1. lecture 22: Global Positioning System (GPS)

2. humans have always been interested in where things are…

3. one of the basic questions has always been… where am I?….which leads to… where am I going and how do I get there? early solutions: marking trails with piles of stones (problems when snow falls…or on ocean) navigating by stars (requires clear nights and careful measurements) most widely used for centuries …location within a mile or so modern ideas: LORAN: radio-based; good for coastal waters …limited outside of coastal areas Sat-Nav: low orbit satellites; use low frequency Doppler …problems with small movements of receivers

4. Department of Defense finally said: “we need something better: all-day and all-night; all terrain” end-product is Global Positioning System (GPS) system (constellation) of 24 satellites in high altitude orbits (cost ~ $12 billion) coded satellite signals that can be processed in a GPS receiver to compute position, velocity, and time parts of system include: space (GPS satellite vehciles, or SVs) control (tracking stations) users first one launched in 1978 ….June 26, 1993 Air Force launched 24th SV

6. orbit ~ 12 hours

8. 27 satellites: 24 operational and 3 spare ground tracks

9. basic concept is that the GPS constellation replaces “stars” and gives us reference points for navigation examples of some applications (users): navigation (very important for ocean travel) zero-visibility landing for aircraft collision avoidance surveying precision agriculture delivery vehicles emergency vehicles electronic maps Earth sciences (volcano monitoring; seismic hazard) tropospheric water vapor anything that involves location, motion, or navigation

10. examples of applications

11. we will break system into five conceptual pieces step 1: using satellite ranging step 2: measuring distance from satellite step 3: getting perfect timing step 4: knowing where a satellite is in space step 5: identifying errors

12. GPS block I GPS block II GSP satellite vehicles (SVs): two generations: block I and block II weigh ~1900 lbs. built by Rockwell

13. step 1: using satellite ranging GPS is based on satellite ranging, i.e. distance from satellites …satellites are precise reference points …we determine our distance from them we will assume for now that we know exactly where satellite is and how far away from it we are… if we are lost and we know that we are 11,000 miles from satellite A… we are somewhere on a sphere whose middle is satellite A and diameter is 11,000 miles

14. if we also know that we are 12,000 miles from satellite B …we can narrow down where we must be… only place in universe is on circle where two spheres intersect if we also know that we are 13,000 miles from satellite C …our situation improves immensely… only place in universe is at either of two points where three spheres intersect

15. three can be enough to determine position… one of the two points generally is not possible (far off in space) two can be enough if you know your elevation …why? one of the spheres can be replaced with Earth… …center of Earth is “satellite position” generally four are best and necessary….why this is a little later this is basic principle behind GPS… …using satellites for triangulation

16. step 2: measuring distance from satellite because GPS based on knowing distance from satellite …we need to have a method for determing how far away the satellites are use velocity x time = distance GPS system works by timing how long it takes a radio signal to reach the receiver from a satellite… …distance is calculated from that time… radio waves travel at speed of light: 180,000 miles per second problem: need to know when GPS satellite started sending its radio message

17. requires very good clocks that measure short times… …electromagnetic waves move very quickly use atomic clocks came into being during World War II; nothing to do with GPS -physicists wanted to test Einstein’s ideas about gravity and time previous clocks relied on pendulums early atomic clocks looked at vibrations of quartz crystal …keep time to < 1/1000th second per day..not accurate enough to assess affect of gravity on time …Einstein predicted that clock on Mt. Everest would run 30 millionths of a second faster than clock at sea level …needed to look at oscillations of atoms

18. principle behind atomic clocks… atoms absorb or emit electomagnetic energy in discrete amounts that correspond to differences in energy between different configurations of the atoms when atom goes from one energy state to lower one, it emits an electromagnetic wave of characteristic frequency …known as “resonant frequency” these resonant frequencies are identical for every atom of a given type: cesium 133 atoms: 9,192,631,770 cycles/second cesium can be used to create extraordinarily precise clock (advances also led to using hydrogen and rubidium) GPS clocks are cesium clocks

19. now that we have precise clocks… …how do we know when the signals left the satellite? this is where the designers of GPS were clever… …synchronize satellite and receiver so they are generating same code at same time analogy: 2 people separated by some distance both start yelling one, two, three…at same time person 2 hears “one” shouted by person 1 when person 2 says “three” …if you both said one at same time, the distance away person 2 is from person 1 is time difference between “one” and “three” times the velocity of the sound let us examine GPS satellite signals more closely…

20. SVs transmit two microwave carrier (carry information) signals L1 (1575.42 MHz): carries navigation message; SPS code (SPS: standard positioning servic) L2 (1227.60 MHz): measures ionospheric delay C/A code (coarse acquisition) modulates L1 carrier phase …repeating 1 MHz pseudo random noise (PRN) code …pseudo-random because repeats every 1023 bits or every millisecond…each SV has its own C/A code …basis for civilian SPS P-code (precise) modulates both L1 and L2 …long (7 days) pseudo random 10 MHz noise code …basis for PPS (precise positioning service) …AS (anti-spoofing) encrypts P-code into Y-code (need classified module for receiver) navigation message modulates L1-C/A; 50 Mhz signal ….describes satellite orbits, clock corrections, etc. 3 binary codes shift L1 and/or L2 carrier phases

22. GPS receiver produces replicas of C/A and/or P (Y) code receiver produces C/A code sequence for specific SV

23. C/A code generator repeats same 1023 chip PRN code sequence every millisecond PRN codes defined for 32 satellite ID numbers modern receivers usually store complete set of precomputed C/A code chips in memory

24. receiver slides replica of code in time until finds correlation with SV signal (codes are series of digital numbers)

25. if receiver applies different PRN code to SV signal …no correlation when receiver uses same code as SV and codes begin to align …some signal power detected

26. when receiver and SV codes align completely …full signal power detected usually a late version of code is compared with early version to insure that correlation peak is tracked

27. receiver PRN code start position at time of full correlation is time of arrival of the SV PRN at receiver the time of arrival is a measure of range to SV offset by amount to which receiver clock is offset from GPS time …the time of arrival is pseudo-range

28. position of receiver is where pseudo-ranges from set of SVs intersect position determined from multiple pseudo-range measurements from a single measurement epoch (i.e. time) psuedo-range measurements used together with SV position estimates based on precise orbital elements (ephemeris data) sent by each SV GPS navigation data from navigation message

29. each SV sends amount to which GPS time is offset from UTC (universal time) time… correction used by receiver to set UTC to within 100 nanoseconds

30. position determined from multiple pseudo-range measurements 4 satellites…3 (X, Y, Z) dimensions and time when clock offsets are determined, the receiver position is known

31. this leads us to why 4 GPS satellites are necessary and to…

32. step 3: getting perfect timing electromagnetic energy travels at 186,000 miles per second …an error of 1/100th second leads to error of 1,860 miles how do we know that receiver and satellite are on same time? satellites have atomic clocks (4 of them for redundancy) …at $100,000 apiece, they are not in receivers! receivers have “ordinary” clocks (otherwise receivers would cost > $100K) …can get around this by having an “extra” measurement …hence 4 satellites are necessary three perfect measurements will lead to unique, correct solution ….four imperfect ones also will lead to appropriate solution

33. illustrate this in 2D… instead of referring to satellite pseudo-range in distance, …we will use time units two satellites: first at distance of 4 seconds second at distance of 6 seconds X location of receiver is X this is if clocks were correct… what if they weren’t correct?

34. X what if receiver wasn’t perfect? …receiver is off by 1 second “real” time wrong time XX position is wrong; caused by wrong time measurements XX

35. how do we know that it is wrong? …measurement from third satellite (fourth in 3D) X 3rd satellite at 3 seconds all 3 intersect at X… if time is correct if time is not correct…

36. add our one second error to the third receiver… XX …circle from 3rd SV cannot intersect where other 2 do purple dots are intersections of 2 SVs define area of solutions …receivers calculate best solution (add or subtract time from each SV)

37. finally… step 4: knowing where a satellite is in space Air Force injected satellites into known orbits orbits known in advance and programmed into receivers satellites constantly monitored by DoD …identify errors (ephemeris errors) in orbits …usually minor corrections relayed back to satellite “data message” about their “health”

38. sites have co-located: VLBI (very long baseline interferometry); lunar laser-ranging (from instrument left by Apollo astronauts) …primarily for length of day considerations satellite laser-ranging

39. step 5: identifying errors ionosphere: electrically charged particles 80-120 miles up; affects speed of electromagnetic energy …amount of affect depends on frequency …look at differences in L1 and L2 (need “dual-frequency” receivers to correct)

41. tropospheric water vapor: affects all frequencies; difficult to correct multipath: reflected signals from surfaces near receiver noise: combined effect of PRN noise and receiver noise bias: SV clock errors; ephemeris errors selective availability: SA; error introduced by DoD; turned off May, 2000 blunders: human error in control segment user mistakes (e.g. incorrect geodetic datum) …more on this in a minute receiver errors geometric dilution of precision (GDOP): errors from range vector differences between receiver and SVs (pictures coming…)

42. effects of noise, bias, and blunder

43. geometric dilution of precision (GDOP) SVs occupy a small volume in the sky

44. SVs occupy a large volume in the sky

45. when measuring must have good GDOP and good visibility …may not always be possible

47. user community… primary application is GPS navigation X, Y, Z (position) and time from 4 satellites to calculate position

48. GPS determines locations in Earth centered, Earth fixed (ECEF)

49. need to convert to latitude, longitude, and height above ellipsoid

50. need to use datum…descriptions of Earth’s surface depends on projections flat Earth for short distances ellipsoidal models for whole Earth GPS uses WGS-84 (ellipsoid) geoid: surface resulted from gravity alone

53. other reference ellipsoids exist

54. can convert from one datum to another (standard equations)

55. note position shifts…important to be consistent

56. differential GPS: improves accuracy correct bias errors at one location using measured bias errors at known position (base station) …requires software in reference receiver that can track all SVs in view and form individual pseudo-range corrections for each

57. can also use carrier phase (L1; L2) two receivers must be < 30 kms from one another (ionospheric delay must be less than one wavelength); requires special software …real-time kinematic (RTK) processing

59. old slide (1994): currently, dual-phase geodetic receivers ~$10K