The Global Positioning The Global Positioning SystemSystem

GPS Technologies and their GPS Technologies and their AccuraciesAccuracies

Joe FrankelJoe FrankelGeorgia Institute of TechnologyGeorgia Institute of Technology

February 10, 2003February 10, 2003

OverviewOverview

1.1. MotivationMotivation2.2. GPS BasicsGPS Basics3.3. Differential GPS (DGPS)Differential GPS (DGPS)4.4. Carrier Phase TrackingCarrier Phase Tracking5.5. Wide Area Augmentation Systems (WAAS)Wide Area Augmentation Systems (WAAS)6.6. Indoor GPS: Constellation 3DiIndoor GPS: Constellation 3Di7.7. Accuracy ComparisonAccuracy Comparison

1.1. Motivation Motivation

Why study GPS?Why study GPS?

Potential applications in robotics and controls:Potential applications in robotics and controls:

► Autonomous navigationAutonomous navigation► Obstacle avoidanceObstacle avoidance► Robot/vehicle positioningRobot/vehicle positioning► Hazardous environmentsHazardous environments► Trajectory calculationsTrajectory calculations

X,Y,Z,tX,Y,Z,t

2.2. GPS Basics GPS Basics

GPS Satellites = Space Vehicles GPS Satellites = Space Vehicles (SVs)(SVs)

► Solar poweredSolar powered

► 3-4000 lbs each3-4000 lbs each

► 10-parameter 10-parameter AlmanacsAlmanacs approximate position approximate position in spacein space

► Input Signals:Input Signals: Corrections from control stationsCorrections from control stations

► Output Signals (2):Output Signals (2):X,Y,Z and t data streams sent continuously from X,Y,Z and t data streams sent continuously from

SVsSVs L1 channel: C/A Code (Coarse Acquistion) – civil useL1 channel: C/A Code (Coarse Acquistion) – civil use L2 channel: P-Code (Precise) – military / special licensees L2 channel: P-Code (Precise) – military / special licensees

onlyonly

GPS BASICSGPS BASICS

Satellite ConstellationSatellite Constellation

► 24-satellite constellation 24-satellite constellation (+3 backup=27)(+3 backup=27)

► Elevation 12,000 miElevation 12,000 mi► 2 orbits/day (each) 2 orbits/day (each) ► Six orbital planes:Six orbital planes:

55° inclination from equator55° inclination from equator 60° spacing about poles60° spacing about poles 4 SVs/plane4 SVs/plane

GPS BASICSGPS BASICS

Air Force Ground ControlAir Force Ground Control

► Continuous time and position corrections sent to space vehicles Continuous time and position corrections sent to space vehicles from ground controlfrom ground control Position corrections based on precise computer trajectory modelsPosition corrections based on precise computer trajectory models Time corrections based on Universal Coordinated Time (UTC)Time corrections based on Universal Coordinated Time (UTC)

► Time and position corrections re-transmitted from SVs to receiversTime and position corrections re-transmitted from SVs to receivers Time error <100ns at receiver after correctionTime error <100ns at receiver after correction Position error at receiver depends on which technology is usedPosition error at receiver depends on which technology is used

► Master control station at Schriever AFB, CO (formerly Falcon AFB)Master control station at Schriever AFB, CO (formerly Falcon AFB)

ControlControlStationStation

UserUser

CorrectionsCorrections

(x,y,z,t)(x,y,z,t)ii(x,y,z,t)(x,y,z,t)ii

+ Corrections+ Corrections

SVSVii

GPS BASICSGPS BASICS

SV Data StructureSV Data Structure

► 50Hz binary data sent in 300-bit packets (subframes)50Hz binary data sent in 300-bit packets (subframes)► 5 subframes per frame, 25 frames per message5 subframes per frame, 25 frames per message► Message restarts every 12.5 minMessage restarts every 12.5 min► Data is encrypted and modulated before transmissionData is encrypted and modulated before transmission► Each subframe contains parity bits for data correctionsEach subframe contains parity bits for data corrections

Data frame:Data frame:1500 bits, 30 sec1500 bits, 30 sec

1

2

Subframe:Subframe:300 bits, 6 sec300 bits, 6 sec

1 2 3 4 5

Clock Clock correctionscorrections

.

.

.25

Precise (ephemeris)Precise (ephemeris)orbital position dataorbital position data SV system dataSV system data

CompleteCompletenavigationnavigationmessage:message:25 frames,25 frames,12.5 min12.5 min

GPS BASICSGPS BASICS

SV Data TransmissionSV Data Transmission

► SV data (position, time, system info, etc.) logical OR’d with PRN code, then used SV data (position, time, system info, etc.) logical OR’d with PRN code, then used to modulate high-freq. carrierto modulate high-freq. carrier

► PRN codes are unique signatures for each SV, one C/A and one P-code for eachPRN 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 L1 = SPS signal (civil use), repeats every 1023 cycles ► L2 = PPS signal (military and special use only), repeats every seven daysL2 = PPS signal (military and special use only), repeats every seven days

SPS Carrier freq.SPS Carrier freq.(uniform)(uniform)

Pseudo-Random Pseudo-Random Noise (PRN)Noise (PRN)

Data Data @ 50Hz@ 50Hz

PPS Carrier freq.PPS Carrier freq.(uniform)(uniform)

GPS BASICSGPS BASICS

Code Phase TrackingCode Phase Tracking

► Receiver slides ‘replica’ of PRN code in time and compares with SV signal until a Receiver slides ‘replica’ of PRN code in time and compares with SV signal until a match is found, identifying SVmatch is found, identifying SV

► Phase shift between signal and replica represents signal transit time (tPhase shift between signal and replica represents signal transit time (t ii-T), t-T), tii=time =time on SV clock, T=receiver timeon SV clock, T=receiver time

Replica of SV PRN Replica of SV PRN from receiver almanacfrom receiver almanac

Actual PRN Actual PRN received from SVreceived from SV

GPS BASICSGPS BASICS

Signal match Signal match strengthstrength

Calculating PositionCalculating Position

► The receiver position is The receiver position is calculated by solving a set of calculated by solving a set of four Pythagorean equations:four Pythagorean equations:

(x1 - X)² + (y1 - Y)² + (z1 - Z)² = c²(t1 - T-d1)² (x1 - X)² + (y1 - Y)² + (z1 - Z)² = c²(t1 - T-d1)² (x2 - X)² + (y2 - Y)² + (z2 - Z)² = c²(t2 - T-d2)² (x2 - X)² + (y2 - Y)² + (z2 - Z)² = c²(t2 - T-d2)² (x3 - X)² + (y3 - Y)² + (z3 - Z)² = c²(t3 - T-d3)² (x3 - X)² + (y3 - Y)² + (z3 - Z)² = c²(t3 - T-d3)² (x3 - X)² + (y3 - Y)² + (z4 - Z)² = c²(t4 - T-d4)² (x3 - X)² + (y3 - Y)² + (z4 - Z)² = c²(t4 - T-d4)²

Where:Where:► X,Y,Z and T are unknown position X,Y,Z and T are unknown position

and time at receiver and time at receiver ► (x,y,z)(x,y,z)ii are the four known are the four known

satellite positionssatellite positions► ddii are the known differences in are the known differences in

data arrival time, from correction data arrival time, from correction datadata

GPS BASICSGPS BASICS

Receiver must Receiver must calculate actual calculate actual position from best fit position from best fit between multiple between multiple range calculationsrange calculations

Receiver must Receiver must calculate actual calculate actual position from best fit position from best fit between multiple between multiple range calculationsrange calculations

Where am I?Where am I?Where am I?Where am I?

Error SourcesError Sources

SOURCESOURCE ERROR ERROR CONTRIBUTIONCONTRIBUTION

Ionospheric delaysIonospheric delays 10 m10 m

Tropospheric delaysTropospheric delays 1 m1 m

PRN Code NoisePRN Code Noise 1 m1 m

SV ClockSV Clock 1 m1 m

SV Ephemeris DataSV Ephemeris Data 1 m1 m

Pseudo-Range NoisePseudo-Range Noise 1 m1 m

Receiver NoiseReceiver Noise 1 m1 m

Multi-PathMulti-Path 0.5 m0.5 m

TYPICAL ERROR WITH TYPICAL ERROR WITH BASIC GPSBASIC GPS 15 m15 m

GPS BASICSGPS BASICS

Note: Selective Availabilty (SA) limited accuracy of SPS service to 100m until Note: Selective Availabilty (SA) limited accuracy of SPS service to 100m until May 2000May 2000

3.3. Differential GPS Differential GPS

► Reference station at a fixed, known location computes its location from SV Reference station at a fixed, known location computes its location from SV signals and computes error correction factorssignals and computes error correction factors

► Correction factors are transmitted to remote receivers at radio frequencyCorrection factors are transmitted to remote receivers at radio frequency► Usable range <30 km from reference stationUsable range <30 km from reference station► Reference receiver must be surveyed and located beforehandReference receiver must be surveyed and located beforehand► Coast Guard maintains ref. stations along most US coastlinesCoast Guard maintains ref. stations along most US coastlines► Typical accuracy 1-5mTypical accuracy 1-5m

Reference station Reference station at known locationat known location

Remote receiverRemote receiver

Correction factors Correction factors transmitted to remote transmitted to remote receiver via radio receiver via radio frequencyfrequency

SV position SV position data received data received by reference by reference stationstation

SV position SV position data received data received by remote by remote receiverreceiver

Remote receiver Remote receiver position modified position modified by correction by correction factorsfactors

Correction Correction factors factors computed from computed from position errorsposition errors

4.4. Carrier Phase Tracking Carrier Phase Tracking

► Reference receiver required, similar to DGPSReference receiver required, similar to DGPS► Utilizes high frequency carrier waves instead of SV data and PRN Utilizes high frequency carrier waves instead of SV data and PRN

codecode► Remote position = reference position + difference in (x,y,z) derived Remote position = reference position + difference in (x,y,z) derived

from difference in carrier cycle measurementsfrom difference in carrier cycle measurements

SV @ tSV @ t11

SV @ tSV @ t22 tt22-t-t11 >15 min >15 min

Reference station Reference station at known locationat known location

Remote receiverRemote receiver

Carrier wavesCarrier waves

Carrier Phase Cycle ChangesCarrier Phase Cycle Changes

► Example: Range from reference to remote receiver has changed by Example: Range from reference to remote receiver has changed by 10 cycles between t10 cycles between t11 and t and t22

► Usable <30km from reference stationUsable <30km from reference station► Accuracy 4-10cm for fast static processing, 1-5cm for post-processingAccuracy 4-10cm for fast static processing, 1-5cm for post-processing► Must acquire signal while stationary for at least 15 minutesMust acquire signal while stationary for at least 15 minutes► Good for mapping and surveying, impractical for real-time navigationGood for mapping and surveying, impractical for real-time navigation

CARRIER PHASE TRACKINGCARRIER PHASE TRACKING

10 cycles10 cycles

Remote receiverRemote receiver

Reference receiverReference receiver

Tagged cycles @ tTagged cycles @ t11 Tagged cycles @ tTagged cycles @ t22

19 cm19 cm

5.5. Wide Area Augmentation Wide Area Augmentation System (WAAS)System (WAAS)

WAAS: Broadcast CorrectionsWAAS: Broadcast CorrectionsWide Area Augmentation SystemWide Area Augmentation System

► 2 geosynchronous satellites2 geosynchronous satellites► 2 main ground stations on east & west coast2 main ground stations on east & west coast► 25 ground substations25 ground substations► Information broadcast with same data structure / same channel as GPSInformation broadcast with same data structure / same channel as GPS► Must have a WAAS-capable receiver to useMust have a WAAS-capable receiver to use► Accuracy <3mAccuracy <3m► Developed by FAA for aircraft landingsDeveloped by FAA for aircraft landings

Substations Substations compute local compute local

errorserrors

Surveyed locations (25)Surveyed locations (25)West coastWest coast East coastEast coast

Correction factors rebroadcast Correction factors rebroadcast across the US to be used by across the US to be used by

anyoneanyone SV data SV data received at received at substationsubstationss

Orbiting GPS Orbiting GPS satellitessatellites

WAASWAAS Geosynchronous WAAS satellitesGeosynchronous WAAS satellites

Local errors Local errors transmitted to main transmitted to main ground stationsground stations

Correction factors Correction factors transmitted to WAAS transmitted to WAAS satellitessatellites

Correction factors computed Correction factors computed at main ground stationsat main ground stations

Other TechniquesOther Techniques

►Post ProcessingPost Processing Data saved and position computed laterData saved and position computed later

►Data LinksData Links Hard-wire connections between reference Hard-wire connections between reference

and remote receiversand remote receivers

► Internet correctionsInternet corrections Correction factors available online for post Correction factors available online for post

processingprocessing

IR Laser beams IR Laser beams rotate and fan rotate and fan

outout

6.6. Indoor GPS: Constellation Indoor GPS: Constellation 3Di3Di

► Factory workspace filled with 3-D coordinate grid of IR lightFactory workspace filled with 3-D coordinate grid of IR light► Receivers key into grid to determine positionReceivers key into grid to determine position► System eliminates the need for awkward, rigid fixtures and hard tooling for accurate alignment of large partsSystem eliminates the need for awkward, rigid fixtures and hard tooling for accurate alignment of large parts► Receivers can be mounted to parts, tools, fixtures, etcReceivers can be mounted to parts, tools, fixtures, etc► Accuracy 4-8ppm – i.e. 0.4-0.8mm over 100m rangeAccuracy 4-8ppm – i.e. 0.4-0.8mm over 100m range► Implemented at Boeing Commercial Airplanes Manufacturing R&DImplemented at Boeing Commercial Airplanes Manufacturing R&D

Factory workspaceFactory workspace

TransmittersTransmitters

Receiver mounted to toolReceiver mounted to tool

LED strobe LED strobe

Each transmitter Each transmitter rotates light rotates light beams at a beams at a

unique frequencyunique frequency

TRANSMITTERTRANSMITTER

Azimuth computed from rotating beamsAzimuth computed from rotating beamsElevation computed from LED pulsesElevation computed from LED pulses

7.7. Accuracy Comparison & Accuracy Comparison & ApplicationsApplications

TechniqueTechnique Accuracy (2Accuracy (2)) ApplicationApplication

Basic GPS (SPS)Basic GPS (SPS) 15 m15 m Worldwide navigationWorldwide navigation

PPS*PPS* 10 m10 m (restricted use)(restricted use)

DGPSDGPS 5 m5 m Navigation over territory Navigation over territory outside USoutside US

Carrier Phase Carrier Phase TrackingTracking 5 cm5 cm Land Surveying Land Surveying

WAASWAAS 3 m3 m Navigation over territory Navigation over territory inside USinside US

LAAS**LAAS** ?? (under development)(under development)

Constellation 3DiConstellation 3Di 4-8ppm4-8ppm Factory tool positioningFactory tool positioning

* Military and special licensees only* Military and special licensees only** Local Area Augmentation System coming soon to an airport near ** Local Area Augmentation System coming soon to an airport near you!you!

ReferencesReferences► Dr. Peter H. Dana, UC Boulder Dept. of GeographyDr. Peter H. Dana, UC Boulder Dept. of Geography

http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.htmlhttp://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html► Garmin International, IncGarmin International, Inc

http://www.garmin.com/http://www.garmin.com/ ► Trimble Navigation Ltd.Trimble Navigation Ltd.

http://www.trimble.com/index.htmlhttp://www.trimble.com/index.html ► Federal Geographic Data CommitteeFederal Geographic Data Committee

http://www.ngs.noaa.gov/FGCS/info/sans_SA/http://www.ngs.noaa.gov/FGCS/info/sans_SA/ ► P. Sharke, “Measuring across space and time”, Mechanical Engineering, P. Sharke, “Measuring across space and time”, Mechanical Engineering,

ASME Jan 2003ASME Jan 2003