民航导航系统原理与应用

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1、民航導航系統原理與應用成大民航研究所詹劭勳 老師9/16/20241(c)Shau-Shiun Jan, IAA, NCKUCourse Information BooksAvionics Navigation Systems, M. Kayton, W. R. Fried, John, ISBN: 0471547956 Many reference books (Keywords: GPS, INS):Global Positioning System (GPS): Signals, Measurements and Performance, P. Misra and P. Enge, Ga

2、nga-Jamuna, 2001Strapdown Inertial Navigation Systems, D. H. Titterton and J. L. WestonThe Global Positioning System and Inertial Navigation, Farrell and Barth, McGraw-Hill, 1999Integrated Aircraft Navigation, J. L. Farrell, Academic Press, 1976Global Positioning Systems, Inertial Navigation and Int

3、egration, Grewal, Weill and Andrews, Wiley Interscience, 20019/16/20242(c)Shau-Shiun Jan, IAA, NCKUOutlinePart 1: IntroductionPart 2: Navigation CoordinatePart 3: Radio Navigation SystemsPart 4: Global Positioning SystemPart 5: Augmentation Systems9/16/20243(c)Shau-Shiun Jan, IAA, NCKUPart 1: Introd

4、uction An Overview of Navigation and Guidance9/16/20244(c)Shau-Shiun Jan, IAA, NCKUNavigation and GuidanceNavigation: The process of determining a vehicles / persons / objects positionGuidance: The process of directing a vehicle / person / object from one point to another along some desired path9/16

5、/20245(c)Shau-Shiun Jan, IAA, NCKUExampleGetting from AA building to Tainan Train StationHow would you tell someone how to get there?How would you tell a robot to get there?Both problems assume there is some agreed upon coordinate system.Latitude, Longitude, Altitude (Geodetic)North, East, Down with

6、 respect to some originAd Hoc system (“starting from AA building you go 1 block”)Most of our work in this class is going to be with the Navigation problem9/16/20246(c)Shau-Shiun Jan, IAA, NCKUApplicationsAir TransportationMarine, Space, and Ground VehiclesPersonal Navigation / Indoor NavigationSurve

7、ying9/16/20247(c)Shau-Shiun Jan, IAA, NCKUA Navigation or Guidance SystemSteering commands: instructions on what to do to get the vehicle going to where it should be goingTurn right / leftGo up / downSpeed up / slow downSensor #1:Sensor #2Sensor #NNavigation and/orGuidanceProcessorSteering commandsN

8、avigation state vector9/16/20248(c)Shau-Shiun Jan, IAA, NCKUNavigation State / State VectorA set of parameters describing the position, velocity, altitude of a vehicleNavigation state vector:Position = 3 coordinates of location, a 3x1 vectorVelocity = derivative of the position vector, a 3x1 vectorA

9、ttitude = a set of parameters which describe the vehicles orientation in space9/16/20249(c)Shau-Shiun Jan, IAA, NCKUPosition and VelocityMore often than not, we are interested in position and velocity vectors expressed in separate coordinates (more on this later)9/16/202410(c)Shau-Shiun Jan, IAA, NC

10、KUAttitudeWe will deal with two ways of describing the orientation of two coordinate framesEuler angles: 3 angles describing relationship between 2-coordinate systemsTransformation matrix: maps vector in “A” coordinate frame to “B”9/16/202411(c)Shau-Shiun Jan, IAA, NCKUAttitude (continued)The first

11、entry of the attitude “vector”, , is called yaw or heading.9/16/202412(c)Shau-Shiun Jan, IAA, NCKUNavigation and Guidance SystemsIn this class we will look at ways to determining some or all of the components of the navigation state vector. Some navigation systems provide all of the entries of the n

12、avigation state vector (inertial navigation systems) and some only provide a subset of the state vector.Guidance systems give instructions on how to achieve the desired position.9/16/202413(c)Shau-Shiun Jan, IAA, NCKUNavigation and Guidance Systems9/16/202414(c)Shau-Shiun Jan, IAA, NCKUCategories of

13、 NavigationDead ReckoningPositioning (position fixing)Navigation systems are either one of the two or are hybrids.9/16/202415(c)Shau-Shiun Jan, IAA, NCKUDead Reckoning Systems“Extrapolation” system: position is derived from a “series” of velocity, heading, acceleration or rotation measurements relat

14、ive to an initial position.To determine current position you must know history of past positionHeading and speed or velocity systemsInertial navigation systemsSystem accuracy is a function of vehicle position trajectory9/16/202416(c)Shau-Shiun Jan, IAA, NCKUPositioning / Position Fixing SystemsDeter

15、mine position from a set of measurements.Knowledge of past position history is not requiredMapping system Pilotage (pp.504-505)Celestial systems Star TrackersRadio systems VOR, DME, ILS, LORANSatellite systems GPS, GLONASS, GalileoSystem accuracy is independent of vehicle position trajectory9/16/202

16、417(c)Shau-Shiun Jan, IAA, NCKUBrief History of NavigationLand Navigation “pilotage” traveling by reference to land marks.Marine Navigation Greeks (300350 B.C.) Record of going far north as Norway, “Periodic Scylax” (Navigation manual).Vikings (1000 A.D.) had compassFerdinand Magellan (1519) recorde

17、d use of charts (maps), devices for getting star fixes, compass, hour glass and log (for speed).The important point to note is that these early navigators were using dead reckoning and position fixing (hybrid system)9/16/202418(c)Shau-Shiun Jan, IAA, NCKUDetermine Your LatitudePolarisEquators=Latitu

18、dehsRE9/16/202419(c)Shau-Shiun Jan, IAA, NCKUHow do you determine longitude?Dead reckoningCompass for heading, log for speedNot very accurate, heading errors, speed errors position errorsErrors grow with time9/16/202420(c)Shau-Shiun Jan, IAA, NCKUThe Longitude ProblemLongitude act of 171420,000 for

19、1/2o solution15,000 for 2/3o solution10,000 for 1o solution (about 111km resolution at equator!)Board of longitudeHalley (“Halley Comet”)NewtonSolution turned out to be a stable watch / clock 9/16/202421(c)Shau-Shiun Jan, IAA, NCKU20th Century and AviationPosition fixing (guidance) systems:PilotageF

20、ires (1920) US mail routesRadio beaconsLate 1940s most of the systems we use today started entering servicesBy 1960s VOR/DME and ILS become standard in commercial aviationDead reckoningInertial navigation (1940)German v-2 RocketNuclear submarine (US NAVY)Oceanic commercial flight9/16/202422(c)Shau-S

21、hiun Jan, IAA, NCKU20th Century and AviationSatellite based navigation systemsUS NAVY Transit System (1964)Global Positioning System1978 first satellite launched1995 declared operationalOther satellite navigation systemsGLONASS Former Soviet UnionGalileo being developed by the EU9/16/202423(c)Shau-S

22、hiun Jan, IAA, NCKUPerformance Metrics and Trade-Off1.Cost2.Autonomy3.Coverage4.Capacity5.Accuracy6.Availability7.Continuity8.IntegrityArea of active research: 5,6,7,8Accuracy: we will visit it in detail later on.9/16/202424(c)Shau-Shiun Jan, IAA, NCKUPart 2: Navigation Coordinate Frames, Transforma

23、tions and Geometry of Earth.Navigation coordinate framesGeometry of earth9/16/202425(c)Shau-Shiun Jan, IAA, NCKUCoordinate FramesThe position vector (the main output of any navigation system and our primary concern in this class) can be expressed in various coordinate frames.Notation9/16/202426(c)Sh

24、au-Shiun Jan, IAA, NCKUWhy Multiple Coordinate Frames?Depending on the application at hand some coordinates can be easier to use. In some applications, multiple frames are used simultaneously because different parts of the problem are easier to manage.For example,GPS: normally position and velocity

25、in “ECEF”INS: normally position in geodetic and velocity in “NED”9/16/202427(c)Shau-Shiun Jan, IAA, NCKUCoordinate FramesCartesianECEFECINED (locally tangent Frames)ENU (locally tangent Frames)Spherical/cylindricalGeodeticAzimuth-Elevation-Range Bearing-Range-AttitudeExcept for ECI, all are non-iner

26、tial frames, an inertial frames is a non-accelerating (translation and rotation) coordinate frames.9/16/202428(c)Shau-Shiun Jan, IAA, NCKUECEF and ECIEarth Centered and Earth Fixed (ECEF) Cartesian Frame with origin at the center of earth. Fixed to and rotates with earth. A non-inertial frame.Earth

27、Centered Inertial (ECI)Cartesian frame with origin at earths center.Z axis along earths rotation vector.X-y plane in equatorial plane.9/16/202429(c)Shau-Shiun Jan, IAA, NCKUGeodeticGeodetic (Latitude, Longitude, Altitude) SphericalLatitude () = north south of equator, range 90oLongitude () = east we

28、st of prime meridian, range 180oAltitude (h) = height above reference datum“+” north latitude, east longitude, down (below) datum altitude9/16/202430(c)Shau-Shiun Jan, IAA, NCKUNED and ENUNorth-East-Down (NED)CartesianNo fixed location for the originLocally tangent to earth at originEast-North-Up (E

29、NU)CartesianSimilar to NED except for the direction of 1-2-3 axes.9/16/202431(c)Shau-Shiun Jan, IAA, NCKUAzimuth-Elevation-RangeAzimuth-Elevation-RangeSphericalNo fixed originAzimuth is angle between a line connecting the origin and the point of interest (in the tangent plane) and a line from origin

30、 to north poleElevation is the angle between the local tangent plane and a line connecting the origin to a point of interestRange is the slant or line-of-sight distance9/16/202432(c)Shau-Shiun Jan, IAA, NCKUAzimuth-Elevation-RangeTwo types of azimuth or heading anglesTrue: measured with respect to t

31、he geographic (true) north pole (T)Magnetic: measured with respect to the magnetic north pole (M)9/16/202433(c)Shau-Shiun Jan, IAA, NCKUEarth Magnetic Field1st order approximation is that of a simple dipolePoles move with time.In 1996 magnetic north pole was located at (79oN,105oW)In 2003 it is loca

32、ted at (82oN,112oW) Also, can “wander” by as much as 80km per day9/16/202434(c)Shau-Shiun Jan, IAA, NCKUEarth Magnetic FieldMagnetic poles are used in navigation because M is easier to measure than T Bx and By are measured by devices called magnetometers (Ch.9)Anomalies such as local iron deposits l

33、ead to erroneous M readingIron range deposits of N.E. Minnesota can lead to errors as large as 50o 9/16/202435(c)Shau-Shiun Jan, IAA, NCKUShape / Geometry of Earth1.Topographical / physical surface2.Geoid3.Reference ellipsoid9/16/202436(c)Shau-Shiun Jan, IAA, NCKUShape / Geometry of Earth (continued

34、)Topographical surface shape assumed by earths crust. Complicated and difficult to model mathematically.Geoid an equipotential surface of earths gravity field which best fits (least squares sense) global mean sea level (MSL)Reference ellipsoid mathematical fit to the geoid that is an ellipsoid of re

35、volution and minimizes the mean-square deviation of local gravity (i.e., local norm to geoid) and ellipsoid norm, WGS-849/16/202437(c)Shau-Shiun Jan, IAA, NCKULatitude9/16/202438(c)Shau-Shiun Jan, IAA, NCKUWGS84 Four defining parametersOther parameters are derived from the fourEquatorial radius = 63

36、78.137kmFlattening = 1/298.257223563Rotation rate of earth in inertial space = 15.041067 degree/hourEarths gravitational constant (GM) = 3.986004x108m3/s29/16/202439(c)Shau-Shiun Jan, IAA, NCKUPart3:Radio Navigation Systems I: FundamentalsI: FundamentalsII: Survey of Current Systems9/16/202440(c)Sha

37、u-Shiun Jan, IAA, NCKURadio Navigation SystemsThese are systems that use Radio Frequency (RF) signals to generate information required for navigation.C = speed of electromagnetic waves in free space (“ speed of light ”)“ Radio waves ” correspond to electromagnetic waves with frequency between 10 KHz

38、 and 300 GHz 9/16/202441(c)Shau-Shiun Jan, IAA, NCKUFrequencyFrequenciesWavelength Very Low Frequency (VLF)10 kmLow Frequency (LF)30 300 KHz1 to 10 kmMedium Frequency (MF)300 KHz 3 MHz100 m to 1 kmHigh Frequency (HF)3 30 MHz10 to 100 mVery High Frequency (VHF)30 300 MHz1 to 10 mUltra High Frequancy

39、(UHF)300 MHz 3 GHz10 cm to 1 mSuper High Frequency (SHF)3 30 GHz1 to 10 cmExtremely High Frequency (EHF)30 300 GHz1 to 10 mm9/16/202442(c)Shau-Shiun Jan, IAA, NCKUFrequencyGPS signals are L band SignalsMLS uses C band signalsExpand9/16/202443(c)Shau-Shiun Jan, IAA, NCKURadio Signal Propagation (1/3)

40、Ground WavesWaves below the HF range (i.e., 30 MHz100 MHz 3 GHz predictableAbove 3 GHz absorptionAbove 10 GHz discrete absorption9/16/202445(c)Shau-Shiun Jan, IAA, NCKURadio Signal Propagation (3/3)Sky WavesHF and below (i.e., 30 MHz)MultipathFadingSkip distance: depends of frequency and ionosphere

41、conditions9/16/202446(c)Shau-Shiun Jan, IAA, NCKUModulation TechniquesModulation how you place information of the RF signalAmplitude modulation (AM) change the amplitude of sinusoid to relay information Frequency modulation (FM) change in frequency of transmitted signal to relay informationPhase mod

42、ulation (PM) change phase of transmitted signal to relay informationThe signal can be transmitted as a pulse or a continuous wave. Either one can be modulated by the above methods. 9/16/202447(c)Shau-Shiun Jan, IAA, NCKUHow do you distinguish one beacon from another?Frequency division multiple acces

43、s (FDMA) each transmitter/beacon uses a different frequency Time division multiple access (TDMA) each transmitter/beacon transmits at a specified timeCode division multiple access (CDMA) each transmitter/beacon uses an identifier code to distinguish itself from the other transmitters or beacons9/16/

44、202448(c)Shau-Shiun Jan, IAA, NCKUImportant ConclusionsLow frequency systems ground wave transmission long range systems, Loran.High frequency systems line of sight systemsPhysical QuantityNameSensor PropertiesDistance / RangeL.O.S.BearingL.O.S.tTDOAGround Wave9/16/202449(c)Shau-Shiun Jan, IAA, NCKU

45、9/16/202450(c)Shau-Shiun Jan, IAA, NCKUPhases of FlightTakeoffDeparture(Climb)En RouteApproach(Descent)Landing9/16/202451(c)Shau-Shiun Jan, IAA, NCKUPhases of FlightTakeoff Starts at takeoff roll and ends when climb is established. Departure Ends when the aircraft has left the so called terminal are

46、a.En Route Majority of a flight is spent in this phase. Ends when the approach phase begins. Navigation error during this phase must be less than 2.8 N.M (2-) over land and 12 N.M over oceans. 9/16/202452(c)Shau-Shiun Jan, IAA, NCKUEn RouteNAV beacon (NAVAID)DestinationRandom or area navigationDepar

47、ture9/16/202453(c)Shau-Shiun Jan, IAA, NCKUPhases of FlightApproach Ends when the runway is in sight. The minimum descent altitude or decision height is reached. (MDA or DH)Landing Begins at the MDA or DH and ends when the aircraft leaves the runway.MDA or DHCeiling heightClouds, Fog, or Haze9/16/20

48、2454(c)Shau-Shiun Jan, IAA, NCKUAccuracy RequirementAccuracy required during the approach and landing phases of flight depend on the type of operation being conducted.Phase of FlightNavigation/Guidance SystemTakeoff Visual, Radar*DepartureVOR, DME, Radar*En RouteVOR, DME, Radar*Approach and LandingV

49、OR, DME, Radar*, ILS, MLS*Used by the ground based controllers to give the user “steering“ directions and to ensure traffic separation between aircraft. 9/16/202455(c)Shau-Shiun Jan, IAA, NCKUVORVOR (VHF Omni-Directional Range)Provides bearing informationUses VHF radio signalsFDMA with frequencies b

50、etween 112 and 117.95 MHZBearing accuracy 1o to 3oWorks by comparing the phase of 2 sinusoids. One has bearing dependent phase the other doesnt.9/16/202456(c)Shau-Shiun Jan, IAA, NCKUDMEDME (Distance Measuring Equipment):Measures slant range Operates between 962 1213 MHzAccuracy 0.1 to 0.17 n.m. (no

51、minal) (185 315 m)Principle of operation1.Airborne unit sends a pair of pulses2.Ground based beacon (transponder) picks up the signal3.After a 50sec delay, transponder replies4.Airborne unit receives pulse pair and computes range by :9/16/202457(c)Shau-Shiun Jan, IAA, NCKUDMEHow does a particular us

52、er distinguish their pulse from that of other users? Normally, VOR and DME are collocated, in the U.S. there are 1000 VOR/DME beacons.9/16/202458(c)Shau-Shiun Jan, IAA, NCKUILSILS (Instrument Landing System):System provides angular information Used exclusively for approach and landing9/16/202459(c)S

53、hau-Shiun Jan, IAA, NCKUILSIt provides information about deviation from the center line () and guide slope ()Includes marker beacons that are installed at discrete distances from the runway .Outer Marker (OM) 4 to 7 n.m. from runwayMiddle Marker (MM) - 3500 ft from runwayInner Marker (IM) - 1000 ft

54、from runway9/16/202460(c)Shau-Shiun Jan, IAA, NCKUDecision Height (DH)Height above the runway at which landing must be aborted if the runway is not in sight. Based on DH, three categories of landing are available:CAT IDH 200 ft2600 ft visibilityCAT IIDH 100 ft1200 ft visibilityCAT IIIIIIA: DH 100 ft

55、700 ft visibilityIIIB: DH 50 ft150 ft visibilityIIIC: No DHNo visibility9/16/202461(c)Shau-Shiun Jan, IAA, NCKUMLSMLS (Microwave Landing System):Designed to “Look” like an ILS but mitigate the weaknesses of ILS. Operates between 5.0 5.2 GHzScanning beam used to provide both lateral (localizer equiva

56、lent) and vertical (glide slope) information.9/16/202462(c)Shau-Shiun Jan, IAA, NCKULORANLORAN (LOng RAnge Navigation): Hyperbolic position fixing system.Operates at 90 to 100 KHz. Area navigation capable. (i.e., not a guidance system only)Consists of chains: 1 master and multiple secondary stations

57、. Master station sends a signal.After a short (known) delay, the secondary stations “fire” in sequence. Accuracy 0.25 n.m. (463 m)9/16/202463(c)Shau-Shiun Jan, IAA, NCKUPart4:Global Positioning System9/16/202464(c)Shau-Shiun Jan, IAA, NCKUSatellite Navigation SystemsSputnik I (1957) Beginning of the

58、 space ageA ground station at a known location can determine the satellites orbit from a record of Doppler shift.US Navys TransitApplied Physics Lab (Johns Hopkins Univ.)Initial concept in 1958. Fully operational in 1964.Used by submarine fleet. Later use by civilians. Decommissioned in 1996. 9/16/2

59、02465(c)Shau-Shiun Jan, IAA, NCKUSatellite Navigation SystemsUS Navy and Air Force programs combined to become GPS Basic architecture approved in 19731st satellite launch in 1978Fully operational in 1995 (23 years!)Other satellite navigation systemsGLONASS (Russia), Galileo (EU), Beiduo (China)Calle

60、d Global Navigation Satellite System (GNSS)9/16/202466(c)Shau-Shiun Jan, IAA, NCKUGPS System ObjectivesTo provide the U.S. military with accurate estimates of position, velocity, and time (PVT).Position accuracy within 10 m, velocity accuracy within 0.1 m/s, and time accuracy within 100 nsec.2-level

61、s of service:Standard positioning service (SPS) For peaceful civilian use. Precise positioning service (PPS) For DoD (Department of Defense) authorized users (military). Selective availability (SA) clock ditherAntispoofing (AS) encryption 9/16/202467(c)Shau-Shiun Jan, IAA, NCKUSystem Design Consider

62、ationsActive or passive? GPS is passivePosition fixing method Doppler, hyperbolic, multilateration. GPS uses multilateration. Pulsed vs. continuous wave (CW) signal CDMA on same frequency (spread spectrum)L1 = 1575.42 MHzL2 = 1227.60 MHzL3, L4 classified payloads on satellitesL5 = 1176.45 MHz, new c

63、ivil frequency, not here yet9/16/202468(c)Shau-Shiun Jan, IAA, NCKUSystem Design ConsiderationsCarrier frequency: L-band. Ionospheric defraction less at higher frequencies but power loss is greater.Constellation LEO, MEO, or GEO?LEO 1020 minutes visibility time per SV, 100 200 SVs required. (cheap)M

64、EO Visible for several hours per pass. Launch more expensive than LEO.GEO Poor coverage at higher latitudes. Global coverage with few SVs. Expensive to launch. 9/16/202469(c)Shau-Shiun Jan, IAA, NCKUSystem Design ConsiderationsGPS uses a MEO constellation. 1st SV launched in 1978. Development of sys

65、tem estimated to be $10 billion. Annual operation and maintenance cost estimated at $500 Million. Technologies that were key to the development of GPS were:Stable space platforms in predictable orbits. Ultrastable clocks.Spread spectrum signaling.Integrated circuits. 9/16/202470(c)Shau-Shiun Jan, IA

66、A, NCKUSystem Architecture9/16/202471(c)Shau-Shiun Jan, IAA, NCKUSpace Segment24+ satellites6 orbital planes55 degree inclination12 hour orbits4 SVs per plane26561 Km from earths center2.7 Km/sec9/16/202472(c)Shau-Shiun Jan, IAA, NCKUControl SegmentControl segment: consists of the master control sta

67、tion (MCS) and five monitor stations. MCS: located at Schriever (formerly Falcon) Air Force base in Colorado Springs, CO.Monitors orbits, maintains SV healthMaintain GPS timePredict SV ephemeredes and clock parametersUpdate navigation messageCommand SV maneuversMonitor stations located at Hawaii*, C

68、ape Canaveral, Ascension Island, Diego Garcia, and Kwajalein.*Does not have S-band data link. 9/16/202473(c)Shau-Shiun Jan, IAA, NCKUGPS Nominal Accuracy (95%)PPSSPS (SA ON)SPS*(SA OFF)Position Vertical22 m100 m10 mPosition Horizontal28 m156 m15 mTime 200 ns340 ns50 ns9/16/202474(c)Shau-Shiun Jan, I

69、AA, NCKUPart5:Augmentation Systems9/16/202475(c)Shau-Shiun Jan, IAA, NCKUAugmentation SystemsImprove system performance by mitigating ranging errors and/or enhancing satellite geometryDifferential GPS (DGPS)Pseudolites9/16/202476(c)Shau-Shiun Jan, IAA, NCKUDifferential GPS (DGPS)Remove common mode e

70、rrors and broadcast corrections to userReferenceStation(Known location)UserUser9/16/202477(c)Shau-Shiun Jan, IAA, NCKUPseudolitesTransmit GPS like signals from some spot on the surface of earth.Enhance the geometry of the ranging signals.9/16/202478(c)Shau-Shiun Jan, IAA, NCKUGPS Range and Time Meas

71、urementsSignal leaves the satellite at time t = t0Receiver gets signal at t = t1Compare replica to received signalCompute the time of flight receiverreplicareceived9/16/202479(c)Shau-Shiun Jan, IAA, NCKUGPS TimeTime kept by the master control station. Consists of a GPS week and GPS second of the wee

72、k (Simply called time of the week or TOW)GPS weeks-range from 0-102 count began midnight Saturday/morning Sunday Jan 5th 1980.1st “roll over“ occurred on 22nd August 1999 (Y2K).TOW begins each Sunday morning (UTC or “GMT”) and continues up to 604,800.Each satellite keeps time using an atomic clock (

73、cesium or rubidium). Monitored by the MCS and its deviation modeled. 9/16/202480(c)Shau-Shiun Jan, IAA, NCKUFactors Effecting GPS AccuracyWe can group the factors affecting GPS errors as:Ranging errors: How good is my pseudorange measurement? How large are the pseudorange error? Residuals after we r

74、emove the part that can be modeled?Troposphere, Ionosphere, Satellites clock, Multipath.Satellite geometry : How are the satellites arranged overhead at the position where I want to compute a position solution?9/16/202481(c)Shau-Shiun Jan, IAA, NCKUIntuitive Explanation of the Effect of Satellite Ge

75、ometry 9/16/202482(c)Shau-Shiun Jan, IAA, NCKUDOPDOP was a very useful concept when the satellite constellation was thin (4-6 SVs). When satellite constellation is full (8-12 SVs in view at once) DOP is less critical.DOP can be calculated ahead of time using the weekly almanac. Plot PDOP (or other D

76、OPs) as a function of time to determine when best satellite geometry occurs. Typical PDOP values range from 1.5 (Good) to 5 (Bad).9/16/202483(c)Shau-Shiun Jan, IAA, NCKUDOPIt is more intuitive to deal with NED or ENU coordinates. Recasting the problem in NED (or ENU),9/16/202484(c)Shau-Shiun Jan, IA

77、A, NCKUHDOP, VDOP, PDOPThen,9/16/202485(c)Shau-Shiun Jan, IAA, NCKUGPS Error SourcesGPS Clock ErrorEphemeris ErrorIonospheric DelayTropospheric DelayReceiver noiseMultipathGPS SatellitesMan-made interference9/16/202486(c)Shau-Shiun Jan, IAA, NCKUDifferential GPS Concepts9/16/202487(c)Shau-Shiun Jan,

78、 IAA, NCKUError Budget for GPS & DGPSSourceGPS Error SizeDGPS Error SizeSatellite clock model2 m0.0 mSatellite ephemeris prediction (LOS)2 m0.1 mIonospheric delay (zenith)2 10 m0.2 mTropospheric delay (zenith)2.3 2.5 m0.2 mMultipathCode: 0.5 1 mCarrier: 0.5 1 cmCode: 0.5 1 mCarrier: 0.5 1 cmReceiver

79、 noiseCode: 0.25 0.5 mCarrier: 1 2 mmCode: 0.25 0.5 mCarrier: 1 2 mm9/16/202488(c)Shau-Shiun Jan, IAA, NCKUWide Area Differential GPSLocal DGPS system provide corrections that are valid only close to the reference station.To cover a large geographical area would require a large number of local refer

80、ence stations. This can be expensive.Wide area systems use a fewer number of reference stations to cover a large area. The stations are part of a large network where the information from each reference station is sent to a master station.9/16/202489(c)Shau-Shiun Jan, IAA, NCKUWide Area Differential

81、GPSMaster station processes the information and constructs a model for the errors as a function of geographical location and time. Model parameters are then broadcast to the user.Corrections are said to be ”vectors” because they are not a simple pseudorange correction but rather a breakdown of each

82、pseudorange error into its constituents.Examples of wide area systems:US Coast Guard DGPSFAA Wide Area Augmentation System (WAAS)European Geostationary Navigation Overlay System (EGNOS)Japanese MSAS9/16/202490(c)Shau-Shiun Jan, IAA, NCKUWAAS 25 WAAS Reference Stations 2 WAAS Master StationsGEOGPS SVs9/16/202491(c)Shau-Shiun Jan, IAA, NCKU