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null民航導航系統原理與應用民航導航系統原理與應用成大民航研究所 詹劭勳 老師Course Information – BooksCourse 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, 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, 2001OutlineOutlinePart 1: Introduction Part 2: Navigation Coordinate Part 3: Radio Navigation Systems Part 4: Global Positioning System Part 5: Augmentation SystemsPart 1: Introduction An Overview of Navigation and GuidancePart 1: Introduction An Overview of Navigation and GuidanceNavigation and GuidanceNavigation and GuidanceNavigation: 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 pathExampleExampleGetting 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 problemApplicationsApplicationsAir Transportation Marine, Space, and Ground Vehicles Personal Navigation / Indoor Navigation SurveyingA Navigation or Guidance SystemA Navigation or Guidance SystemSteering 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 downNavigation State / State VectorNavigation State / State VectorA 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 spacePosition and VelocityPosition and VelocityMore often than not, we are interested in position and velocity vectors expressed in separate coordinates (more on this later…)AttitudeAttitudeWe 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”Attitude (continued)Attitude (continued)The first entry of the attitude “vector”, ψ, is called yaw or heading.Navigation and Guidance SystemsNavigation 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 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.Navigation and Guidance SystemsNavigation and Guidance SystemsCategories of NavigationCategories of NavigationDead Reckoning Positioning (position fixing) Navigation systems are either one of the two or are hybrids.Dead Reckoning SystemsDead 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 trajectoryPositioning / Position Fixing SystemsPositioning / Position Fixing SystemsDetermine 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 trajectoryBrief History of NavigationBrief History of NavigationLand 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)Determine Your LatitudeDetermine Your LatitudePolarisEquatorsΛ=LatitudeΛγhsREHow do you determine longitude?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 timeThe Longitude ProblemThe Longitude ProblemLongitude 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 20th Century and Aviation20th Century and AviationPosition 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 flight20th Century and Aviation20th Century and AviationSatellite 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 EUPerformance Metrics and Trade-OffPerformance Metrics and Trade-OffCost Autonomy Coverage Capacity Accuracy Availability Continuity Integrity Area of active research: 5,6,7,8 Accuracy: we will visit it in detail later on.Part 2: Navigation Coordinate Frames, Transformations and Geometry of Earth.Part 2: Navigation Coordinate Frames, Transformations and Geometry of Earth.Navigation coordinate frames Geometry of earth Coordinate FramesCoordinate FramesThe position vector (the main output of any navigation system and our primary concern in this class) can be expressed in various coordinate frames. Notation Why Multiple Coordinate Frames?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”Coordinate FramesCoordinate FramesCartesian 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.ECEF and ECIECEF 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 Centered Inertial (ECI) Cartesian frame with origin at earth’s center. Z axis along earth’s rotation vector. X-y plane in equatorial plane.GeodeticGeodeticGeodetic (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 altitude NED and ENUNED and ENUNorth-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.Azimuth-Elevation-RangeAzimuth-Elevation-RangeAzimuth-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 distanceAzimuth-Elevation-RangeAzimuth-Elevation-RangeTwo 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)Earth Magnetic FieldEarth Magnetic Field1st 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 dayEarth Magnetic FieldEarth Magnetic FieldMagnetic 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 Shape / Geometry of EarthShape / Geometry of EarthTopographical / physical surface Geoid Reference ellipsoidShape / Geometry of Earth (continued)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-84LatitudeLatitudeWGS–84 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/s2Part3:Radio Navigation Systems I: FundamentalsPart3:Radio Navigation Systems I: FundamentalsI: Fundamentals II: Survey of Current SystemsRadio Navigation SystemsRadio 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 and 300 GHz FrequencyFrequencyFrequencyFrequencyRadio Signal Propagation (1/3)Radio Signal Propagation (1/3)Ground Waves Waves below the HF range (i.e., < 3 MHz) Unpredictable path characteristics Required large antenna Atmospheric noise Radio Signal Propagation (2/3)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 absorptionRadio Signal Propagation (3/3)Radio Signal Propagation (3/3)Sky Waves HF and below (i.e., < 30 MHz) Multipath Fading Skip distance: depends of frequency and ionosphere conditionsModulation TechniquesModulation TechniquesModulation – 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. How do you distinguish one beacon from another?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 beaconsImportant ConclusionsImportant ConclusionsLow frequency systems – ground wave transmission – long range systems, Loran. High frequency systems – line of sight systemsnullPhases of FlightPhases of FlightTakeoffDeparture (Climb)En RouteApproach (Descent)LandingPhases of FlightPhases of FlightTakeoff – 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. En RouteEn RoutePhases of FlightPhases 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.Accuracy RequirementAccuracy RequirementAccuracy required during the approach and landing phases of flight depend on the type of operation being conducted.*Used by the ground based controllers to give the user “steering“ directions and to ensure traffic separation between aircraft. VORVORVOR (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.DMEDMEDME (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 operation Airborne unit sends a pair of pulses Ground based beacon (transponder) picks up the signal After a 50μsec delay, transponder replies Airborne unit receives pulse pair and computes range by :DMEDMEHow 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.ILSILSILS (Instrument Landing System): System provides angular information Used exclusively for approach and landingILSILSIt 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 runwayDecision Height (DH)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:MLSMLSMLS (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.LORANLORANLORAN (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)Part4:Global Positioning SystemPart4:Global Positioning SystemSatellite Navigation SystemsSatellite Navigation SystemsSputnik 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. Satellite Navigation SystemsSatellite Navigation SystemsUS 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)GPS System ObjectivesGPS 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-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 System Design ConsiderationsSystem Design ConsiderationsActive 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 yetSystem Design ConsiderationsSystem Design ConsiderationsCarrier 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. System Design ConsiderationsSystem Design ConsiderationsGPS 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. System ArchitectureSystem ArchitectureSpace SegmentSpace Segment24+ satellites 6 orbital planes 55 degree inclination ~12 hour orbits 4 SVs per plane 26561 Km from earth’s center 2.7 Km/secControl SegmentControl SegmentControl 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. GPS Nominal Accuracy (95%)GPS Nominal Accuracy (95%)Part5:Augmentation SystemsPart5:Augmentation SystemsAugmentation SystemsAugmentation SystemsImprove system performance by mitigating ranging errors and/or enhancing satellite geometry Differential GPS (DGPS) PseudolitesDifferential GPS (DGPS)Differential GPS (DGPS)Remove common mode errors and broadcast corrections to userPseudolitesPseudolitesTransmit GPS like signals from some spot on the surface of earth. Enhance the geometry of the ranging signals.GPS Range and Time MeasurementsGPS Range and Time MeasurementsSignal leaves the satellite at time t = t0 Receiver gets signal at t = t1 Compare replica to received signal Compute the time of flight τGPS TimeGPS TimeTime 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. Factors Effecting GPS AccuracyFactors 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, Mu