GPS: Theory of Operation and Applications

Transcription

1 GPS: Theory of Operation and Applications Christopher R. Carlson March 18, 2004 D D L ynamic esign aboratory.

2 Motivation There are many interesting applications for GPS technology 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

3 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 to a 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

4 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

5 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

6 There are three GPS Segments Space Segment Monitor Stations Master Control User Segment Control Segment Control, Space and User Segment Stanford University GPS: Theory of Operation and Applications - 6 Dynamic Design Lab

7 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

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

9 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

10 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

11 Triangulation 3 3 x, y ρ 3 ρ 1 x, y ρ x, y 1 1 x, y Fundamentally, GPS is a triangulation like system Satellite positions are known, need to know distances Stanford University GPS: Theory of Operation and Applications - 11 Dynamic Design Lab

12 Speed of Light 11:30.00 am D = c * t 11:30.08 am GPS uses time and the speed of light to get distance GPS Satellites are synchronized atomic clocks Stanford University GPS: Theory of Operation and Applications - 12 Dynamic Design Lab

13 Triangulation (again) 3 3 x, y t ρ 3 ρ 1 Time Bias 1 1 x, y ρ x, y Users have piezo clocks, error is common to all satellites Now there are 4 equations and 4 unknowns Stanford University GPS: Theory of Operation and Applications - 13 Dynamic Design Lab

14 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

15 Clock Error Applications GPS knows the exact time of day within 1e-9 seconds Used to synchronize international banking transactions Stanford University GPS: Theory of Operation and Applications - 15 Dynamic Design Lab

16 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

17 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 1.8m Stanford University GPS: Theory of Operation and Applications - 17 Dynamic Design Lab

18 Principle Error Sources: Iono Military Civilian Iono Tropo 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

19 Principle Error Sources: Iono The military can actually correct for this since they have two 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 differently Like red light and blue light travelling though a prism Stanford University GPS: Theory of Operation and Applications - 19 Dynamic Design Lab

20 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

21 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

22 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

23 DGPS Very accurate difference user ref 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

24 DGPS Applications Automatic farming Autonomous golf caddies Automobile lane keeping Stanford University GPS: Theory of Operation and Applications - 24 Dynamic Design Lab

25 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

26 GPS Velocity d1 d2 d3 t0 t1 t2 t3 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

27 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

28 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

29 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

30 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

31 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

32 GPS Roll and Road Grade 4 GPS Road Grade Measurement (Right Turn) Grade [deg] GPS Roll Angle Measurement Roll Angle [deg] Time [s] Continuous 30km/h circle spanning test track Road crown is clearly measurable as roll and grade Stanford University GPS: Theory of Operation and Applications - 32 Dynamic Design Lab

33 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

34 Double Lane Change Zoom Double Lane Change (Zoom) GPS Kinematic Correlation Observer Sideslip [deg] Time [s] Sideslip = Velocity Direction - Heading Stanford University GPS: Theory of Operation and Applications - 34 Dynamic Design Lab

35 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

36 GPS Based Crash Testing Current systems often use cable drives and sleds to command a desired speed and direction It may be possible to recreate collisions with GPS not otherwise feasible with cable system Stanford University GPS: Theory of Operation and Applications - 36 Dynamic Design Lab

37 GPS Based Crash Testing Desired Collision Paths Throttle Steering Control GPS measurement system Desired crash trajectories set by crash engineer Reusable control system controls steering and throttle for each vehicle GPS measures vehicle speed, position and updates the control unit Stanford University GPS: Theory of Operation and Applications - 37 Dynamic Design Lab

38 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

39 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

40 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 error sources What are the advantages of differential GPS? DGPS improves GPS accuracy by cancelling out common mode errors Stanford University GPS: Theory of Operation and Applications - 40 Dynamic Design Lab

41 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

42 Fin Questions? Stanford University GPS: Theory of Operation and Applications - 42 Dynamic Design Lab