Section 5 Basics of the Global Positioning System

Section 5: Basics of the Global Positioning System (GPS) and Geodesy for Lidar Applications

Outline Q GPS Facts Q GPS signal types Q GPS solutions Q GPS errors Q Geodesy and Surveying Q Reference Systems/Frames Q Ellipsoid and Geoid Q Local Datums Q Map Coordinate Systems Q Map Projections and Grids

GPS Facts Q US Department of Defense satellite navigation system composed of three segments: Space, Control, and User Q First GPS satellite launched in February 1978 Q Four or more satellites visible at all times anywhere in the world Q Space segment consists of a nominal constellation of 24 satellites at an altitude of ~20, 200 km; distributed in six orbital planes inclined 55º with respect to the equator; evenly spaced in right ascension; non-geostationary orbits with an orbital period of half a sidereal day.

GPS Facts Q Control segment consists of tracking stations located around the world and a Master Control Station (MCS) at Schriever AFB in Colorado Q MCS broadcasts corrected orbital data (ephemerides) and clock corrections back to satellites or space vehicles (SVs) source: http: //www. colorado. edu/geography/gcraft/notes/gps/*. *

GPS Facts Q User segment consists of the GPS receivers and the user community

GPS Signal Types Q GPS satellites broadcast pseudo-random codes on Lband carrier waves (L 1 and L 2) from known positions (orbital ephemerides) at very precise time intervals Q Single frequency codes: C/A-code – 1. 023 MHz chipping rate and P-code (becomes Y-code when encrypted) – 10. 23 MHz chipping rate Q Dual frequency carrier phase (L 1 and L 2) – L 1 frequency = 1575. 42 MHz (λ = 19 cm), L 2 frequency = 1227. 6 MHz (λ = 24. 4 cm) Q L 1 carries C/A-code, P-code, and navigation message; L 2 carries P-code only

Pseudorange Measurements Code generated by satellite 12 9 3 6 +1 -1 DT +1 -1 12 9 3 6 Code generated by receiver 1000 Pseudorange = C*DT

Carrier Phase Measurements +1 -1 Carrier signal generated by Satellite 12 9 3 6 F = phase difference 12 9 Carrier signal generated by Receiver 1000 3 6

GPS Solutions Q Ground coordinates are determined using satellite positions and the calculated distances between those satellites and the unknown position at a precise time; data from at least four satellites is necessary to compute the x, y, z position Q Code-phase or Pseudorange – uncorrected single difference solution with accuracy of +/- 2025 m with Selective Availability (SA) off Q SA – introduction of timing and orbital errors

GPS Solutions Q Differential correction method uses a precisely known terrestrial position (base station) to reduce errors between satellites and unknown position Q Real-time differential – automated correction using “virtual base stations” such as wide area augmentation signal (WAAS), Omnistar satellite, or Coast Guard beacons; Accuracy of +/- 1 to 5 m Q Post-processed differential – correction using terrestrial base station with known position; processing after precise ephemerides are available using C/A code or carrier phase data; cm-scale accuracy

GPS Solutions Q Carrier phase solutions can be computed using L 1, L 2 or ion-free combination of L 1 and L 2 (L 3) phase observations. Q L 1 solutions have lower RMS errors over short distances; L 3 solutions have higher RMS but are better over long baselines due to reduction of ionospheric effects Q Carrier phase solutions require ambiguity resolution

Carrier Phase Ambiguity Carrier signal generated by Satellite Phase range = N l + F N = Phase Ambiguity

Ambiguity Resolution Resolve N's if we - observe a few satellites for a long time or - observe many satellites for a short time.

GPS Solution Errors GPS Error Sources Q Satellite clocks Q SA (selective availability) Q Ephemerides (satellite orbits) Q Atmospheric delays Q Multipathing Q Receiver clocks ? ? ? Satellite Orbit Error 12 9 3 6 Satellite Clock Error including Selective Availability Ionospheric refraction L 2 L 1 Tropospheric Delay Multi-pathing 12 Receiver Clock Error 9 3 6 1000

Geodesy and Surveying Q Geodesy – study of the gravitational field and shape of the earth; involves locating of points on the earth with respect to reference systems (Sheriff, R. E. , 1982) Q Geodetic surveying - mapping over long distances must consider the curvature of the earth. There are many different reference systems and ellipsoid models used in geodetic surveying Q Planar surveying - mapping over short distances using a horizontal plane as the reference surface

Reference Systems/Frames Q Celestial, Terrestrial, and Local reference frames are reference systems with a defined set of station coordinates Q International Celestial Reference Frame (ICRF) – orientation of the earth relative to extragalactic radio sources measured by Very Long Baseline Interferometry (VLBI) Q Terrestrial Reference Frames (ITRF 00, WGS 84) – origin is center of mass of the earth; coordinate updates are based on measurements of tectonic plate movements Q Terrestrial reference frames have their own datums, ellipsoid, and geoid models

Terrestrial Reference Frames Q World Geodetic System of 1984 (WGS 84) – terrestrial reference frame used by U. S. Department of Defense; has been updated several times such that the most recent version is WGS 84(G 873) Q International Terrestrial Reference Frame (ITRF); most recent version is ITRF 00; the international GPS service publishes precise ephemerides in ITRF 00. ITRF uses the GRS 80 ellipsoid, which is slightly more precise than the WGS 84 ellipsoid

Ellipsoids Q Heights from GPS receivers are given in HAE (height above reference ellipsoid) Q Reference ellipsoids used can vary among different generations of GPS receivers; most receivers use the WGS 84 datum Q Reference ellipsoids are defined by semimajor or equatorial (a) and semi-minor or polar (b) axes and flattening: f=(a-b)/a From Torge, W. , 1980, Geodesy

Geoid http: //www. ngs. noaa. gov/GEOID/research. html Q Geoid – Surface of constant gravitational potential (level surface) that best approximates mean sea level Q The geoid anomaly (n) is the difference between the geoid surface and a reference ellipsoid http: //maic. jmu. edu/sic/standards/ellipsoid. htm

Ellipsoid and Geoid Heights Q Orthometric Height (H) – perpendicular vertical distance between the geoid and land surface H = hae + n where hae = height above ellipsoid; n = geoid anomaly Hoar, G. J, 1982, Satellite Surveying, Magnavox Advanced Products & Systems, Torrance CA

Local Datums Q North American Datum of 1983 (NAD 83) is the horizontal datum for North America, Central America and the Carribbean. • Based on National Geodetic Survey’s continuously operating reference stations (CORS) • Based on the GRS 80 reference ellipsoid Q North American Vertical Datum of 1988 (NAVD 88) • Based on adjustment of 625, 000 km of first-order leveling • Constrained to LMSL at the primary tidal benchmark at Father Point/Rimouski, Quebec, Canada Q NAVD 88 orthometric heights are referenced to an equipotential surface, but NAVD 88 is not a true, meansea level datum.

Continuously Operating GPS Reference Stations

Map Coordinate Systems Q Geodetic latitude/longitude is more appropriate for larger scale maps and is still preferred by pilots and sailors Q The Prime Meridian and the Equator are the reference planes used to define latitude and longitude http: //www. colorado. edu/geography/gcraft/notes/coordsys/gif/primequ. gif

Map Projections and Grids Q Universal Transverse Mercator (UTM) - meters; 60 N-S elongate zones each 6 degrees in longitude; UTM zone 1 starts at 180 degrees longitude (international date line); zone numbers increase to the east Q UTM northing coordinates are measured relative to the equator. For locations north of the equator is assigned the northing value of 0 meters North. To avoid negative numbers, locations south of the equator are made with the equator assigned a value of 10, 000 meters North Q UTM coordinates are most appropriate for map scales of 1: 250, 000 and larger (Terry, 1996) Q X = Easting and Y = Northing; the origin of x and y in UTM is the intersection of the equator and central meridian, where E = 500, 000 m and N = 10, 000 m Q Eastings decrease to the east and increase to the west; Northings increase to the north and decrease to the south Q Easting normally precedes Northing http: //www. nps. gov/prwi/readutm. htm (e. g. coordinates of Capitol Building in Austin, TX: 14 621, 161 E; 3, 349, 894 N

Worldwide UTM zones