Transcript - Intelligent Machine Dynamics Lab at Georgia Tech

The Global Positioning
System
GPS Technologies and their Accuracies
Joe Frankel
Georgia Institute of Technology
February 10, 2003
Overview
1.
2.
3.
4.
5.
6.
7.
Motivation
GPS Basics
Differential GPS (DGPS)
Carrier Phase Tracking
Wide Area Augmentation Systems (WAAS)
Indoor GPS: Constellation 3Di
Accuracy Comparison
1. Motivation
Why study GPS?
Potential applications in robotics and controls:
► Autonomous
navigation
► Obstacle avoidance
► Robot/vehicle positioning
► Hazardous environments
► Trajectory calculations
X,Y,Z,t
2. GPS Basics
GPS BASICS
GPS Satellites = Space Vehicles (SVs)
►
Solar powered
►
3-4000 lbs each
►
10-parameter Almanacs approximate position
in space
►
Input Signals:
Corrections from control stations
►
Output Signals (2):
X,Y,Z and t data streams sent continuously from SVs
 L1 channel: C/A Code (Coarse Acquistion) – civil use
 L2 channel: P-Code (Precise) – military / special licensees only
GPS BASICS
Satellite Constellation
►
24-satellite constellation
(+3 backup=27)
Elevation 12,000 mi
► 2 orbits/day (each)
► Six orbital planes:
►
 55° inclination from equator
 60° spacing about poles
 4 SVs/plane
GPS BASICS
Air Force Ground Control
SVi
Corrections
(x,y,z,t)i
Control
Station
►
(x,y,z,t)i
+ Corrections
User
Continuous time and position corrections sent to space vehicles from
ground control
 Position corrections based on precise computer trajectory models
 Time corrections based on Universal Coordinated Time (UTC)
►
Time and position corrections re-transmitted from SVs to receivers
 Time error <100ns at receiver after correction
 Position error at receiver depends on which technology is used
►
Master control station at Schriever AFB, CO (formerly Falcon AFB)
GPS BASICS
SV Data Structure
1
2
Data frame:
1500 bits, 30 sec
3
4
5
1
Subframe:
300 bits, 6 sec
Complete
navigation
message:
25 frames,
12.5 min
Clock
corrections
Precise (ephemeris)
orbital position data
SV system data
2
.
.
.
25
►
►
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50Hz binary data sent in 300-bit packets (subframes)
5 subframes per frame, 25 frames per message
Message restarts every 12.5 min
Data is encrypted and modulated before transmission
Each subframe contains parity bits for data corrections
GPS BASICS
SV Data Transmission
SPS Carrier freq.
(uniform)
Pseudo-Random
Noise (PRN)
Data
@ 50Hz
PPS Carrier freq.
(uniform)
SV data (position, time, system info, etc.) logical OR’d with PRN code, then used to
modulate high-freq. carrier
► PRN codes are unique signatures for each SV, one C/A and one P-code for each
► L1 = SPS signal (civil use), repeats every 1023 cycles
► L2 = PPS signal (military and special use only), repeats every seven days
►
GPS BASICS
Code Phase Tracking
Actual PRN
received from SV
Replica of SV PRN
from receiver almanac
Signal match
strength
►
Receiver slides ‘replica’ of PRN code in time and compares with SV signal until a match is found,
identifying SV
►
Phase shift between signal and replica represents signal transit time (ti-T), ti=time on SV clock,
T=receiver time
GPS BASICS
Calculating Position
Where am I?
►
The receiver position is
calculated by solving a set of
four Pythagorean equations:
(x1
(x2
(x3
(x3
-
X)²
X)²
X)²
X)²
+
+
+
+
(y1
(y2
(y3
(y3
-
Y)²
Y)²
Y)²
Y)²
+
+
+
+
(z1
(z2
(z3
(z4
-
Z)²
Z)²
Z)²
Z)²
=
=
=
=
c²(t1
c²(t2
c²(t3
c²(t4
-
T-d1)²
T-d2)²
T-d3)²
T-d4)²
Where:
X,Y,Z and T are unknown position
and time at receiver
► (x,y,z)i are the four known satellite
positions
► di are the known differences in data
arrival time, from correction data
►
Receiver must calculate
actual position from best
fit between multiple
range calculations
GPS BASICS
Error Sources
SOURCE
ERROR CONTRIBUTION
Ionospheric delays
10 m
Tropospheric delays
1m
PRN Code Noise
1m
SV Clock
1m
SV Ephemeris Data
1m
Pseudo-Range Noise
1m
Receiver Noise
1m
Multi-Path
0.5 m
TYPICAL ERROR WITH
BASIC GPS
15 m
Note: Selective Availabilty (SA) limited accuracy of SPS service to 100m until May 2000
3. Differential GPS
SV position data
received by
reference station
Correction factors
computed from
position errors
Reference station
at known location
►
►
►
►
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►
SV position data
received by
remote receiver
Correction factors
transmitted to remote
receiver via radio frequency
Remote receiver
position modified by
correction factors
Remote receiver
Reference station at a fixed, known location computes its location from SV signals and
computes error correction factors
Correction factors are transmitted to remote receivers at radio frequency
Usable range <30 km from reference station
Reference receiver must be surveyed and located beforehand
Coast Guard maintains ref. stations along most US coastlines
Typical accuracy 1-5m
4. Carrier Phase Tracking
SV @ t2
t2-t1 >15 min
SV @ t1
Carrier waves
Reference station
at known location
Remote receiver
Reference receiver required, similar to DGPS
► Utilizes high frequency carrier waves instead of SV data and PRN code
► Remote position = reference position + difference in (x,y,z) derived from
difference in carrier cycle measurements
►
CARRIER PHASE TRACKING
Carrier Phase Cycle Changes
Remote receiver
Tagged cycles @ t1
10 cycles
Tagged cycles @ t2
Reference receiver
19 cm
►
►
►
►
►
Example: Range from reference to remote receiver has changed by 10
cycles between t1 and t2
Usable <30km from reference station
Accuracy 4-10cm for fast static processing, 1-5cm for post-processing 
Must acquire signal while stationary for at least 15 minutes 
Good for mapping and surveying, impractical for real-time navigation
5. Wide Area Augmentation System
(WAAS)
Wide Area Augmentation System
WAAS: Broadcast Corrections
Orbiting GPS
satellites
Geosynchronous WAAS satellites
Correction factors transmitted
to WAAS satellites
Correction factors rebroadcast across
the US to be used by anyone
Correction factors computedSVatdata
received at
Substations main
compute
ground stations
substations
local errors
Local errors transmitted to
main ground stations
West coast
►
►
►
►
►
►
►
Surveyed locations (25)
East coast
2 geosynchronous satellites
2 main ground stations on east & west coast
25 ground substations
Information broadcast with same data structure / same channel as GPS
Must have a WAAS-capable receiver to use
Accuracy <3m
Developed by FAA for aircraft landings
Other Techniques
► Post
Processing
 Data saved and position computed later
► Data
Links
 Hard-wire connections between reference and
remote receivers
► Internet
corrections
 Correction factors available online for post
processing
6. Indoor GPS: Constellation 3Di
TRANSMITTER
Transmitters
Each transmitter
rotates light beams
at a unique
frequency

Factory workspace
Receiver mounted to tool
IR Laser beams
rotate and fan out
►
►
►
►
►
►
LED strobe
Azimuth computed from rotating beams
Elevation computed from LED pulses
Factory workspace filled with 3-D coordinate grid of IR light
Receivers key into grid to determine position
System eliminates the need for awkward, rigid fixtures and hard tooling for accurate alignment of
large parts
Receivers can be mounted to parts, tools, fixtures, etc
Accuracy 4-8ppm – i.e. 0.4-0.8mm over 100m range
Implemented at Boeing Commercial Airplanes Manufacturing R&D
7. Accuracy Comparison & Applications
Technique
Accuracy (2)
Application
Basic GPS (SPS)
15 m
Worldwide navigation
PPS*
10 m
(restricted use)
DGPS
5m
Navigation over territory
outside US
Carrier Phase
Tracking
5 cm
Land Surveying
WAAS
3m
Navigation over territory
inside US
LAAS**
?
(under development)
Constellation 3Di
4-8ppm
Factory tool positioning
* Military and special licensees only
** Local Area Augmentation System coming soon to an airport near you!
References
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Dr. Peter H. Dana, UC Boulder Dept. of Geography
http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html
Garmin International, Inc
http://www.garmin.com/
Trimble Navigation Ltd.
http://www.trimble.com/index.html
Federal Geographic Data Committee
http://www.ngs.noaa.gov/FGCS/info/sans_SA/
P. Sharke, “Measuring across space and time”, Mechanical Engineering, ASME Jan
2003