Gps Theory and Applications

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GPS: Theory of Operation andApplications

Christopher R. Carlson

March 18, 2004

D

D

L

ynamic

esign

aboratory

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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


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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



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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



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There are three GPS Segments

Monitor Stations

User SegmentControl Segment

Space Segment

Master Control

Control, Space and User SegmentStanford University GPS: Theory of Operation and Applications - 6 Dynamic Design Lab


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Control Segment

Control segment tracks satellites and updates their orbit

information (the satellites know their own positions)Stanford University GPS: Theory of Operation and Applications - 7 Dynamic Design Lab


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Space Segment

Needs at least 24 satellites for full coverageStanford University GPS: Theory of Operation and Applications - 8 Dynamic Design Lab


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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


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Outline

GPS system description

How GPS works

Error sources

Differential GPS

GPS velocity

GPS heading determination

GPS for crash testing (?)

Summary



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Triangulation

1

3

2

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


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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


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Triangulation (again)

1

3

2

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


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GPS Position Applications

Navigating with a clear view of the sky

Sailing, hiking, most driving, geocachingStanford University GPS: Theory of Operation and Applications - 14 Dynamic Design Lab


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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

O li


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Outline


How GPS works

Error Sources

Differential GPS

GPS velocity



Summary


P i i l E S


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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 before

transmission 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 1.8mStanford University GPS: Theory of Operation and Applications - 17 Dynamic Design Lab

P i i l E S I


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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


P i i l E S I


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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


P i i l E S M lti th


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Principle Error Sources: Multipath

Reflected GPS signals have longer pseudoranges

Antenna placement and clever algorithms are all we can do


Principle Error So rces Satellite Geometr


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Principle Error Sources: Satellite Geometry

Better measurements from diverse satellite geometry

Vertical measurements 50% less accurate than horizontal


Outline


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Outline


How GPS works

Error sources

Differential GPS

GPS velocity



Summary


DGPS


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DGPS

user ref

Very accurate

difference

Cancels out common mode errors (primarily Ionosphere)

Good quality DGPS is good to 2cm


DGPS Applications


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DGPS Applications

Automatic farming Autonomous golf caddies

Automobile lane keepingStanford University GPS: Theory of Operation and Applications - 24 Dynamic Design Lab

Outline


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Outline


How GPS works

Error sources

Differential GPS

GPS Velocity



Summary


GPS Velocity


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GPS Velocity

d1 d3d2

t0 t2 t3t1

GPS velocity is differential GPS in time

Velocity calculated bydistance 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 cms


GPS Velocity Applications


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GPS Velocity Applications

GPS provides vehicle velocity in global frame

Can act as a measurement of road grade

Very handy for vehicles research


Outline


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Outline


How GPS works

Error sources

Differential GPS

GPS velocity



Summary


GPS Heading


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GPS Heading

Vehicle velocity not necessarily along heading

Two antennas measure heading directly


GPS Roll


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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


Experimental Setup


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Experimental Setup

Road Crown

Continuous 30km/h circle spanning test track Road crown for water drainage


GPS Roll and Road Grade


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G S G

-4

-2

0

2

4

Grade[deg]

GPS Road Grade Measurement (Right Turn)

0 10 20 30 40 50 60 70 80

-4

-2

0

2

Time [s]

RollA

ngle[d

eg]

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


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p p

Double lane change maneuver

Driver swerves in and out of lane


Double Lane Change Zoom


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g

13 14 15 16 17 18 19 20-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Time [s]

S

ideslip[deg]

Double Lane Change (Zoom)

GPSKinematicCorrelationObserver

Sideslip = Velocity Direction - Heading


Outline


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How GPS works

Error sources

Differential GPS

GPS velocity



Summary


GPS Based Crash Testing


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g

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 not

otherwise feasible with cable systemStanford University GPS: Theory of Operation and Applications - 36 Dynamic Design Lab



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GPS

measurement

system

ThrottleSteering

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 the

control unitStanford University GPS: Theory of Operation and Applications - 37 Dynamic Design Lab



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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 hardwareStanford University GPS: Theory of Operation and Applications - 38 Dynamic Design Lab

Summary Quiz


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Cocktail conversation questions,

What is the basic idea of how GPS works ?

What causes GPSs biggest errors ? What are the advantages of differential GPS ?

What is one non-obvious application of GPS ?


Summary Quiz Answers


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What is the basic idea of how GPS works ?

GPS uses satellites and timing to triangulate user position

What causes GPSs biggest errors?

Atmospheric uncertainty and multipath are the biggest error

sources

What are the advantages of differential GPS ?

DGPS improves GPS accuracy by cancelling out common modeerrors


Summary Quiz Answers


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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 ?


Fin


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Questions ?


Documents

Gps Theory and Applications