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GPS: Theory of Operation andApplications
Christopher R. Carlson
March 18, 2004
D
D
L
ynamic
esign
aboratory.
Motivation
� There are many interesting applications for GPS tech-nology
• Sailing, flying or hiking navigation
• Racing
• Automatic farming
• Bank transaction time stamping
� New applications are being discovered all of the time
Stanford University GPS: Theory of Operation and Applications - 2 Dynamic Design Lab
Goal of this Talk
� Introduce GPS technology
• There are obvious and non-obvious kinds of GPS information
� By the end of this talk, you should be able to explain toa friend
• How GPS works
• What causes the biggest errors in the GPS measurement
• What the advantages of Differential GPS are
• One non-obvious application of GPS
Stanford University GPS: Theory of Operation and Applications - 3 Dynamic Design Lab
Overview
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 4 Dynamic Design Lab
What is GPS?
� GPS: Global Position System
� Designed and built by the US DOD
• Completely passive for the user
• Has both a military and a civilian channel
� Now quickly becoming a commodity
• GPS will soon appear in cell phones
• Already an option on many cars
• Available for less than $100 at REI
Stanford University GPS: Theory of Operation and Applications - 5 Dynamic Design Lab
There are three GPS Segments
Monitor Stations
User SegmentControl Segment
Space Segment
Master Control
� Control, Space and User Segment
Stanford University GPS: Theory of Operation and Applications - 6 Dynamic Design Lab
Control Segment
� Control segment tracks satellites and updates their orbitinformation (the satellites know their own positions)
Stanford University GPS: Theory of Operation and Applications - 7 Dynamic Design Lab
Space Segment
� Needs at least 24 satellites for full coverage
Stanford University GPS: Theory of Operation and Applications - 8 Dynamic Design Lab
User Segment
� Users are completely passive observers of GPS signals
� (Once you have a receiver, there is no subscription)
Stanford University GPS: Theory of Operation and Applications - 9 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 10 Dynamic Design Lab
Triangulation
ρ1
ρ3
ρ2
x, y1 1x, y2 2
x, y
x, y3 3
� Fundamentally, GPS is a triangulation like system
� Satellite positions are known, need to know distancesStanford University GPS: Theory of Operation and Applications - 11 Dynamic Design Lab
Speed of Light
11:30.00 am
11:30.08 am
D = c * t
� GPS uses time and the speed of light to get distance
� GPS Satellites are synchronized atomic clocksStanford University GPS: Theory of Operation and Applications - 12 Dynamic Design Lab
Triangulation (again)
ρ1
ρ3
ρ2
x, y1 1
t
x, y2 2
x, y3 3
Time Bias
� Users have piezo clocks, error is common to all satellites
� Now there are 4 equations and 4 unknownsStanford University GPS: Theory of Operation and Applications - 13 Dynamic Design Lab
GPS Position Applications
� Navigating with a clear view of the sky
� Sailing, hiking, most driving, geocaching
Stanford University GPS: Theory of Operation and Applications - 14 Dynamic Design Lab
Clock Error Applications
� GPS knows the exact time of day within 1e-9 seconds
� Used to synchronize international banking transactionsStanford University GPS: Theory of Operation and Applications - 15 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error Sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 16 Dynamic Design Lab
Principle Error Sources
� The sky is totally or partially occluded
• Need a minimum of 4 satellites for a position solution
• Most of the time we have more than that
• Good GPS receivers know when their measurements are poor
� Selective Availability (SA)
• Deliberate white noise added to the clock information beforetransmission from the satellites
• Stand alone GPS was good to about 100 m
• Clinton turned SA off in May 2000
• Stand alone GPS is now as good as 1.8m
Stanford University GPS: Theory of Operation and Applications - 17 Dynamic Design Lab
Principle Error Sources: Iono
Iono
Tropo
Military
Civilian
� Ionosphere and Troposphere lengthen GPS carrier path
• About 50% of this error may be compensated with a model
Stanford University GPS: Theory of Operation and Applications - 18 Dynamic Design Lab
Principle Error Sources: Iono
� The military can actually correct for this since they havetwo GPS channels
• This is somewhat possible even for civilian users
• Is an option on most high end receivers
� Requires double the hardware (and costs more than double)
� Military and civilian channels are different frequencies
• They are each effected by the ionosphere and troposphere dif-ferently
• Like red light and blue light travelling though a prism
Stanford University GPS: Theory of Operation and Applications - 19 Dynamic Design Lab
Principle Error Sources: Multipath
� Reflected GPS signals have longer pseudoranges
• Antenna placement and clever algorithms are all we can do
Stanford University GPS: Theory of Operation and Applications - 20 Dynamic Design Lab
Principle Error Sources: Satellite Geometry
� Better measurements from diverse satellite geometry
• Vertical measurements ∼50% less accurate than horizontal
Stanford University GPS: Theory of Operation and Applications - 21 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 22 Dynamic Design Lab
DGPS
user ref
Very accurate
difference
� Cancels out common mode errors (primarily Ionosphere)
• Good quality DGPS is good to 2cm
Stanford University GPS: Theory of Operation and Applications - 23 Dynamic Design Lab
DGPS Applications
� Automatic farming
� Autonomous golf caddies
� Automobile lane keepingStanford University GPS: Theory of Operation and Applications - 24 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS Velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 25 Dynamic Design Lab
GPS Velocity
d1 d3d2
t0 t2 t3t1
� GPS velocity is differential GPS in time
• Velocity calculated by distance travelled
time to travel
• The principle errors due to the atmosphere are slowly varying
• Subtracting to positions removes them
• GPS velocity in practice is accurate to about 2 cm
s
Stanford University GPS: Theory of Operation and Applications - 26 Dynamic Design Lab
GPS Velocity Applications
θ
θ
� GPS provides vehicle velocity in global frame
� Can act as a measurement of road grade
� Very handy for vehicles research
Stanford University GPS: Theory of Operation and Applications - 27 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 28 Dynamic Design Lab
GPS Heading
� Vehicle velocity not necessarily along heading
� Two antennas measure heading directly
Stanford University GPS: Theory of Operation and Applications - 29 Dynamic Design Lab
GPS Roll
� Can just as easily place antennas across roof
� Now have a direct measurement of vehicle roll
• This is very useful for vehicle dynamics researchers
• May be included in future stability control systems
Stanford University GPS: Theory of Operation and Applications - 30 Dynamic Design Lab
Experimental Setup
Road Crown
� Continuous 30km/h circle spanning test track
� Road crown for water drainage
Stanford University GPS: Theory of Operation and Applications - 31 Dynamic Design Lab
GPS Roll and Road Grade
-4
-2
0
2
4
Gra
de [deg]
GPS Road Grade Measurement (Right Turn)
0 10 20 30 40 50 60 70 80-4
-2
0
2
Time [s]
Roll
Angle
[deg]
GPS Roll Angle Measurement
� Continuous 30km/h circle spanning test track
� Road crown is clearly measurable as roll and gradeStanford University GPS: Theory of Operation and Applications - 32 Dynamic Design Lab
Experimental Setup II
� Double lane change maneuver
� Driver swerves in and out of lane
Stanford University GPS: Theory of Operation and Applications - 33 Dynamic Design Lab
Double Lane Change Zoom
13 14 15 16 17 18 19 20-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
Time [s]
Sid
esl
ip [deg]
Double Lane Change (Zoom)
GPSKinematicCorrelationObserver
� Sideslip = Velocity Direction - Heading
Stanford University GPS: Theory of Operation and Applications - 34 Dynamic Design Lab
Outline
� GPS system description
� How GPS works
� Error sources
� Differential GPS
� GPS velocity
� GPS heading determination
� GPS for crash testing (?)
� Summary
Stanford University GPS: Theory of Operation and Applications - 35 Dynamic Design Lab
GPS Based Crash Testing
� Current systems often use cable drives and sleds to com-mand a desired speed and direction
� It may be possible to recreate collisions with GPS nototherwise feasible with cable system
Stanford University GPS: Theory of Operation and Applications - 36 Dynamic Design Lab
GPS Based Crash Testing
GPS
measurement
system
Throttle
Steering
Control
Desired Collision Paths
� Desired crash trajectories set by crash engineer
� Reusable control system controls steering and throttlefor each vehicle
� GPS measures vehicle speed, position and updates thecontrol unit
Stanford University GPS: Theory of Operation and Applications - 37 Dynamic Design Lab
GPS Based Crash Testing
� Advantages
• Different locations possible with relatively minor preparation
• Independent of road condition: snow, sand, asphalt
• Independent of road grade
• Can still use cameras
• Still possible to know precise speed and heading at impact
• No limit to the number of vehicles involved in the collision
� Disadvantages
• May be a little on the expensive side
• Requires customized hardware
Stanford University GPS: Theory of Operation and Applications - 38 Dynamic Design Lab
Summary Quiz
� Cocktail conversation questions,
• What is the basic idea of how GPS works ?
• What causes GPS’s biggest errors ?
• What are the advantages of differential GPS ?
• What is one non-obvious application of GPS ?
Stanford University GPS: Theory of Operation and Applications - 39 Dynamic Design Lab
Summary Quiz Answers
� What is the basic idea of how GPS works ?
• GPS uses satellites and timing to triangulate user position
� What causes GPS’s biggest errors?
• Atmospheric uncertainty and multipath are the biggest errorsources
� What are the advantages of differential GPS ?
• DGPS improves GPS accuracy by cancelling out common modeerrors
Stanford University GPS: Theory of Operation and Applications - 40 Dynamic Design Lab
Summary Quiz Answers
� What is one non-obvious application of GPS ?
• Global transaction synchronization
• Automatic farming
• Vehicle velocity measurement
• Road grade measurement
• Vehicle heading estimation
• Coordinated collision of vehicles ?
Stanford University GPS: Theory of Operation and Applications - 41 Dynamic Design Lab
Fin
Questions ?
Stanford University GPS: Theory of Operation and Applications - 42 Dynamic Design Lab