GPS and Recent Alternatives for
Localisation
Dr. Thierry Peynot
Australian Centre for Field Robotics
The University of Sydney
Global Positioning System (GPS)
•  All-weather and continuous signal system designed to
provide information to evaluate accurate position
worldwide, using a constellation of satellites
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Robots and GPS
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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: 24th satellite launched (full constellation)
•  Cost at that point: USD $5 billion
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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.”
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Applications
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Navigation
Fleet Tracking
Transport
Cartography
Surveying
Clock Synchronisation
Robotics
Etc…
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Global Positioning System (GPS)
GPS consists of 3 major segments:
•  Space Segment
•  Control Segment
•  User Segment
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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
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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
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User Segment
•  (Passive) GPS receivers using GPS signal
information
•  Requirement: satellite needs to be in the line of sight
of the antenna
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GPS Operation Overview
•  Satellites transmit information at two frequencies:
–  L1 = 1575.42 MHz
–  L2 = 1227.6 MHz
•  GPS signal modulated with C/A (Coarse Acquisition) and P
(Precision) codes and with a 50 BPS navigation message:
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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 t0 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
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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
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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
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GPS Obervables
•  Precision of the solution affected by two main factors:
–  PDOP (Position Dilution of Precision)
–  Precision in range determination
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Position Determination
•  Position univocally determined when ranges to at
least 3 satellites are available
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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
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Position Determination
•  Known
–  Ephemerides of 4 satellites in view (xi, yi, zi)
–  Ranges from these 4 satellites (ri)
•  Unknown:
–  GPS receiver position (x,y,z)
–  Clock drift
•  => Set of non-linear equations:
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Position Determination
•  GPS receivers usually linearise these equations:
where 𝜀 = errors due to range noise and missing higher order terms
in the linearisation.
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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:
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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
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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
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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: 0.2-0.5m
•  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
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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
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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:
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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
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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)
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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)
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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
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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
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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)
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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
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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
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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
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(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)
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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
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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 (L1
1597-1617 MHz and L2 1240-1260 MHz)
–  Better positioning than GPS in high latitudes (north or south)
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GLONASS
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Image from Wikipedia 38
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
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Coordinate Transformation
•  GPS solution in ECEF coordinates (Earth-Centered,
Earth-Fixed)
Latitude
Longitude
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Coordinate Transformations
•  From ECEF coordinates to geodetic coordinates
(latitude and longitude):
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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
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UTM Grid
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GPS Limitations
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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
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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
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SLAM Estimation Process
 Prediction
Use vehicle model to predict vehicle
position
VehiclePath
Path
Vehicle
Vehicle
Path
Z2
 Observation
Z1
Z3
Take feature observation(s)
0
x5
Z4
 Update
00x
00xx
2x22
2
0x
6
Validated observations used to
generate optimal estimate
Initialise new target
Vehicle Path
000x
xxvvv
0000
xx3333
0x
v
FFF
0000 0000
xx1x111
000xx
x444
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Visual SLAM
Video - Click Here
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IR SLAM
Video - Click Here
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3D Laser SLAM
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Main References
•  US Department of Defense. Global Positioning System Precise
Positioning Service Performance Standard. February 2007.
http://www.gps.gov/technical/ps/2007-PPS-performance-standard.pdf
•  US Department of Defense. Global Positioning System Standard
Positioning Service Performance Standard. 4th edition,
September 2008. http://www.gps.gov/technical/ps/2008-SPSperformance-standard.pdf
•  E. Nebot. Navigation System Design. The University of Sydney.
2008.
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GPS and Recent Alternatives for
Localisation
Dr. Thierry Peynot
Australian Centre for Field Robotics
The University of Sydney