The Global Positioning System GPS Technologies and their Accuracies Joe Frankel Georgia Institute of Technology February 10, 2003

Overview 1. Motivation 2. GPS Basics 3. Differential GPS (DGPS) 4. Carrier Phase Tracking 5. Wide Area Augmentation Systems (WAAS) 6. Indoor GPS: Constellation 3Di 7. 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 Satellites = Space Vehicles (SVs) ► Solar powered ► 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 ► 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) ControlStation User Corrections (x,y,z,t) i + Corrections SV i GPS BASICS

SV Data Structure ► 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 Data frame: 1500 bits, 30 sec 1 2 Subframe: 300 bits, 6 sec Clockcorrections Precise (ephemeris) orbital position data SV system data Completenavigationmessage: 25 frames, 12.5 min GPS BASICS

SV Data Transmission ► 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 SPS Carrier freq. (uniform) Pseudo-Random Noise (PRN) 50Hz PPS Carrier freq. (uniform) GPS BASICS

Code Phase Tracking ► 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 (t i -T), t i =time on SV clock, T=receiver time Replica of SV PRN from receiver almanac Actual PRN received from SV GPS BASICS Signal match strength

Calculating Position ► The receiver position is calculated by solving a set of four Pythagorean equations: (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 (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 Where: ► X,Y,Z and T are unknown position and time at receiver ► (x,y,z) i are the four known satellite positions ► d i are the known differences in data arrival time, from correction data GPS BASICS Receiver must calculate actual position from best fit between multiple range calculations Where am I?

Error Sources SOURCE ERROR CONTRIBUTION Ionospheric delays 10 m Tropospheric delays 1 m PRN Code Noise 1 m SV Clock 1 m SV Ephemeris Data 1 m Pseudo-Range Noise 1 m Receiver Noise 1 m Multi-Path 0.5 m TYPICAL ERROR WITH BASIC GPS 15 m GPS BASICS Note: Selective Availabilty (SA) limited accuracy of SPS service to 100m until May 2000

3. Differential GPS ► 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 Reference station at known location Remote receiver Correction factors transmitted to remote receiver via radio frequency SV position data received by reference station SV position data received by remote receiver Remote receiver position modified by correction factors Correction factors computed from position errors

4. Carrier Phase Tracking ► 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 t 1 t 2 t 2 -t 1 >15 min Reference station at known location Remote receiver Carrier waves

Carrier Phase Cycle Changes ► Example: Range from reference to remote receiver has changed by 10 cycles between t 1 and t 2 ► 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 CARRIER PHASE TRACKING 10 cycles Remote receiver Reference receiver Tagged t 1 Tagged t 2 19 cm 

5. Wide Area Augmentation System (WAAS)

WAAS: Broadcast Corrections Wide Area Augmentation System ► 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 Substations compute local errors Surveyed locations (25) West coast East coast Correction factors rebroadcast across the US to be used by anyone SV data received at substations Orbiting GPS satellites WAAS Geosynchronous WAAS satellites Local errors transmitted to main ground stations Correction factors transmitted to WAAS satellites Correction factors computed at main ground stations

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

IR Laser beams rotate and fan out 6. Indoor GPS: Constellation 3Di ► 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 mm over 100m range ► Implemented at Boeing Commercial Airplanes Manufacturing R&D Factory workspace Transmitters Receiver mounted to tool LED strobe  Each transmitter rotates light beams at a unique frequency TRANSMITTER Azimuth computed from rotating beams Elevation computed from LED pulses

7. Accuracy Comparison & Applications Technique Accuracy (2  ) Application Basic GPS (SPS) 15 m Worldwide navigation PPS* 10 m (restricted use) DGPS 5 m Navigation over territory outside US Carrier Phase Tracking 5 cm Land Surveying WAAS 3 m Navigation over territory inside US LAAS**? (under development) Constellation 3Di 4-8ppm Factory tool positioning * Military and special licensees only * Military and special licensees only ** Local Area Augmentation System coming soon to an airport near you!

References ► Dr. Peter H. Dana, UC Boulder Dept. of Geography ► Garmin International, Inc ► Trimble Navigation Ltd. ► Federal Geographic Data Committee ► P. Sharke, “Measuring across space and time”, Mechanical Engineering, ASME Jan 2003