9. Systems1 Agenda 1. Time 2. Position 3. Altitude 4. Air data 5. Components 6. Nav systems

9. Systems 1

Agenda

1. Time

2. Position

3. Altitude

4. Air data

5. Components

6. Nav systems

9. Systems 2

1. Time (1 of 2)

UTCUT1GMTLeap secondsLeap yearsGPS timeOther timesYear-month-day formatYear-week formatYear-day format

1. Time

9. Systems 3

Time (2 of 2)Time-of-day formatMidnight formatCombined-data-and-time formatUTC formatTime zonesAtomic clocksCesium atomic clocksHydrogen atomic clocksRubidium atomic clocksTime taggingTime distribution

1. Time

9. Systems 4

UTC

Universal Time Coordinated (UTC) -- Time scale based on atomic clocks

Maintained by the international bureau of weights and measurements, in Paris.-- also known as BIPM Bureau International des Poids et Mesure

Distributed by standard radio stations that broadcast time, such as WWV and WWVH.

Obtained readily from the Global Positioning System (GPS) satellites.

1. Time

9. Systems 5

UT1

Universal Time (UT1) determined by the rotation of the Earth, over which we have no control, whereas UTC is a human invention.

Highly precise clocks that keep UTC whereas UT1 is kept precisely precisely by the Earth itself.

The difference between UTC and UT1 is made available electronically and broadcasted so that navigators can obtain UT1.

1. Time

9. Systems 6

GMT

Greenwich Mean Time (GMT) refers to time kept on the Greenwich meridian, which is longitude zero

GMT is a widely used historical term, but one that has been used in several ways. Because of the ambiguity, its use is no longer recommended in technical contexts

1. Time

9. Systems 7

Leap second

By international agreement, UTC is not permitted to differ from UT1 by more than 0.9 second.

A single leap second 23:59:60 is inserted into the UTC time scale every few years to keep UTC from becoming more than 0.9 s from UT1

Leap seconds occurs on average about once every year to a year and a half.

1. Time

9. Systems 8

Leap year

Leap years are years with an additional day YYYY-02-29

• The year number is a multiple of four with the following exception:

• If a year is a multiple of 100, then it is only a leap year if it is also a multiple of 400

• For example, 1900 was not a leap year, but 2000 was one

1. Time

9. Systems 9

GPS timeGPS epoch is 0000 UT (midnight) on January 6,

1980. GPS time is not adjusted and therefore is

offset from UTC by an integer number of seconds due to the insertion of leap seconds.

The number remains constant until the next leap second occurs

This offset is in the navigation message, and GPS receivers apply the correction automatically.

GPS time was ahead of UTC by 13 seconds on January 1, 1999

1. Time

9. Systems 10

Other times

GLONASS time datum -- Moscow-based UTC. Takes at least 15 minutes to reset when UTC leap seconds change. During this time the whole system is inoperative.

International Atomic Time -- based on Cesium clocks, has no leap seconds, and in 1995 was 29 sec different from UTC

1. Time

9. Systems 11

Year-month-day format (1 of 3)

ISO 8601 date notation -- YYYY-MM-DD

• YYYY is the year

• MM is the month of the year

• DD is the day of the month Example

• Fourth day of February in the year 1995 is 1995-02-04

1. Time

9. Systems 12


Hyphens may be omitted for compactness

• Example -- 19950204Century may be omitted:

• Example -- 95-02-04 or 950204Day and/or month may be omitted

• Examples -- 1995-02 or 1995

1. Time

9. Systems 13


Advantages

• Easily handled by software Consistent with 24-hour time notation Constant length makes both data entry

and table layout easier Language independent; not confused

with other date notations Used by many countries already

1. Time

9. Systems 14

Year-week format (1 of 3)

Often required to refer to a week of a year. Week 01 of a year is

• Week that has the first Thursday equivalent to the week that contains the fourth day of January.

• May contain days from the previous yearWeek before week 01

• Last week (52 or 53) of the previous year even if it contains days from the new year.

1. Time

9. Systems 15


Week definition

• Starts with Monday as day 1

• Ends with Sunday as day 7

• Example -- the first week of the year 1997

• lasts from 1996-12-30 to 1997-01-05

• 1997-W01 or 1997W01

1. Time

9. Systems 16


Can show day of the week.

• Example -- Tuesday, 1996-12-31 is day 2 of week 1 of the first week of 1997 -- 1997-W01-2 or 1997W012

• Application -- industrial planning where many things like shift rotations are organized per week and knowing the week number and the day of the week is more handy than knowing the day of the month.

1. Time

9. Systems 17

Year-day format

ISO 8601 date notation -- YYYY-DDD

• YYYY is the year

• DDD is the day of the year Example -- the day 1995-02-04 (that is day

035 of the year 1995) is 1995-035 or 1995035

1. Time

9. Systems 18

Time-of-day format (1 of 2)

The international standard notation for the time of day is hh:mm:ss

• hh -- the number of complete hours that have passed since midnight (00-24),

• mm -- the number of complete minutes that have passed since the start of the hour (00-59)

• ss -- the number of complete seconds since the start of the minute (00-59).

• If the hour value is 24, then the minute and second values must be zero.

1. Time

9. Systems 19

Time-of-day format (2 of 2)

Example -- 23:59:59, which represents the time one second before midnight.

Separating colons can be omitted -- 235959Seconds and/or minutes can be removed --

23:59, 2359, or 23Fractions of a second can be used -- the time

5.8 ms before midnight can be written as 23:59:59.9942 or 235959.9942

1. Time

9. Systems 20

Midnight format

Every day both starts and ends with midnight 00:00 and 24:00 distinguishes the two

midnights The following two notations refer to exactly

the same point in time: 1995-02-04 24:00 = 1995-02-05 00:00

In case an unambiguous representation of time is required, 00:00 is usually the preferred notation for midnight and not 24:00.

1. Time

9. Systems 21

Combined-date-and-time format

If a date and a time are displayed on the same line, then always write the date in front of the time.

If a date and a time value are stored together in a single data field, they should be separated by a Latin capital letter T, as in 19951231T235959.

1. Time

9. Systems 22

UTC format

Without any further additions, a date and time as written above is assumed to be in some local time zone.

Z indicates UTC -- 23:59:59Z or 2359Z Z stands for the zero meridian, which goes

through Greenwich in London, and it is also commonly used in radio communication where it is pronounced "Zulu"

Civil time zones are now related to UTC, which is slightly different from the old and now unused GMT

1. Time

9. Systems 23

Time zones (1 of 2)25 integer world time zones from -12

through 0 (GMT) to +12Each zone one is 15° of longitude as

measured east and west from the prime meridian at Greenwich, England.

Time zones are centered on the 15° of longitude

1. Time

9. Systems 24

Time zones (2 of 2)In addition there are military designations.

• A-M except for I to the east

• N-Y to the west

• M and Y are 7.5 degreesCivilian time zones are superimposed upon

these. Civilian designations are typically three letter abbreviations (e.g. EST) for most time zones.

There are summer and winter time zonesNot all time zones are integer differences --

some are 0.25, 0.5, and 0.75 hour offset

1. Time

9. Systems 25

Atomic clocks (1 of 2)

There are different types of atomic clocksThe principle behind all of them is the same. Major difference is associated with the element

used and the means of detecting when the energy level changes.

1. Time

9. Systems 26

Atomic clocks (2 of 2) Atomic clocks have increased the accuracy of

time measurement about one million times in comparison with the measurements carried out by means of astronomical techniques.

New technology continues to improve performance. The most accurate laboratory cesium atomic clocks are thousands of times better than commercially produced units.

1. Time

9. Systems 27

Cesium atomic clocks (1 of 2)

Employ a beam of cesium atoms. Clock separates cesium atoms of different

energy levels by magnetic field. The most accurate atomic clocks available

today use the cesium atom and the normal magnetic fields and detectors.

In addition, the cesium atoms are stopped from zipping back and forth by laser beams, reducing small changes in frequency due to the Doppler effect.

1. Time

9. Systems 28

Cesium atomic clocks (2 of 2)

Frequency for the cesium resonance is 9,192,631,770 Hz so that when divided by this number the output is exactly 1 Hz

Long-term accuracy is better than one second in one million years.

Produced by manufacturers including Hewlett Packard and Frequency Electronics

1. Time

9. Systems 29

Hydrogen atomic clocks

Maintain hydrogen atoms at the required energy level in a container with walls of a special material so that the atoms don't lose their higher energy state too quickly.

Show a one week accuracy approximately 10 times the accuracy of cesium

1. Time

9. Systems 30

Rubidium atomic clocks

The simplest and most compact of all, use a glass cell of rubidium gas that changes its absorption of light at the optical rubidium frequency when the surrounding microwave frequency is just right.

1. Time

9. Systems 31

Time tagging

Many reasons for time tagging• performance• instrumentation • display

system recording

time of validity

time of message creation

time of message transmission

time of message receipt1. Time

9. Systems 32

Time distribution

unit 1

time

unit 2

time

unit 3

time

message sync

unit 1

time

unit 2

time

unit 3

time

message sync

hardwire sync

1. Time

9. Systems 33

2. Position

ECEFMap datumsUTM/UPS

2. Position

9. Systems 34

ECEF (1 of 8)Earth-centered, earth-fixed coordinates

(ECEF)Cartesian co-ordinate system with x, y,

and z axes mutually perpendicularZ-axis along axis of rotation with north

being positiveX-axis passing through prime meridianAxes rotate with the earth

2. Position

9. Systems 35

ECEF (2 of 8) = latitude = longitudeh = altitude above the ellipsoida = semi-major axisb = semi-minor axise = eccentricityf = flatteningRn = a/SQRT[1 - e2 sin2 ]

xn = (Rn + h) * cos cos yn = (Rn + h) * cos sin

zn = [Rn (1 - e2) + h] sin 2. Position

9. Systems 36

ECEF (3 of 8)f = 1 - b/ae2 = f (2 - f)

• = (1 -b/a) [2 - (1 + b/a)]• = (1 - b/a)( 1 + b/a)• = 1 - (b/a)2

2. Position

9. Systems 37

ECEF (4 of 8)

u

v

v/ (1 - e2)

Rn

2. Position

9. Systems 38

ECEF (5 of 8)

Definition of v’• v' = dv/du

Definition of ellipse• (u/a)2 + (v/b)2 = 1

Take derivative wrt u• 2u/a2 + 2v/b2 v' = 0

Solve for v’• v' = -(u/v) (b/a)2 • = -(u/v) (1 - e2) • = tan

2. Position

9. Systems 39

ECEF (6 of 8)

Perpendicular lines • tan = -1/ tan

Solve for tan • -(u/v)*(1 - e2) = -1/ tan • tan = v/[u (1 - e2)]

Solve for Rn

• Rn sin = v/(1 - e2)

• Rn cos = u

2. Position

9. Systems 40

ECEF (7 of 8)

• (u/a)2 + (v/b)2 = 1

• Rn2 cos2 /a2 + Rn

2 sin2 (1 - e2)2/b2 = 1

• Rn2 cos2 /a2 + Rn

2 sin2 (1 - e2)2/[a2 (1 - e2)] = 1

• Rn2 / a2 [ cos2 + sin2 (1 - e2)] = 1

• Rn2 / a2 [ cos2 + sin2 - e2 sin2 ] = 1

• Rn2 = a2 /[ 1 - e2 sin2 ]

• Rn = a /SQRT[ 1 - e2 sin2 ]

2. Position

9. Systems 41

ECEF (8 of 8)

a = 6378,137.0 meters (major semi-axis, ie equatorial radius)

Ellipsoid flattening ratio 1/f = 298.257 223 563 where f is flattening.

Flattening f = 0.00 335 281 0665 Flattening distance (a × f) is 21.38468575

kilometers so Polar radius b is (a - a × f) = 6356,752.314 m (minor semi-axis) UTM

2. Position

9. Systems 42

Map datums

GPS based on World Geodetic Survey 1984 (WGS-84)

There are 192 countries in the world described by 104 different map datums

WGS-84 can be converted to any of the other map datums, and many GPS sets will do this conversion

Some maps in the United States still refer to the North American 1927 Datum

There can be errors of thousands of feet between datums.

2. Position

9. Systems 43

UTM/UPS

Grid Reference Systems: Reference: US Army Field Manual 21-26, Map Reading and Land Navigation

Military grids

• Transverse Mercator projections have latitude and longitude as curved lines and the quadrangles formed by their intersections are of different shapes.

• Rectangular military grids are superimposed upon the projections to add in navigation

2. Position

9. Systems 44

UTM/UPSMilitary grids (continued)

• This grid provides a system of squares similar to the block system of city streets

• Three properties are common to all military grid systems:

• Rectangular grids

• Superimposed on the geographic projection

• Permit linear and angular measurements

2. Position

9. Systems 45

UTM/UPS

Universal Transverse Mercator (TM) grid

• Cover area between 84°N and 80°S latitude

• 60 zones, each 6° wide and 164° tall

• Each has it's origin at the equator

• Grid identical in all zones

2. Position

9. Systems 46

UTM/UPS

UTM (continued)

• Base values in meters are assigned to the central meridian of each of the 6° zones, and the equator and the grid lines are drawn at regular intervals parallel to these lines

• Each grid line is assigned a value denoting its distance from the origin, usually at 1000 meter intervals

2. Position

9. Systems 47

UTM/UPS

UTM (continued)

• False values are added to the base lines resulting in positive values for all points within each zone.

• This is 500,000 meters false easting for each central meridian and 10,000,000 meters false northing for the southern hemisphere.

2. Position

9. Systems 48

UTM/UPS

Universal Polar Stereographic (UPS) grid

• The UPS system is used in the polar regions above 84°N and 80°S latitude

• The north-south base line is the 0°/180° meridian and the east- west base lines are the two 90° meridians.

2. Position

9. Systems 49

UTM/UPS

US Army Military Grid Reference System (US MGRS)

• MGRS is designed for use with both UTM and UPS grids.

• Either of these grids can include as many as 15 digits

• MGRS substitutes a single letter for several numbers and reduces the length.

• GPS users need to be aware that map datum for a grid may not be WGS-84

2. Position

9. Systems 50

3. Altitude

Sources of altitudeSea levelTidesTerrain

3. Altitude

9. Systems 51

Sources of altitudeBarometric altimeter -- determines altitude

based on air pressureRadar altimeter -- determines altitude

above terrain by measuring distance using a radar

Laser altimeter -- determines altitude above terrain by measuring distance using a laser

GPS -- determines altitude about WGS-84 spheroid using time of arrival signals from multiple space vehicles

3. Altitude

9. Systems 52

Sea level

Mean sea level (MSL) is the average height of the oceans over time and position

MSL can be predicted using a modelGPS outputs can be converted to MSLAltitude above the ocean at any time

depends upon tides

3. Altitude

9. Systems 53

Tides (1 of 6)

The alternating rise and fall in sea level with respect to the land produced by the gravitational attraction of the moon and the sun.

Observed recurrence of high and low water - usually, but not always, twice daily.

Refers only to relatively short-period, astronomically induced vertical change in the height of the sea surface

Tides can be 15-20 meters between high and low

3. Altitude

9. Systems 54

Tides (2 of 6)

High tides -- horizontal flow of water toward two regions of the earth representing positions of maximum attraction of combined lunar and solar gravitational forces.

Low tides -- compensating maximum withdrawal of water from regions around the earth midway between these two humps.

Alternation of high and low tides -- caused by the daily (or diurnal) rotation of the earth with respect to these two tidal humps and two tidal depressions.

3. Altitude

9. Systems 55

Tides (3 of 6)The gravitational attraction of the moon

superimposes its effect upon, but does not overcome, gravity of the earth

Earth gravity and centrifugal force, although always present, play no direct part in the tide-producing action.

Moon gravity on earth is only about one 9-millionth part of the force of earth gravity

3. Altitude

9. Systems 56

Tides (4 of 6)

The tide raising force of the moon does not lift the water

Tides are produced by the component that draw the waters horizontally

Since the horizontal component is not opposed by gravity, it is the force in generating tides.

3. Altitude

9. Systems 57

Tides (5 of 6)The gravitational attraction of the moon

superimposes its effect upon, but does not overcome, gravity of the earth

Earth gravity and centrifugal force, although always present, play no direct part in the tide-producing action.

Moon gravity on earth is only about one 9-millionth part of the force of earth gravity

3. Altitude

9. Systems 58

Tides (6 of 6)

point of rotation

lunar gravity matches centrifugal force

lunar gravity > centrifugal force

lunar gravity < centrifugal force

net tidal force

net tidal force

x

3. Altitude

9. Systems 59

Terrain (1 of 7)

Digital Terrain Elevation Data (DTED®)

• The National Imagery and Mapping Agency (NIMA) has developed standard digital data sets that are matrices of terrain elevation values

• This data allows determining elevation, slope, and surface roughness

3. Altitude

9. Systems 60

Terrain (2 of 7)

DTED level 0

• Spacing is 30 arc second --nominally one kilometer.

• Derived from NIMA DTED Level 1 to support a federal agency requirement.

3. Altitude

9. Systems 61

Terrain (3 of 7)

DTED level 1• The basic medium-resolution elevation data

source for all military activities and systems that require landform, slope, elevation, and/or gross terrain roughness in a digital format.

• Uniform matrix of terrain elevation values with spacing every 3 arc seconds (approximately 100 meters).

3. Altitude

9. Systems 62

Terrain (4 of 7)

DTED level 1 (continued)• Approximately equivalent to the contour

information represented on a 250,000 scale map.

• One degree by one-degree cell has 1,442,401 data points for a total of 5 megabytes

3. Altitude

9. Systems 63

Terrain (5 of 7)

DTED level 2• The basic high-resolution elevation data

source for all military activities and systems that require landform, slope, elevation, and/or terrain roughness in a digital format.

• Uniform matrix of terrain elevation values with post spacing of one arc second (approximately 30 meters).

3. Altitude

9. Systems 64

Terrain (6 of 7)

DTED level 2 (continued)

• Due to extremely sparse area coverage there is no catalog listing for DTED2. The information content is equivalent to the contour information represented on a 1: 50,000 scale map.

• One degree by one-degree cell has 1,442,401 data points for a total of 5 megabytes

• Will be available through the 2000 STS-99 Shuttle IFSAR mission in 2001.

3. Altitude

9. Systems 65

Terrain (7 of 7)

DTED levels 3-5

• Level 3 --10 m data, 144,024,001 data points in 583 megabytes

• Level 4 -- 3m data, 1,296,072,001 data points in 6,297 megabytes

• Level 5 -- 1m data, 11,660,000,000 data points in 68,001 megabytes

3. Altitude

9. Systems 66

4. Air data

Air data systemAir data variablesAtmospherePhysics

4. Air data

9. Systems 67

Air data system

airspeedindicator

altimeterverticalspeed

indicator

transducer

transducer Airdata

computer

pressure altitude

vertical speed

calibrated airspeed

mach number

true airspeed

static air temp

air density ratio

total pressure

static pressure

total temp probe

pitot static probe

4. Air data

9. Systems 68

Air data variables (1 of 3)Pressure altitude -- derived from static

pressure assuming a standard atmosphere

Vertical speed -- derived by differentiating static pressure

4. Air data

9. Systems 69

Air data variables (2 of 3)

Static air temperature -- temperature of the air when not moving relative to the sensor

Total temperature -- static air temperature plus the kinetic rise in temperature caused by bringing air to a stop relative to sensor

Air density ratio ratio -- ratio of air density at altitude to the air density at sea level

4. Air data

9. Systems 70

Air data variables (3 of 3)

Calibrated airspeed -- derived from the impact pressure, which is the the difference between the total and static pressures

Indicated airspeed -- calibrated airspeed plus the error in the pitot static system -- often the quantity displayed on simple airspeed indicators

True airspeed -- speed through the airMach number -- ratio of speed to speed of

sound

4. Air data

9. Systems 71

Atmosphere (1 of 3)

Tropopause -- The transition region in the atmosphere where the drop in temperature with increasing height ceases. 6 miles above poles; 12 above equator

Stratopause -- The transition region in the atmosphere where the temperature ceases being constant and starts increasing with altitude

4. Air data

9. Systems 72

Atmosphere (2 of 3)

Troposphere -- Region of atmosphere from the surface of the earth to the tropopause

Stratosphere -- Region of atmosphere from tropopause to stratopause. Temperature -45o C to -75o C

Chemosphere -- Region of atmosphere above stratosphere where temperature increases with altitude

4. Air data

9. Systems 73

Atmosphere (3 of 3)

Standard atmosphere• Pressure at sea level -- 1013.25 mb• Temperature at sea level -- 59oF• Troposphere -- -3000 feet to 11,000 m• Stratosphere -- 11,000 m to 20,000 m• Chemosphere -- 20,000 m to 105,000 feet• Troposphere lapse rate -- 0.0065oC/m• Chemosphere lapse rate -- 0.001oC/m

4. Air data

9. Systems 74

Physics (1 of 2)Ideal gas law

• pV = nR*T = mRT• p =pressure• V = volume• m = mass• MW = molecular weight• n = number of moles = m/MW• R* = universal gas constant = 8.314 J/mole- oK• R = specific gas constant = R*/MW

– air: R= 53.35 ft-lbf/lbm-oR = 287 J/kg- oK– nitrogen: R = 55.16 ft-lbf/lbm-oR = 287 J/kg- oK

• T = temperature

4. Air data

9. Systems 75

Physics (2 of 4)

Ideal gas law• Example: What is the mass of air contained

in a 500 cubic foot tank at 100 degrees Fahrenheit and one atmosphere

• p = 14.7 X 144 = 2116.8 lbf/ft2

• V = 500 ft3

• R = 53.35 ft-lbf/lbm-oR • T = 100 + 460 = 560 oR• m =pV/RT =(14.7 x 500)/(53.35 x 560) = 35.4 lbm

4. Air data

9. Systems 76

Physics (3 of 4)Bernoulli equation

• Et = Ep + Ev+ Ez = p/ + v2/2 + zg = c (SI)

• Et = p/ + v2/2gc + zg/gc = c (English)• Et = total energy

• Ep = pressure energy

• Ez = potential energy

• p = pressure = density

• v = velocity

• z = height

• g = acceleration of gravity

• gc = 32.2 lbm-ft/lbf-sec2

• c = a constant 4. Air data

9. Systems 77

Physics (4 of 4)Bernoulli equation

• Example: Still water at 2 atmospheres is discharged through a pipe 100 feet below into the outside atmosphere. What is the velocity of the water at discharge?

• Ep1 = 2x14.7 x 144 /62.4 = 67.8

• Ev1 = 0

• Ez1 = 100 * 32.2/32.2 = 100

• Ep2 = 14.7 x 144/62.4 = 33.9

• Ev2 = v22/2gc

• Ez2 = 0

• v2 = sqrt[2 x 32.2 x (67.8 + 100 - 33.9)] = 92.8 ft/sec4. Air data

9. Systems 78

5. Components

Angle measurementsAngle rate measurementsAcceleration measurements

5. Components

9. Systems 79

Angle measurement (1 of 4)Compasses

• Types• Magnetic -- measure direction from

magnetic north • Gyro -- measures direction from arbitrary

inertial reference

• Magnetic deviation• East is least -- subtract east deviation• West is best -- add west deviation

• Types of magnetic compasses• Suspended magnet• Flux gate

5. Components

9. Systems 80

Angle measurement (2 of 4)

Resolvers• Purpose -- Measure angle from a

reference zero• Construction

• Variation of a synchro• Operates with multi-phase A/C

• Accuracy• Generally less than an encoder

5. Components

9. Systems 81

Angle measurement (3 of 4)Encoders

• Purpose -- Measure angle from a reference zero

• Construction -- A mechanical wheel with encoding that allows read out in digital format

5. Components

9. Systems 82

Angle measurements (4 of 4)Binary angle measure (BAM)

• Purpose -- a format for encoding angles within a digital word to get the greatest resolution from the word

-180o 180o/2 180o/4 180o/8 180o/16 180o/32 180o/64 180o/128

1 0 1 1 0 0 0 0

0 1 1 0 0 0 0 0

-112.5o

67.5o

0 1 1 1 1 1 1 1 ~180o

5. Components

9. Systems 83

Angle rate measurements (1 of 3)

Tachometers• Purpose -- Measure angular velocity

with respect to a mounting, usually for damping a servo loop

• Construction -- sometimes embedded with another instrument such as motor or a resolver

5. Components

9. Systems 84


Inertial gyros• Purpose -- Measure angular velocity

relative to inertial space• Construction -- Spinning rotor • Dimensions -- 1 or 2• Types -- Rate gyro and rate integrating

gyro

5. Components

9. Systems 85


Optical gyros• Purpose -- Measure angular velocity

relative to inertial space• Construction -- Sense the difference in

times for laser light waves traveling around a close path in opposite directions to complete the path

• Types -- Laser gyro and fiber-optic gyro (FOG)

5. Components

9. Systems 86

Acceleration measurements

Accelerometers• Purpose -- Measure linear velocity

relative to inertial space• Construction -- Suspended pendulum• Types -- Simple pendulous

accelerometer and torque-balance accelerometer

5. Components

9. Systems 87

6. Navigation systems

Types of navigationVORDMETACANILSLoranGPSDoppler/heading referenceInertial navigation systems


9. Systems 88

Types of navigation

Rhumb-line navigation -- maintains a constant compass heading on each leg

Great-circle navigation -- travels along a plane that passes through the center of the earth

Navigation systems• Air-data based dead reckoning system• Doppler/heading-reference system• Inertial navigation systems• Doppler/inertial navigation systems


9. Systems 89

VORIndicates direction from aircraft to VOR

station independent of aircraft headingTransmits two signals

• Omni-directional reference signal• Rotating signal with 360 increments• Reference and rotating signals in phase

for magnetic northOperates 108.0 - 117.95 MHz

• T (terminal) <25 nm @12,000 feet• L (low altitude) <40 nm @ 18,000 feet• H (high altitude) <200 m @ 20,000 feet


9. Systems 90

DME

Gives distance to DME stationAirborne DME transmits and VORTAC

station responds; DME uses round-trip time to compute range

Operates 960 - 1213 MHzAccuracy 0.2% - 3%


9. Systems 91

TACAN

Combination of VOR and DME used by militaryOften co-located with VOR stationsOperates 960 - 1215 MHzRange limited line of sight ~ 200 nm at 18,000 ft


9. Systems 92

ILS (1 of 2)A precision VHF approach and landing systemOperation

• Glideslope• Located 1000 feet from approach end• UHF 328.6 - 335.4 MHz• Vertical accuracy 7%• Course accuracy 25 feet at threshold

• Localizer• Located 1000 feet beyond stop end of runway


9. Systems 93

ILS (2 of 2)

Operation (continued)• 75 MHz marker beacons along approach

• Outer -- marks initial approach at 4-7 miles prior to runway

• Middle -- marks impending visual acquisition of runway at 3500 feet prior to runway for Category I approaches

• Inner -- supports Category II and III approaches at 1000 feet prior to runway


9. Systems 94

Loran-C

A positioning system for marine and general aviation use

Operation• Not maintained by FAA navaid system• Based on chains of transmitting stations

each consisting of a master station and two or more secondary stations operating near 100 kHz

• Uses time of arrival of signals from each station to determine position


9. Systems 95

GPS (1 of 15)GPS

• Provides• Three-dimensional position• Three-dimensional velocity• Precision time

• It’s not a navigation system in itself, but provides information to navigation systems


9. Systems 96

GPS (2 of 15)

Space segment• Space vehicles (SVs) -- up to 24• Orbits

• Six orbital planes• 3-4 SVs per orbit• 10,900 miles• 55 degrees relative to equator


9. Systems 97

GPS (3 of 15)

Space segment (continued)• Frequencies

• L1 = 1575.42 MHz• L2 = 1227.60 MHz

• Modulation• Peudorandom noise (PRN)• Clear/acquisition (C/A) code -- 1.023 MHz• Precision (P) code -- 10.23 MHz• Navigation message data -- 50 Hz


9. Systems 98

GPS (4 of 15)

L1 carrier

C/A code

nav message

P code

L2 carrier +

+

+

90 degrees

+

+

+

SV signal and frequency schemes

SV signal and frequency schemes

L1 signal

L2 signal


9. Systems 99

GPS (5 of 15)

Ground segment• Master control station in Colorado and

five monitor stations• Tracks all SVs and predicts orbits• Sends uploads to SVs


9. Systems 100

GPS (6 of 15)User equipment

• Receives signal• L1 C/A code: -160 dBW• L1 P code: -163 dBW• L2 P code: -166 dbW

• Tracks codes• Extracts position, velocity, and time


9. Systems 101

GPS (7 of 15)

transmit

receive SV 2

T1

T2

T3

T4

receive SV 1

receive SV 3

receive SV 4

PR1 = c T1

PR2 = c T2

PR3 = c T3

PR4 = c T4

Pri = pseudo range (I = 1, 2, 3, 4) •Pseudorange includes distance between SV and UE, SV clock bias, atmospheric distortion, relativity effects, receiver noise, and receiver clock bias• SV clock bias, atmospheric distortions, and relativity effects are compensated for before computing time and position

Pri = pseudo range (I = 1, 2, 3, 4) •Pseudorange includes distance between SV and UE, SV clock bias, atmospheric distortion, relativity effects, receiver noise, and receiver clock bias• SV clock bias, atmospheric distortions, and relativity effects are compensated for before computing time and position

Time of arrival


9. Systems 102

GPS (8 of 15)

(x1 - ux)2 + (y1 - uy)2 + (z1 - uz)2 = (PR1 - c b)2

(x2 - ux)2 + (y2 - uy)2 + (z2 - uz)2 = (PR2 - c b)2

(x3 - ux)2 + (y3 - uy)2 + (z3 - uz)2 = (PR3 - c b)2

(x4 - ux)2 + (y4 - uy)2 + (z4 - uz)2 = (PR4 - c b)2

c = speed of lightxi, yi, zi = SV locationux, uy, uz = UE positionb = clock bias

Position and clock solution


9. Systems 103

GPS (9 of 15)

Nav message data• Subframes

• 1 -- clock correction• 2 -- ephemeris• 3 -- ephemeris• 4 -- message that changes through 25 frames • 5 -- almanac and health data that changes

through 25 frames

• Rates• Subframe -- 6 seconds• Entire message -- 12.5 minutes


9. Systems 104

GPS (10 of 15)Threat countermeasures

• Space• High-altitude orbits• Orbit spacing• Spare SVs• Gradual degradation of coverage• Natural replacement• Nuclear and laser hardening


9. Systems 105

GPS (11 of 15)Threat countermeasures (continued)

• Control• Security measures• Redundant monitor stations and antennas• Graceful degradation of accuracy• Encrypted telemetry and command links


9. Systems 106

GPS (12 of 15)

Threat countermeasures (continued)• User

• EMP shielding• Nuclear hardening• Spread spectrum• Adaptive arrays• Nav system aiding• Crypto and anti-spoofing


9. Systems 107

GPS (13 of 15)Accuracy control

• Selective accuracy (SA) -- Inserts controlled errors into SV signal that require crypto code to correct

• Anti-spoofing (A-S) -- Randomly alter P-code cryptographically into Y-code that requires crypto code to correct

• Precision positioning service (PPS) -- Can recover full SA plus Y code, SA only, or Y-code only

• Standard positioning service (SPS) -- Can recover only SPS accuracy


9. Systems 108

GPS (14 of 15)

Accuracy• PPS receiver -- 7 m, one-sigma• SPS receiver -- 32 m, one-sigma• Accuracy depends upon dilution of

precision caused by SV relative locations

• Accuracy also dependent upon dynamics and time or dwell


9. Systems 109

GPS (15 of 15)

Differential GPS• technique to improve accuracy by

determining position error at a known location and transmitting corrections to users in area


9. Systems 110

Doppler/heading reference (1 of 3)

Four doppler antenna patterns in Janus pattern


9. Systems 111


V G


9. Systems 112


Doppler radar

Attitudeand heading reference systems

+

resolvespeed

1/R 1/s

1/R 1/sx

T

V G V N

V E V E /R

d /dt = V N /R

d /dt

1/cos

= drift angle = headingT =ground trackV G = ground speed

V N = north velocityV E = east velocityR = earth radius = latitude = longitude


9. Systems 113

Inertial navigation systems (1 of 2)

Inertial navigation systemsTypes• Platform• Strapdown

Primary components• Accelerometers• Gyros

Alignment• Stationary• While moving


9. Systems 114

Inertial navigation systems (2 of 2)

Primary concerns• Coriolis and centrifugal acceleration

corrections• Schuler corrections• Vertical loop stability• Integration with other sensors


Documents

9. Systems1 Agenda 1. Time 2. Position 3. Altitude 4. Air data 5. Components 6. Nav systems