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REAL-TIME SURVEYING WITH GPS

REAL-TIME SURVEYING WITH GPS. Important Phone Numbers. Trimble support T echnical A ssistance C enter ftp://ftp.trimble.com www.trimble.com (hardware and software support) 1-800-SOS-4TAC 1-800-767- 4822 Computer Bulletin Board 408-732-6717

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REAL-TIME SURVEYING WITH GPS

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  1. REAL-TIME SURVEYINGWITH GPS

  2. Important Phone Numbers Trimble support Technical Assistance Center ftp://ftp.trimble.com www.trimble.com (hardware and software support) 1-800-SOS-4TAC 1-800-767- 4822 Computer Bulletin Board 408-732-6717 System Operator (David Elms) 408-481-6049 Coast Guard Navigation Centerwww.navcen.uscg.mil Recorded message 703-313-5907 Live voice 703-313-5900 Computer Bulletin Board 703-313-5910 National Geodetic Survey www.ngs.noaa.gov Information Center 301-713-3242 Computer Bulletin Board 301-713-4181 or 4182

  3. GPS some background • Satellite based positioning in development since mid 1960’s • NAVSTAR GPS • NAVigation Satellite Timing And Ranging • Global Positioning System • NAVSTAR GPS - Merging of two military programs in 1973 • Naval Research Laboratory - TIMATION program • Air Force - 621B Project • Managed by the Department of Defense • System tested with Ground Transmitters (pseudo-satellites) • First test satellites (Block I) launched in 1978 • Operational satellites began launching in 1989 (Block II & Block IIA) • Block II & Block IIA launched by Delta II rockets from Cape Canaveral • Next generation of satellites (Block IIR) are already on contract

  4. GPS the segments Space Segment Monitor Stations User Segment Diego Garcia Ascension Is. Kwajalein Hawaii Colorado Springs Control Segment

  5. Control / Monitor Segment • 5 Stations world-wide • Monitored by Department of Defense • All perform monitor functions • Receive all satellite signals • Collect Meteorological data ( used for ionospheric modelling ) • Transmit data to MCS • Master Control Station • Upload to Satellites • Orbital prediction parameters • SV Clock corrections • Ionospheric models (Basically everything in NAVDATA) • SV commands

  6. Space Segment • 25 satellites in final constellation • 6 planes with 55° rotation • each plane has 4/5 satellites • Very high orbit • 20,183 KM, 12,545 miles • approximately 1 revolution in 12 hours • for accuracy • survivability • coverage Copied from “GPS Navstar User’s Overview” prepare by GPS Joint Program Office, 1984

  7. User Segment • Surveyors • Anyone with GPS equipment • Hardware and Software can be application specific • Vehicle Tracking Ambulances • Navigation Police • Mapping Cruise Ships • Hydrographics Courier Services • Aircraft Approach and Landing Hikers • Dredging • Sunken ship salvage • Oil Exploration

  8. Working surfaces • A Datum is described by a specifically oriented reference ellipsoid defined by 8 elements • Position of the network (3 elements) • Orientation of the network (3 elements) • Parameters of the reference ellipsoid (2 elements) Ellipsoid fitting North America Ellipsoid fitting Europe Geoid Regional Datums are designed so that the ellipsoid conforms to the geoid over the desired region rather than the whole Earth

  9. Earth-Centered, Earth Fixed System • Z axis = Mean rotational axis (Polar axis) • X axis = 0 longitude • X axis in plane of equator • Y axis = 90 E longitude • Y axis in plane of equator

  10. SEMI-MAJOR AXIS Elements of an ellipse • a = semi-major axis b = semi-minor axis • f = flattening = (a-b)/a • Parameters used most often: a and 1/f SEMI-MINOR AXIS

  11. SEMI-MAJOR AXIS Ellipse in 3-D: an Ellipsoid • Rotate ellipse about semi-minor (polar) axis to obtain 3-d ellipsoid • Semi-major axis is equatorial axis SEMI-MINOR AXIS

  12. Common ellipsoids in surveying • WGS-84 (Datum = WGS-84) • a = 6378137.000 b = 6356752.310 1/f = 298.2572235630 • GRS-80 (Datum = NAD83) • a = 6378137.000 b = 6356752.310 1/f = 298.2572221010 • Clarke 1866 (Datum = NAD27) • a = 6378206.400 b = 6356583.800 1/f = 294.9786982000 • NOTE SIMILARITY BETWEEN WGS-84 AND GRS-80

  13. Datum (WGS 84)

  14. Datum (NAD 27)

  15. x Datum One point can have different sets of coordinates depending on the datum used

  16. Coordinate Systems Z P H Cartesian coordinates (X, Y, Z) Ellipsoidal coordinates (f, l, H) Z Y f l X Y X

  17. Altitude Reference • Ellipsoid • A smooth, mathematically defined model of the earths surface • Geiod • A surface of equal gravitational pull (equipotential) best fitting the average sea surface over the whole globe HAE MSL Earths Surface Ellipsoid Geoid

  18. Notes about the geoid • The geoid approximates mean sea level • The geoid is a function of the density of the earth • The geoid is a level surface which undulates • Conventional levels are referenced to the geoid

  19. Reference Surfaces B.M. “A” elevation 84 ft B.M. “ B ” elevation 73 ft Earths Surface 50 ft Ellipsoid Height = H H = 41 ft Ellipsoid 84 ft h = 73 ft Orthometric Height = h 34 ft N = 32 ft Geoid Geoid Height = N DE = B.M “A” - B.M. “B” = ORTHOMETRIC 84 ft - 73 ft = 11 ft ELLIPSOID 50 ft - 41 ft = 9 ft

  20. Conditions for surveying with GPS • At least 2 receivers required • At least 4 common SV’s must be tracked from each station • Visibility to the sky at all stations should be sufficient to track 4 SV’s with good geometry • Data must be logged at common times (sync rates, or epochs) • Receivers must be capable of logging carrier phase observables (not just C/A code) • At some point in the survey, at least one point must be occupied which has known coordinates in the datum and coordinate system desired • 2 horizontal and 3 vertical control points are required for complete transformation to the desired datum

  21. What the surveyor gets in GPS • 2 Types of Measurements: • Change in phase of the code • Change in phase of the carrier wave • 2 Types of Results: • Single point positioning and navigation -- from code • Baseline vectors from one station to another (post-processed or processed as “real time”)--from carrier wave

  22. WHAT IS A VECTOR?

  23. Satellite Signal Structure • Two Carrier Frequencies • L1 - 1575.42 Mhz • L2 - 1227.6 MHz • Three modulations • Two PRN codes • Civilian C/A code • L1 -160 dBw • Option for L2 in future • Military P code (Y code if encrypted) • L1 -163 dBw • L2 -166 dBw • Navigation message (NAVDATA) • L1 • L2 • Spread Spectrum

  24. Who uses the code? • Code-based applications: • Rough mapping • GIS data acquisition • Navigation • Any applications able to tolerate accuracies in range of sub-meter - 5 meters

  25. Measure Ranges to the satellites • Use the simple formula: Distance = Rate X Time • Distance = RANGE to the satellite (Pseudorange) • Time = travel time of the signal from the satellite to the user • When did the signal leave the satellite? • When did it arrive at the receiver? • Rate = speed of light SV Time SV Time User Time

  26. measure time difference between same part of code from satellite from ground receiver How do we know when the signal left the satellite? One of the Clever Ideas of GPS: • Use same code at receiver and satellite • Synchronize satellites and receivers so they're generating same code at same time • Then we look at the incoming code from the satellite and see how long ago our receiver generated the same code

  27. The Integer Ambiguity--What is it? • Receiver measures partial wavelength when it first logs on • Receiver counts successive cycles after this • Receiver does not know whole number of wavelengths behind that first partial one, which exists between the receiver and the SV • This unknown, N, is called the integer ambiguity or bias (also called phase ambiguity or bias)

  28. How carrier waves produce baselines • At least 4 common SV’s must be observed from at least 2 separate stations • The processor uses a technique called “differencing” • Single difference compares data from 2 SV’s to 1 station, or from 1 SV to 2 stations • Double difference combines these two types of single differences • Single and double differences performed at specific epochs in time • Triple difference combines double differences over successive epochs in time (every 10th epoch normally)

  29. Sequence in processing carrier waves • Begin with a code estimate of receiver locations • First generate the triple difference solution • Based on triple difference processing, find and correct cycle slips • Using improved estimate of dx,dy,dz from triple difference solution, compute double difference float solution • Set estimates of N from float solution to integers and re-compute baseline: double difference, fixed integer solution • Final result of processing is baseline vector, dx,dy,dz, estimated to centimeter-level or better precision

  30. We are somewhere on the surface of this sphere. Calculate your position With range measurments to several satellites you can figure your position using mathematics • One measurement narrows down our position to the surface of a sphere 11,000 miles 4 unknowns Latitude Longitude Height Time Need 4 equations

  31. 11,000 Miles 12,000 Miles Intersection of two spheres is a circle Calculate your position cont’d Second measurement narrows it down to intersection of two spheres

  32. Calculate your position cont’d Third measurement narrows to just two points Intersection of three spheres is only two points In practice 3 measurements are enough to determine a position. We can usually discard one point because it will be a ridiculous answer, either out in space or moving at high speed.

  33. Calculate your position cont’d Fourth measurement will decide between the two points. Fourth measurement will only go through one of the two points The fourth measurement allows us to solve for the receiver clock bias.

  34. Dilution of precision (DOP) An indication of the stability of the resulting position • DOP is dependent upon the geometry of the constellation • DOP is a magnification factor that relates satellite measurement noise (input) to solution noise (output) • The lower the DOP, the more accurate the position is. • The higher the DOP, the less accurate the position is. • In surveying, we care most about PDOP and RDOP • PDOP = Position dilution of precision--refers to instantaneous SV geometry • RDOP = Relative dilution of precision--refers to change in SV geometry over the observation period • For all DOP’s, the lower, the better

  35. Dilution of precision (DOP) • Relative position of satellites can affect error 4 secs 6 secs idealized situation

  36. Dilution of precision (DOP) Real situation - fuzzy circles 6 ‘ish secs 4 ‘ish secs uncertainty uncertainty Point representing position is really a box

  37. Dilution of precision (DOP) Even worse at some angles Area of uncertainty becomes larger as satellites get closer together

  38. Dilution of precision (DOP) Can be expressed in different dimensions • GDOP - Geometric dilution of precision • PDOP - Position dilution of precision • HDOP - Horizontal dilution of precision • VDOP - Vertical dilution of precision • EDOP - East dilution of precision • NDOP - North dilution of precision • TDOP - Time dilution of precision • GDOP2 = PDOP2 + TDOP2 • PDOP2 = HDOP2 + VDOP2 • HDOP2 = EDOP2 + NDOP2

  39. Selective Availability (S/A) Govt. introduces artificial clock and ephemeris errors to throw the system off. • Prevents hostile forces from using it. • When turned up, it's the largest source of error • Selective Availability is the sum of two effects: • Epsilon, or data manipulation term - ephemeris “fibbing” • Epsilon term changes very slowly - rate change once/hour • Dither, or clock variations • Dither term has cyclical variations from 1 cycle every 4 minutes to once every 15 minutes

  40. Satellite Clocks Ephemeris Receivers Tropo/Iono S/A 0 20 40 60 80 100 Feet Error Budget • Typical observed errors • satellite clocks 2 feet • ephemeris error 2 feet • receiver errors 4 feet • tropospheric/iono 12 feet • S/A Range error 100 feet • No S/A Total (rt sq sum) 13 feet • Then multiply by HDOP (usually 2-3) which gives a total error of: • typical good receiver 25-40 feet (7-10 meters) • with S/A Total (rt sq sum) 100 feet • Multiply by HDOP (usually 2-3) • which gives a total error of: • typically 200-300 feet (60 to 100 meters)

  41. DGPS • DGPS = “Differential” GPS • Generally refers to real-time correction of code-based positions • Real-time capabilities presume radio link between receivers • The “differential” is the difference between a GPS code position and a known position at a single receiver

  42. Differential Correction BASE • If you collect data at one location there are going to be errors • Each of these errors are tagged with GPS time . t+1 Time, t

  43. ROVER ? t+1 Time, t Differential Correction (Cont.) • At the same time, the errors occurring at one location are occuring everywhere within the same vicinity

  44. ROVER ? t+1 Time, t Differential Correction (Cont.) BASE . t+1 Time, t Satellites Seen Satellites Used 1 2 3 4 5 6 1 2 3 4 1 3 5 6 Any Combination of Base SV's

  45. GPS Error Sources • Dilution of Precision (DOP) • Satellite ephemeris removed by differencing • Satellite clock drift removed by differencing • Ionospheric delay removed by differencing • Tropospheric delay removed by differencing • Selective Availability removed by differencing • Multipath • Receiver clock drift • Receiver noise • Unhealthy Satellites

  46. Summary • 3 Segments of GPS • Space • Control • User • GPS Signals • L1 - c/a code, P-code • L2 - P-code • Differentials • Code - sub-meter precision • Carrier - cm precision • Integer Ambiguity

  47. Real-Time vs. Post-Processed • Results are available in the field, so checks can be verified immediately • Staking out is now possible • One base receiver supports multiple rovers (unlimited) • No post-processing time required in office • Transformation parameters needed prior to survey, for proper relationship between GPS WGS84 and local system

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