL.

In order to gain more confidence in the sensitivity of the HPLto ionospheric residual errors, the ratio of the effect of this errorin the position domain, i.e., the HPE to the HPL is plotted inFig. 12 for the two cases (i.e., with and without ionosphericerror corrections). The results show that for both sets the ratiosare always below 1 confirming the observation made on over-bounding above. Furthermore, as expected, the HPE/HPL ratiofor the case with ionospheric error corrections is significantlysmaller (after convergence and wide lane ambiguity fixing) thanthe case without ionospheric corrections, further demonstratingthat the HPL algorithm is sensitive to the effect of ionosphericerrors and wide lane ambiguity fixing.

B. Sensitivity of Ambiguity Validation to Ionosphere Errors

Figs. 13 and 14 each show the ratio of residuals from the bestand second best sets of ambiguities, the number of ambiguities,and the confidence level of the best set of ambiguities for thescenarios with and without ionosphere corrections. The keyparameter for ambiguity validation—the confidence level—iscalculated by using a doubly noncentral F distributions asexplained earlier. The wide lane ambiguities are constrainedwhile the N1 ambiguities are fixed with LAMBDA.



Fig. 14. Ambiguity validation for G_ni_fw scenario.

From the results in the figures above, it can be seen that theimpact of the ionospheric error corrections is a higher confi-dence level in the ambiguities, compared to the case withoutionospheric error corrections.

C. Sensitivity of Test Statistics to Failure

In order to analyze the impact of failure on integrity mon-itoring in the ambiguity and position domain, the followingerrors were simulated and injected to specific measurementsseparately:

1) A bias of one cycle is added to the L1 carrier phasemeasurements from one (random) satellite. The bias isadded to the measurements after preprocessing startingfrom the first epoch to the end. This should enable thecapability for ambiguity resolution to be tested.

2) A bias of half a cycle is added to the L1 carrier phasemeasurement from one (random) satellite. The bias isadded to the measurements after preprocessing startingfrom the first epoch to the end. This represents a poten-tial worst case for ambiguity validation. Therefore, thisshould enable the capability for ambiguity validation tobe tested.

3) Slowly growing error is added in the L1 carrier phasemeasurements of a specific satellite. The quantity of thedrift applied to the measurements accumulates to onewavelength in about 300 s. The drift starts at 100th epochand ends at 700th. This should enable the capability forearly detection algorithms to be tested.

4) Large error—In January 2004, there was a significantclock failure on SVN23. The average clock accelerationwas estimated at 1.88 × 10–11 s/s2. This is applied toP1 measurements of one satellite, starting from the 100thepoch to the 700th. This should confirm the capability forintegrity algorithms to deal with gross errors.

5) Critical error—The critical bias in any measurement re-sults in the test statistic being very close to the threshold,thus presenting a challenge for failure detection.

Fig. 15 is an example of the results of the test statisticsfor the first case. It can be seen that the integrity algorithmdoes not detect a failure before the bias is injected. However,immediately after the injection of the bias (at 900), the integrityalgorithm detects the presence of failure and raises an integrity

Fig. 15. Test statistics and thresholds for G_I_fw scenario.

flag. This flag is fed back to the positioning module for promptand appropriate action (e.g., exclusion) to be taken to mitigatethe negative impacts.

VI. CONCLUSION

In this paper, detailed results on enhanced precise pointpositioning strategies have been presented, centering on theextensive signal simulations of GPS and Galileo observationsincorporating realistic user errors that affect PPP performance(code multipath, real-time orbits, clocks, and ionospheric cor-rections). This paper includes the identified EPPP modes (PPPclassical approach, adding undifferenced ambiguity fixing andusing precise ionospheric corrections) and different related as-pects (multiconstellation versus single constellation, LAMBDAambiguity fixing method, etc.).

The main conclusions can be summarized in terms of demon-strating the central role of the precise ionospheric correc-tions to provide a centimeter-error-level accuracy with verysmall convergence times, in both the single-constellation/dual-frequency scenario and the dual-constellation/three-frequenciesscenario.

The advantage of undifferenced ambiguity fixing has beenconfirmed in line with insights of previous authors ([1]–[3]).The availability of precise ionospheric corrections is also im-portant to guarantee the right carrier phase ambiguity fixing.

Additionally, it has been confirmed that resetting the userfilter every 900 s, the positioning protection levels alwaysoverbound the actual positioning errors. The overboundingbecomes particularly large when dual-constellation, three-frequency measurements, and precise ionospheric correctionsare used.

Finally, it has been shown that the integrity monitoringalgorithms developed (including ambiguity validation) are verysensitive to failures, including ionospheric residual errors. Thisshould facilitate the use of PPP to support critical mission appli-cations. Regarding ambiguity validation, the method developedbased on doubly noncentral F-distributions is capable of gener-ating reliably the confidence level of the resolved ambiguitiesat every epoch. The application of good quality ionosphericerror corrections has been demonstrated to be crucial to theconfidence level associated with ambiguity resolution.



ACKNOWLEDGMENT

The authors acknowledge the use of IGS data and products.

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