民航导航系统原理与应用.ppt

民航導航系統原理與應用成大民航研究所詹劭勳 老師8/31/20241(c)Shau-Shiun Jan, IAA, NCKUCourse Information – Books•Avionics 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, Ganga-Jamuna, 2001–Strapdown Inertial Navigation Systems, D. H. Titterton and J. L. Weston–The Global Positioning System and Inertial Navigation, Farrell and Barth, McGraw-Hill, 1999–Integrated Aircraft Navigation, J. L. Farrell, Academic Press, 1976–Global Positioning Systems, Inertial Navigation and Integration, Grewal, Weill and Andrews, Wiley Interscience, 20018/31/20242(c)Shau-Shiun Jan, IAA, NCKUOutline•Part 1: Introduction•Part 2: Navigation Coordinate•Part 3: Radio Navigation Systems•Part 4: Global Positioning System•Part 5: Augmentation Systems8/31/20243(c)Shau-Shiun Jan, IAA, NCKUPart 1: Introduction An Overview of Navigation and Guidance8/31/20244(c)Shau-Shiun Jan, IAA, NCKUNavigation and Guidance•Navigation: The process of determining a vehicle’s / person’s / object’s position•Guidance: The process of directing a vehicle / person / object from one point to another along some desired path8/31/20245(c)Shau-Shiun Jan, IAA, NCKUExample•Getting from AA building to Tainan Train Station–How 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 respect to some origin–Ad Hoc system (“starting from AA building you go 1 block…”)•Most of our work in this class is going to be with the Navigation problem8/31/20246(c)Shau-Shiun Jan, IAA, NCKUApplications•Air Transportation•Marine, Space, and Ground Vehicles•Personal Navigation / Indoor Navigation•Surveying8/31/20247(c)Shau-Shiun Jan, IAA, NCKUA Navigation or Guidance System•Steering commands: instructions on what to do to get the vehicle going to where it should be going–Turn right / left–Go up / down–Speed up / slow downSensor #1::Sensor #2Sensor #NNavigation and/orGuidanceProcessorSteering commandsNavigation state vector8/31/20248(c)Shau-Shiun Jan, IAA, NCKUNavigation State / State Vector•A set of parameters describing the position, velocity, altitude… of a vehicle•Navigation state vector:–Position = 3 coordinates of location, a 3x1 vector–Velocity = derivative of the position vector, a 3x1 vector–Attitude = a set of parameters which describe the vehicle’s orientation in space8/31/20249(c)Shau-Shiun Jan, IAA, NCKUPosition and Velocity•More often than not, we are interested in position and velocity vectors expressed in separate coordinates (more on this later…)8/31/202410(c)Shau-Shiun Jan, IAA, NCKUAttitude•We will deal with two ways of describing the orientation of two coordinate frames–Euler angles: 3 angles describing relationship between 2-coordinate systems–Transformation matrix: maps vector in “A” coordinate frame to “B”8/31/202411(c)Shau-Shiun Jan, IAA, NCKUAttitude (continued)•The first entry of the attitude “vector”, ψ, is called yaw or heading.8/31/202412(c)Shau-Shiun Jan, IAA, NCKUNavigation and Guidance Systems•In 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 navigation 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.8/31/202413(c)Shau-Shiun Jan, IAA, NCKUNavigation and Guidance Systems8/31/202414(c)Shau-Shiun Jan, IAA, NCKUCategories of Navigation•Dead Reckoning•Positioning (position fixing)•Navigation systems are either one of the two or are hybrids.8/31/202415(c)Shau-Shiun Jan, IAA, NCKUDead Reckoning Systems•“Extrapolation” system: position is derived from a “series” of velocity, heading, acceleration or rotation measurements relative to an initial position.•To determine current position you must know history of past position•Heading and speed or velocity systems•Inertial navigation systems•System accuracy is a function of vehicle position trajectory8/31/202416(c)Shau-Shiun Jan, IAA, NCKUPositioning / Position Fixing Systems•Determine position from a set of measurements.•Knowledge of past position history is not required–Mapping system – Pilotage (pp.504-505)–Celestial systems – Star Trackers–Radio systems – VOR, DME, ILS, LORAN…–Satellite systems – GPS, GLONASS, Galileo…•System accuracy is independent of vehicle position trajectory8/31/202417(c)Shau-Shiun Jan, IAA, NCKUBrief History of Navigation•Land Navigation – “pilotage” traveling by reference to land marks.•Marine Navigation –Greeks (300~350 B.C.) – Record of going far north as Norway, “Periodic Scylax” (Navigation manual).–Vikings (1000 A.D.) – had compass–Ferdinand Magellan (1519) – recorded 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)8/31/202418(c)Shau-Shiun Jan, IAA, NCKUDetermine Your LatitudePolarisEquatorsΛ=LatitudeΛγhsRE8/31/202419(c)Shau-Shiun Jan, IAA, NCKUHow do you determine longitude?•Dead reckoning–Compass for heading, log for speed•Not very accurate, heading errors, speed errors → position errors•Errors grow with time8/31/202420(c)Shau-Shiun Jan, IAA, NCKUThe Longitude Problem•Longitude act of 1714–£20,000 for 1/2o solution–£15,000 for 2/3o solution–£10,000 for 1o solution (about 111km resolution at equator!)•Board of longitude–Halley (“Halley Comet”)–Newton•Solution turned out to be a stable watch / clock 8/31/202421(c)Shau-Shiun Jan, IAA, NCKU20th Century and Aviation•Position fixing (guidance) systems:–Pilotage–Fires (1920) – US mail routes–Radio beacons•Late 1940’s most of the systems we use today started entering services•By 1960’s VOR/DME and ILS become standard in commercial aviation•Dead reckoning–Inertial navigation (1940)•German v-2 Rocket•Nuclear submarine (US NAVY)•Oceanic commercial flight8/31/202422(c)Shau-Shiun Jan, IAA, NCKU20th Century and Aviation•Satellite based navigation systems–US NAVY Transit System (1964)–Global Positioning System•1978 first satellite launched•1995 declared operational•Other satellite navigation systems–GLONASS – Former Soviet Union–Galileo – being developed by the EU8/31/202423(c)Shau-Shiun Jan, IAA, NCKUPerformance Metrics and Trade-Off1.Cost2.Autonomy3.Coverage4.Capacity5.Accuracy6.Availability7.Continuity8.Integrity•Area of active research: 5,6,7,8•Accuracy: we will visit it in detail later on.8/31/202424(c)Shau-Shiun Jan, IAA, NCKUPart 2: Navigation Coordinate Frames, Transformations and Geometry of Earth.–Navigation coordinate frames–Geometry of earth8/31/202425(c)Shau-Shiun Jan, IAA, NCKUCoordinate Frames•The position vector (the main output of any navigation system and our primary concern in this class) can be expressed in various coordinate frames.•Notation8/31/202426(c)Shau-Shiun Jan, IAA, NCKUWhy 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 in “ECEF”–INS: normally position in geodetic and velocity in “NED”8/31/202427(c)Shau-Shiun Jan, IAA, NCKUCoordinate Frames•Cartesian–ECEF–ECI–NED (locally tangent Frames)–ENU (locally tangent Frames)•Spherical/cylindrical–Geodetic–Azimuth-Elevation-Range –Bearing-Range-AttitudeExcept for ECI, all are non-inertial frames, an inertial frames is a non-accelerating (translation and rotation) coordinate frames.8/31/202428(c)Shau-Shiun Jan, IAA, NCKUECEF and ECI•Earth 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 Centered Inertial (ECI)–Cartesian frame with origin at earth’s center.–Z axis along earth’s rotation vector.–X-y plane in equatorial plane.8/31/202429(c)Shau-Shiun Jan, IAA, NCKUGeodetic•Geodetic (Latitude, Longitude, Altitude) – Spherical–Latitude (Λ) = north – south of equator, range ± 90o–Longitude (λ) = east – west of prime meridian, range ± 180o–Altitude (h) = height above reference datum–“+” north latitude, east longitude, down (below) datum altitude8/31/202430(c)Shau-Shiun Jan, IAA, NCKUNED and ENU•North-East-Down (NED)–Cartesian–No fixed location for the origin–Locally tangent to earth at origin•East-North-Up (ENU)–Cartesian–Similar to NED except for the direction of 1-2-3 axes.8/31/202431(c)Shau-Shiun Jan, IAA, NCKUAzimuth-Elevation-Range•Azimuth-Elevation-Range–Spherical–No fixed origin–Azimuth is angle between a line connecting the origin and the point of interest (in the tangent plane) and a line from origin to north pole–Elevation is the angle between the local tangent plane and a line connecting the origin to a point of interest–Range is the slant or line-of-sight distance8/31/202432(c)Shau-Shiun Jan, IAA, NCKUAzimuth-Elevation-Range•Two types of azimuth or heading angles•True: measured with respect to the geographic (true) north pole (ψT)•Magnetic: measured with respect to the magnetic north pole (ψM)8/31/202433(c)Shau-Shiun Jan, IAA, NCKUEarth Magnetic Field•1st order approximation is that of a simple dipole•Poles move with time.–In 1996 magnetic north pole was located at (79oN,105oW)–In 2003 it is located at (82oN,112oW) –Also, can “wander” by as much as 80km per day8/31/202434(c)Shau-Shiun Jan, IAA, NCKUEarth Magnetic Field•Magnetic poles are used in navigation because ψM is easier to measure than ψT •Bx and By are measured by devices called magnetometers (Ch.9)•Anomalies such as local iron deposits lead to erroneous ψM reading–Iron range deposits of N.E. Minnesota can lead to errors as large as 50o 8/31/202435(c)Shau-Shiun Jan, IAA, NCKUShape / Geometry of Earth1.Topographical / physical surface2.Geoid3.Reference ellipsoid8/31/202436(c)Shau-Shiun Jan, IAA, NCKUShape / Geometry of Earth (continued)•Topographical surface – shape assumed by earth’s crust. Complicated and difficult to model mathematically.•Geoid – an equipotential surface of earth’s 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 revolution and minimizes the mean-square deviation of local gravity (i.e., local norm to geoid) and ellipsoid norm, WGS-848/31/202437(c)Shau-Shiun Jan, IAA, NCKULatitude8/31/202438(c)Shau-Shiun Jan, IAA, NCKUWGS–84 •Four defining parameters•Other parameters are derived from the four–Equatorial radius = 6378.137km–Flattening = 1/298.257223563–Rotation rate of earth in inertial space = 15.041067 degree/hour–Earth’s gravitational constant (GM) = 3.986004x108m3/s28/31/202439(c)Shau-Shiun Jan, IAA, NCKUPart3:Radio Navigation Systems I: FundamentalsI: FundamentalsII: Survey of Current Systems8/31/202440(c)Shau-Shiun Jan, IAA, NCKURadio Navigation Systems•These 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 and 300 GHz 8/31/202441(c)Shau-Shiun Jan, IAA, NCKUFrequencyFrequenciesWavelength Very Low Frequency (VLF)< 30 KHz>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 (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 mm8/31/202442(c)Shau-Shiun Jan, IAA, NCKUFrequency•GPS signals are L band Signals•MLS uses C band signalsExpand8/31/202443(c)Shau-Shiun Jan, IAA, NCKURadio Signal Propagation (1/3)•Ground Waves–Waves below the HF range (i.e., < 3 MHz)–Unpredictable path characteristics–Required large antenna–Atmospheric noise 8/31/202444(c)Shau-Shiun Jan, IAA, NCKURadio Signal Propagation (2/3)•Line of Sight Waves:–Signals > 30 MHz–100 MHz – 3 GHz – predictable–Above 3 GHz – absorption–Above 10 GHz – discrete absorption8/31/202445(c)Shau-Shiun Jan, IAA, NCKURadio Signal Propagation (3/3)•Sky Waves–HF and below (i.e., < 30 MHz)–Multipath–Fading–Skip distance: depends of frequency and ionosphere conditions8/31/202446(c)Shau-Shiun Jan, IAA, NCKUModulation Techniques•Modulation – how you place information of the RF signal•Amplitude modulation (AM) – change the amplitude of sinusoid to relay information •Frequency modulation (FM) – change in frequency of transmitted signal to relay information•Phase modulation (PM) – change phase of transmitted signal to relay information•The signal can be transmitted as a pulse or a continuous wave. Either one can be modulated by the above methods. 8/31/202447(c)Shau-Shiun Jan, IAA, NCKUHow do you distinguish one beacon from another?•Frequency division multiple access (FDMA) – each transmitter/beacon uses a different frequency •Time division multiple access (TDMA) – each transmitter/beacon transmits at a specified time•Code division multiple access (CDMA) –each transmitter/beacon uses an identifier code to distinguish itself from the other transmitters or beacons8/31/202448(c)Shau-Shiun Jan, IAA, NCKUImportant Conclusions•Low frequency systems – ground wave transmission – long range systems, Loran.•High frequency systems – line of sight systemsPhysical QuantityNameSensor PropertiesDistance / RangeρL.O.S.BearingθL.O.S.ΔtTDOAGround Wave8/31/202449(c)Shau-Shiun Jan, IAA, NCKU8/31/202450(c)Shau-Shiun Jan, IAA, NCKUPhases of FlightTakeoffDeparture(Climb)En RouteApproach(Descent)Landing8/31/202451(c)Shau-Shiun Jan, IAA, NCKUPhases of Flight•Takeoff – Starts at takeoff roll and ends when climb is established. •Departure – Ends when the aircraft has left the so called terminal area.•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-σ) over land and 12 N.M over oceans. 8/31/202452(c)Shau-Shiun Jan, IAA, NCKUEn RouteNAV beacon (NAVAID)DestinationRandom or area navigationDeparture8/31/202453(c)Shau-Shiun Jan, IAA, NCKUPhases of Flight•Approach – 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 Haze8/31/202454(c)Shau-Shiun Jan, IAA, NCKUAccuracy Requirement•Accuracy 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 LandingVOR, DME, Radar*, ILS, MLS*Used by the ground based controllers to give the user “steering“ directions and to ensure traffic separation between aircraft. 8/31/202455(c)Shau-Shiun Jan, IAA, NCKUVORVOR (VHF Omni-Directional Range)•Provides bearing information•Uses VHF radio signals–FDMA with frequencies between 112 and 117.95 MHZ–Bearing accuracy 1o to 3o•Works by comparing the phase of 2 sinusoids. One has bearing dependent phase the other doesn’t.8/31/202456(c)Shau-Shiun Jan, IAA, NCKUDMEDME (Distance Measuring Equipment):•Measures slant range ρ•Operates between 962 – 1213 MHz•Accuracy – 0.1 to 0.17 n.m. (nominal) (185 ~ 315 m)•Principle of operation1.Airborne unit sends a pair of pulses2.Ground based beacon (transponder) picks up the signal3.After a 50μsec delay, transponder replies4.Airborne unit receives pulse pair and computes range by :8/31/202457(c)Shau-Shiun Jan, IAA, NCKUDME•How does a particular user distinguish their pulse from that of other users? •Normally, VOR and DME are collocated, in the U.S. there are ~1000 VOR/DME beacons.8/31/202458(c)Shau-Shiun Jan, IAA, NCKUILSILS (Instrument Landing System):•System provides angular information •Used exclusively for approach and landing8/31/202459(c)Shau-Shiun Jan, IAA, NCKUILS•It provides information about deviation from the center line (θ) and guide slope (γ)•Includes marker beacons that are installed at discrete distances from the runway .–Outer Marker (OM) – 4 to 7 n.m. from runway–Middle Marker (MM) - ~3500 ft from runway–Inner Marker (IM) - 1000 ft from runway8/31/202460(c)Shau-Shiun Jan, IAA, NCKUDecision 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 ft700 ft visibilityIIIB: DH < 50 ft150 ft visibilityIIIC: No DHNo visibility8/31/202461(c)Shau-Shiun Jan, IAA, NCKUMLSMLS (Microwave Landing System):•Designed to “Look” like an ILS but mitigate the weaknesses of ILS. •Operates between ~ 5.0 – 5.2 GHz•Scanning beam used to provide both lateral (localizer equivalent) and vertical (glide slope) information.8/31/202462(c)Shau-Shiun Jan, IAA, NCKULORANLORAN (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. –Master station sends a signal.–After a short (known) delay, the secondary stations “fire” in sequence. •Accuracy ~ 0.25 n.m. (463 m)8/31/202463(c)Shau-Shiun Jan, IAA, NCKUPart4:Global Positioning System8/31/202464(c)Shau-Shiun Jan, IAA, NCKUSatellite Navigation Systems•Sputnik I (1957) – Beginning of the space age–A ground station at a known location can determine the satellite’s orbit from a record of Doppler shift.•US Navy's Transit–Applied Physics Lab (Johns Hopkins Univ.)–Initial concept in 1958. Fully operational in 1964.•Used by submarine fleet. •Later use by civilians. Decommissioned in 1996. 8/31/202465(c)Shau-Shiun Jan, IAA, NCKUSatellite Navigation Systems•US Navy and Air Force programs combined to become GPS –Basic architecture approved in 1973–1st satellite launch in 1978–Fully operational in 1995 (23 years!)•Other satellite navigation systems–GLONASS (Russia), Galileo (EU), Beiduo (China)•Called Global Navigation Satellite System (GNSS)8/31/202466(c)Shau-Shiun Jan, IAA, NCKUGPS System Objectives•To 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-levels 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 dither•Anti–spoofing (AS) – encryption 8/31/202467(c)Shau-Shiun Jan, IAA, NCKUSystem Design Considerations•Active or passive? → GPS is passive•Position fixing method → Doppler, hyperbolic, multilateration. GPS uses multilateration. •Pulsed vs. continuous wave (CW) signal → CDMA on same frequency (spread spectrum)–L1 = 1575.42 MHz–L2 = 1227.60 MHz–L3, L4 classified payloads on satellites–L5 = 1176.45 MHz, new civil frequency, not here yet8/31/202468(c)Shau-Shiun Jan, IAA, NCKUSystem Design Considerations•Carrier frequency: L-band. Ionospheric defraction less at higher frequencies but power loss is greater.•Constellation → LEO, MEO, or GEO?–LEO – 10–20 minutes visibility time per SV, 100 – 200 SVs required. (cheap)–MEO – 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. 8/31/202469(c)Shau-Shiun Jan, IAA, NCKUSystem Design Considerations•GPS uses a MEO constellation. 1st SV launched in 1978. •Development of system 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. –Ultra–stable clocks.–Spread spectrum signaling.–Integrated circuits. 8/31/202470(c)Shau-Shiun Jan, IAA, NCKUSystem Architecture8/31/202471(c)Shau-Shiun Jan, IAA, NCKUSpace Segment•24+ satellites•6 orbital planes•55 degree inclination•~12 hour orbits•4 SVs per plane•26561 Km from earth’s center•2.7 Km/sec8/31/202472(c)Shau-Shiun Jan, IAA, NCKUControl Segment•Control segment: consists of the master control station (MCS) and five monitor stations. •MCS: located at Schriever (formerly Falcon) Air Force base in Colorado Springs, CO.–Monitors orbits, maintains SV health–Maintain GPS time–Predict SV ephemeredes and clock parameters–Update navigation message–Command SV maneuvers•Monitor stations located at Hawaii*, Cape Canaveral, Ascension Island, Diego Garcia, and Kwajalein.*Does not have S-band data link. 8/31/202473(c)Shau-Shiun Jan, IAA, NCKUGPS Nominal Accuracy (95%)PPSSPS (SA ON)SPS*(SA OFF)Position Vertical22 m100 m10 mPosition Horizontal28 m156 m15 mTime 200 ns340 ns50 ns8/31/202474(c)Shau-Shiun Jan, IAA, NCKUPart5:Augmentation Systems8/31/202475(c)Shau-Shiun Jan, IAA, NCKUAugmentation Systems•Improve system performance by mitigating ranging errors and/or enhancing satellite geometry–Differential GPS (DGPS)–Pseudolites8/31/202476(c)Shau-Shiun Jan, IAA, NCKUDifferential GPS (DGPS)•Remove common mode errors and broadcast corrections to userReferenceStation(Known location)UserUser8/31/202477(c)Shau-Shiun Jan, IAA, NCKUPseudolites•Transmit GPS like signals from some spot on the surface of earth.•Enhance the geometry of the ranging signals.8/31/202478(c)Shau-Shiun Jan, IAA, NCKUGPS Range and Time Measurements•Signal leaves the satellite at time t = t0•Receiver gets signal at t = t1•Compare replica to received signal•Compute the time of flight τreceiverreplicareceived8/31/202479(c)Shau-Shiun Jan, IAA, NCKUGPS Time•Time kept by the master control station. Consists of a GPS week and GPS second of the week (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 (cesium or rubidium). Monitored by the MCS and its deviation modeled. 8/31/202480(c)Shau-Shiun Jan, IAA, NCKUFactors 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 remove 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?8/31/202481(c)Shau-Shiun Jan, IAA, NCKUIntuitive Explanation of the Effect of Satellite Geometry 8/31/202482(c)Shau-Shiun Jan, IAA, NCKUDOP•DOP 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 DOPs) as a function of time to determine when best satellite geometry occurs. •Typical PDOP values range from 1.5 (Good) to 5 (Bad).8/31/202483(c)Shau-Shiun Jan, IAA, NCKUDOP•It is more intuitive to deal with NED or ENU coordinates. Recasting the problem in NED (or ENU),8/31/202484(c)Shau-Shiun Jan, IAA, NCKUHDOP, VDOP, PDOP•Then,8/31/202485(c)Shau-Shiun Jan, IAA, NCKUGPS Error SourcesGPS Clock ErrorEphemeris ErrorIonospheric DelayTropospheric DelayReceiver noiseMultipathGPS SatellitesMan-made interference8/31/202486(c)Shau-Shiun Jan, IAA, NCKUDifferential GPS Concepts8/31/202487(c)Shau-Shiun Jan, IAA, NCKUError 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 noiseCode: 0.25 – 0.5 mCarrier: 1 – 2 mmCode: 0.25 – 0.5 mCarrier: 1 – 2 mm8/31/202488(c)Shau-Shiun Jan, IAA, NCKUWide Area Differential GPS•Local 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 reference 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.8/31/202489(c)Shau-Shiun Jan, IAA, NCKUWide Area Differential GPS•Master 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 pseudorange error into its constituents.•Examples of wide area systems:–US Coast Guard DGPS–FAA Wide Area Augmentation System (WAAS)–European Geostationary Navigation Overlay System (EGNOS)–Japanese MSAS8/31/202490(c)Shau-Shiun Jan, IAA, NCKUWAAS· 25 WAAS Reference Stations· 2 WAAS Master StationsGEOGPS SVs8/31/202491(c)Shau-Shiun Jan, IAA, NCKU。