GPS and Recent Alternatives for Localisation. Dr. Thierry Peynot Australian Centre for Field Robotics The University of Sydney

Transcription

1 GPS and Recent Alternatives for Localisation Dr. Thierry Peynot Australian Centre for Field Robotics The University of Sydney

2 Global Positioning System (GPS) All-weather and continuous signal system designed to provide information to evaluate accurate position worldwide, using a constellation of satellites Thierry Peynot GPS and Alternative Localisation Methods 2

3 Robots and GPS Thierry Peynot GPS and Alternative Localisation Methods 3

4 A Bit of History 1973: Defense Navigation Satellite System (DNSS) Navigation System Using Timing and Ranging (Navstar) Navstar-GPS Global Positioning System (GPS) 1989: first satellite launch 1994: 24 th satellite launched (full constellation) Cost at that point: USD $5 billion Thierry Peynot GPS and Alternative Localisation Methods 4

5 A Bit of History (cont d) Initially high quality signal reserved for military Signal for civilian use intentionally degraded (Selective Availability, SA). Precision ~100m Turned off 1 May 2000 => precision ~20m GPS: owned and operated by the United States government as a national resource The DoD is required by law to "maintain a Standard Positioning Service that will be available on a continuous, worldwide basis," and "develop measures to prevent hostile use of GPS and its augmentations without unduly disrupting or degrading civilian uses. Thierry Peynot GPS and Alternative Localisation Methods 5

6 Navigation Fleet Tracking Transport Cartography Surveying Applications Clock Synchronisation Robotics Etc Thierry Peynot GPS and Alternative Localisation Methods 6

7 Global Positioning System (GPS) GPS consists of 3 major segments: Space Segment Control Segment User Segment Thierry Peynot GPS and Alternative Localisation Methods 7

8 Space Segment (Original) Operational Constellation: 24 satellites that orbit the Earth with a period of 12 hours 6 orbital planes with 55 degrees inclination Radius of each plane: 20,200 km At least 4 satellites always in view anywhere in the world 8 or more 80% of the time Current constellation: 31 satellites Thierry Peynot GPS and Alternative Localisation Methods 8

9 Control Segment System of tracking stations distributed around the world Main objective: determine the position of the satellites to update their ephemeris Satellite clock correction also updated Thierry Peynot GPS and Alternative Localisation Methods 9

10 User Segment (Passive) GPS receivers using GPS signal information Requirement: satellite needs to be in the line of sight of the antenna Thierry Peynot GPS and Alternative Localisation Methods 10

11 GPS Operation Overview Satellites transmit information at two frequencies: L1 = MHz L2 = MHz GPS signal modulated with C/A (Coarse Acquisition) and P (Precision) codes and with a 50 BPS navigation message: Thierry Peynot GPS and Alternative Localisation Methods 11

12 GPS Operation Overview C/A (Coarse acquisition) code: 1 MHz pseudo-random binary sequence (PRBS) Separate C/A code (or Gold code) for each satellite Used by the receiver to identify satellite and obtain range information Each GPS receiver has a correlator and the PRBS for all 31 possible satellites Receiver correlates the received PRBS with each of the sequences stored on the board Done by shifting receiver own sequence from an estimated time t 0 until a peak of correlation is achieved This peak identifies the satellite number and the shift w.r.t. time indicates the distance to the satellite Thierry Peynot GPS and Alternative Localisation Methods 12

13 GPS Operation Overview Navigation message present in both L1 and L2 frequencies Contains information about the satellite ephemeris, clock correction parameters, and low precision ephemeris data for the other satellites After 30 seconds of continuous satellite tracking, the GPS receiver is able to achieve position determination After ~12.5min. of uninterrupted tracking of a given satellite the low precision ephemeris for the whole satellite constellation is downloaded (Almanac) The Standard Positioning Service (SPS) is based on C/A code in L1 frequency, available to general public The Precise Positioning Service (PPS) uses the P code available in both L1 and L2 frequencies, reserved to authorised users, encrypted Thierry Peynot GPS and Alternative Localisation Methods 13

14 GPS Obervables Pseudo-range: distance from satellite to receiver, plus additional errors due to clock drifts, ionosphere, troposphere, multi-path Doppler frequency information: receiver and satellites in constant motion w.r.t. each other => receiver signal experiences change in frequency proportional to relative velocities. Can be used for very accurate velocity estimation Makes velocity information independent of position (important for data fusion) Not all GPS receivers can exploit Doppler observation Thierry Peynot GPS and Alternative Localisation Methods 14

15 GPS Obervables Precision of the solution affected by two main factors: PDOP (Position Dilution of Precision) Precision in range determination Thierry Peynot GPS and Alternative Localisation Methods 15

16 Position Determination Position univocally determined when ranges to at least 3 satellites are available Thierry Peynot GPS and Alternative Localisation Methods 16

17 Position Determination The system uses 4 satellites to solve for the other unknown: time to synchronise receiver and satellite clocks => Receivers can have inexpensive clocks (satellites have very accurate atomic clocks). Latitude Longitude Thierry Peynot GPS and Alternative Localisation Methods 17

18 Position Determination Known Ephemerides of 4 satellites in view (x i, y i, z i ) Ranges from these 4 satellites (r i ) Unknown: GPS receiver position (x,y,z) Clock drift => Set of non-linear equations: Thierry Peynot GPS and Alternative Localisation Methods 18

19 Position Determination GPS receivers usually linearise these equations: where ε = errors due to range noise and missing higher order terms in the linearisation. Thierry Peynot GPS and Alternative Localisation Methods 19

20 Position Determination Change in position can then be evaluated by: When ranges from more than 4 satellites available, a least square solution can be implemented: Position updated with the correction to obtain the position of the receiver at the time stamp of the pseudo-range information: Thierry Peynot GPS and Alternative Localisation Methods 20

21 Most Common GPS Errors Satellite Clock Errors Ground Stations responsible for estimating the clock errors Parameters of the correction formula uploaded to satellite, which broadcasts them as part of the navigation message Each GPS receiver needs to compensate the pseudorange information accordingly Ephemeris Errors Ephemeris parameters transmitted with errors These errors grow with time since last updated from ground stations GPS receivers usually do not use satellites with ephemerides older than 2 hours Thierry Peynot GPS and Alternative Localisation Methods 21

22 Most Common GPS Errors Ionosphere Errors Free elections in the Ionosphere => GPS signal does not travel at the speed of light while in transit in this region These errors can be compensated using a diurnal model of these delays. Parameters of this model are in the GPS navigation message Errors after this compensation: in the order of 2-5m Other compensation method: using signals at both frequencies (L1 and L2) to solve for the delay. Can reduce errors to 1-2m Troposphere Errors Variation of speed of signal due to variation in temperature, pressure and humidity Model correction can reduce this error to order of 1m Thierry Peynot GPS and Alternative Localisation Methods 22

23 Most Common GPS Errors Receiver Errors Introduced by the GPS receiver when evaluating the range through the correlation process Mostly dependent on non-linear effects and thermal noise Magnitude of the error: m Multipath Errors Signal reaches the receiver through indirect path by multiple reflections => erroneous range and phase carrier difference information Can be reduced with: appropriate antenna selection, GPS receiver, accepting observations only from satellites with minimum elevation angle Thierry Peynot GPS and Alternative Localisation Methods 23

24 Most Common GPS Errors Selected Availability (SA) Deliberate error introduced by the US DoD Additional noise included in the transmitted satellite clock and satellite ephemeris of the SPS Disconnection announced in 2000 Thierry Peynot GPS and Alternative Localisation Methods 24

25 Most Common GPS Errors Geometric Dilution of Precision (GDOP) Quality of the solution of the position and clock bias error in relation with the error in the pseudo-range measurement is a function of the matrix A Assuming sigma standard deviation for the pseudo-range observation, the matrix covariance for the state p is: From this equation the various definitions of estimation accuracy can be defined: Thierry Peynot GPS and Alternative Localisation Methods 25

26 Most Common GPS Errors Geometric Dilution of Precision (GDOP) The estimated error of the individual component of the state vector p can be given as function of the DOP variables: Most GPS receivers evaluate these uncertainties in real time, allowing the user to monitor the accuracy of the solution Thierry Peynot GPS and Alternative Localisation Methods 26

27 Fundamental of Differential GPS (DGPS) Position errors can be significantly reduced with another station placed at a known surveyed locations Base station evaluates the range errors and broadcasts them to the other stations Usually placed in location with good sky visibility Processes information from satellites with at least 5 degrees over the horizon (to avoid multipath problems) Thierry Peynot GPS and Alternative Localisation Methods 27

28 Fundamental of Differential GPS (DGPS) DGPS significantly reduces errors due to delays in the Troposphere and Ionosphere (also could eliminate almost all the errors due to SA) With SA on, DGPS reduced positioning errors from ~100m to under a few metres Without SA the gain is less significant, except if fusion with INS (can achieve cm-accuracy) Thierry Peynot GPS and Alternative Localisation Methods 28

29 Phase Carrier GPS Advanced GPS receivers make use of phase carrier information to improve accuracy of the position fix Differential carrier phase tracking consists of measuring the phase shift between the same signal received at the base and the vehicle station. This phase shift is proportional to the distance between the two stations More complicated hardware and software needed Because measurements subject to phase ambiguities Real-Time Kinematic (RTK) satellite navigation Thierry Peynot GPS and Alternative Localisation Methods 29

30 Phase Carrier GPS When receiver unit is switched on and commences logging the initial whole cycle difference (ambiguity) between the satellite and the receiver is unknown Once the state of the ambiguity is held fixed, the receiver is said to have converged and the ambiguity is resolved. Each corresponding satellite signal ambiguity is held constant and the change in phase is used to calculate the change in the receiver s position Thierry Peynot GPS and Alternative Localisation Methods 30

31 Phase Carrier GPS Convergence time depends on a number of factors, including: Number of visible satellites Satellite configuration Baseline (i.e. distance between remote and reference stations) Method of ambiguity resolution (single frequency, dual frequency, or combined dual frequency and code pseudorange data) Thierry Peynot GPS and Alternative Localisation Methods 31

32 Phase Carrier GPS Experimental data from a Novatel GPS receiver working with 2 different algorithms: RT20: 20cm accuracy using L1 frequency RT2: 2cm accuracy using both L1 and L2 frequencies RT2 Thierry Peynot GPS and Alternative Localisation Methods 32

33 GPS/INS Fusion Inertial Measurement Unit (IMU): Composed of accelerometers and gyroscopes Provides raw accelerations and rotation rate data Inertial Navigation System (INS): IMU used for navigation Provides position, velocities and attitude information Thierry Peynot GPS and Alternative Localisation Methods 33

34 GPS/INS Fusion GPS: Good global accuracy Limited local accuracy (at least metre) Low update frequency (typically ~1 Hz) Rely on satellite visibility (line of sight) GPS signal can be jammed INS (Inertial Navigation System): Good local accuracy High update frequency (can be several hundreds Hz) Non-radiating and cannot be jammed Drift over time GPS/INS Fusion => best of both worlds Thierry Peynot GPS and Alternative Localisation Methods 34

35 (Some) External Aiding Signals Time of Arrival (Range Measurements) GSM (Global System for Mobile Communications) Good urban coverage DAB (Digital Audio Broadcasting) Poor coverage DVB (Digital Video Broadcasting) 3G Good urban coverage High bandwidth Carrier Phase Measurements MW (Medium Wave radio signals) Thierry Peynot GPS and Alternative Localisation Methods 35

36 GPS Alternatives Russian Global Navigation Satellite System (GLONASS). Development started 1976 Satellite constellation completed 1995 (24 operational satellites) Down to 6 operational satellites in 2001 Back to complete constellation and full coverage by 2011 Full precision signal available to public in 2007 Only alternative to GPS in operation with global coverage and of comparable precision Limited commercialisation, but new rules from Russian government aimed at encouraging/forcing products using GPS to be compatible with GLONASS as well Thierry Peynot GPS and Alternative Localisation Methods 36

37 GLONASS Russian Global Navigation Satellite System (GLONASS). Also transmits navigation and range data on freq. L1 and L2 Satellites distinguished by frequency of the signal (L MHz and L MHz) Better positioning than GPS in high latitudes (north or south) Thierry Peynot GPS and Alternative Localisation Methods 37

38 GLONASS Thierry Peynot GPS and Alternative Localisation Methods Image from Wikipedia 38

39 GPS Alternatives (cont d) European Union Galileo Planned to be operational by 2014 Fully deployed by 2019 Chinese COMPASS (Beidou 2) Beidou 1: limited to Asia and West Pacific Beidou 2: Global coverage by 2020 Indian Regional Navigational System (IRNSS) Coverage: India & Northern Indian Ocean ETA: 2014 Thierry Peynot GPS and Alternative Localisation Methods 39

40 Coordinate Transformation GPS solution in ECEF coordinates (Earth-Centered, Earth-Fixed) Latitude Longitude Thierry Peynot GPS and Alternative Localisation Methods 40

41 Coordinate Transformations From ECEF coordinates to geodetic coordinates (latitude and longitude): Thierry Peynot GPS and Alternative Localisation Methods 41

42 Representations Universal Transverse Mercator (UTM) geographic system 2D Cartesian coordinate system for locations on the surface of the Earth Earth divided in 60 zones, each a 6 -band of longitude Uses a secant transverse Mercator projection in each zone Each zone segmented into 20 latitude bands (of 8 ), lettered C to X (except I & O ) Zone + latitude band = grid zone Thierry Peynot GPS and Alternative Localisation Methods 42

43 UTM Grid Thierry Peynot GPS and Alternative Localisation Methods 43

44 GPS Limitations Thierry Peynot GPS and Alternative Localisation Methods 44

45 Localisation using Landmarks Landmarks whose locations are known a priori (E.g. beacon-based navigation) Similar to a GPS with fixed satellites Landmarks a priori unknown Thierry Peynot GPS and Alternative Localisation Methods 45

46 Simultaneous Localisation and Mapping (SLAM) Process: Start at an unknown location with no a priori knowledge of landmark locations From relative observations of landmarks, compute estimate of vehicle location and estimate of landmark locations While continuing in motion, build complete map of landmarks and use these to provide continuous estimates of vehicle location Correlated Landmark Errors Estimated Vehicle Path True Vehicle Path Estimated Landmark True Thierry Peynot GPS and Alternative Localisation Methods Landmark 46

47 SLAM Estimation Process Prediction Use vehicle model to predict vehicle position Z 2 Vehicle Path Vehicle Path Observation Take feature observation(s) 0 x 5 Z 1 Z 3 Update Validated observations used to generate optimal estimate 0 x 0 2 x x v v 0 x v 0 x 6 0 x 3 Z 4 Initialise new target F 0 F x x 4 4 Thierry Peynot GPS and Alternative Localisation Methods 47

48 Visual SLAM Video - Click Here Thierry Peynot GPS and Alternative Localisation Methods 48

49 IR SLAM Video - Click Here Thierry Peynot GPS and Alternative Localisation Methods 49

50 3D Laser SLAM Thierry Peynot GPS and Alternative Localisation Methods 50

51 Main References US Department of Defense. Global Positioning System Precise Positioning Service Performance Standard. February US Department of Defense. Global Positioning System Standard Positioning Service Performance Standard. 4 th edition, September E. Nebot. Navigation System Design. The University of Sydney Thierry Peynot GPS and Alternative Localisation Methods 51

52 GPS and Recent Alternatives for Localisation Dr. Thierry Peynot Australian Centre for Field Robotics The University of Sydney