The Global Positioning System Rebecca C. Smyth April 17 - May 2, 2001

GPS-Global Positioning System Department of Defense navigation system Triangulation from a constellation of 24 satellites broadcasting pseudo-randomly coded signals on radio waves (speed of light) from known positions (given by orbital ephemerides) at very precise time intervals. Satellites at altitude of 20,200 km; distributed in 6 orbital planes with inclination of 55 degrees to equator Four or more satellites visible at all times anywhere in world. First satellite launched February 22, 1978

GPS-Global Positioning System Coordinates are determined using known satellite positions and the measured distances between those satellites and the unknown position at a precise time. A GPS receiver determines its position in three dimensions: x, y, and z. The height (z) coordinate is different from the horizontal coordinates (x and y) both in how it is defined and how accurately it can be measured.

GPS Data - Signal Types Single frequency C/A-code (Civilian Access; Coarse Acquisition) MHz chipping rate Single frequency P code (Precise; Protected, or Precision); becomes Y-code when encrypted MHz chipping rate; only 2 satellites have P-code, the rest have Y- code. Dual frequency Carrier Phase (L1 and L2) - L1 frequency = MHz (λ = 19 cm), L2 frequency = MHz (λ = 24.4 cm). L1 carries C/A code, P code, and Navigation message L2 carries P code only

GPS Solutions Simple, Typical, or Pseudo-range - accuracy of +/- 100m with SA turned on or +/- 20 to 25m with SA off (ex. uncorrected solutions using GeoExplorer or Garman receivers) –SA (Selective Availability) - dithering or introduction of a clock timing error and introduction of an orbital error. Differential - correction uses a terrestrial point with precisely known position between the satellites and the unknown points to reduce errors.

GPS Solutions Real-time differential - correction using a virtual base station (ex. Omnistar satellite system or coast guard system) Post processed differential - correction using base station of known coordinates using single frequency C/A-code or dual frequency carrier phase (ex. corrected GeoExplorer, Trimble 4000ssi or Ashtech Z- 12)

GPS Solution Details Pseudo-range solution (single difference solution)- difference between time of signal transmission from satellite and time of arrival at receiver times speed of light (c ~ 3 x 10 8 m/sec); Double-difference solutions - linear combinations of difference solutions; further reduces errors by canceling out differences between receivers, satellites, and epochs. Widelaning of the dual frequency - differencing between the phase observations made on L1 and L2.

GPS Solution Errors Satellight clocks SA Ephemerides (satellight orbits) Atmospheric delays Multipathing Receiver clocks

Error Budget (m)

Coordinate Systems Conventional Terrestrial Reference System (CTRS) aka Geocentric XYZ aka Earth Centered Earth Fixed (ECEF) - origin at mass center of earth; z-axis aligned with mean spin axis of earth; x-axis points toward the Greenwich Meridian; y-axis is at right angles to x in direction determined by right-hand rule. Universal Transverse Mercator (UTM) - meters; 60 N-S elongate zones each 6 degrees in longitude; zone 1 starts at 180 degrees longitude and they proceed east; x is called easting and y is called northing; the origin of x and y in UTM is the intersection of the equator and central meridian, where x=500,000m (numbers decrease to east and increase to west) and y=10,000,000m (numbers increase to north and decrease to south); easting normally precedes northing. Geographic Coordinates (latitude and longitude) = ellipsoidal coordinates

GPS-Vertical Measurements Ellipsoid - surface of an ellipsoid of revolution Ellipsoidal Heights - Based on WGS-84 (World Geodetic System last updated in 1984) Orthometric Heights - height above the geoid; equipotential surface that closely approximates the idealized surface of the oceans (aka) height above mean sea level (AMSL) Geoidal Undulations - geoidal height which is the geoid-ellipsoid separation. Geoid models are based on satellight and terrestrial gravity data.

Ellipsoid and Geoid Heights h H N Earth’s surface Geoid Ellipsoid h, measured by GPS N, Geoid anomaly provided by GEOID99 model H, orthometric height = h - N GEOID99 converts GPS ellipsoidal heights to NAVD 88 orthometric heights

GPS-Vertical Datums GPS height - ellipsoid height given in CTRS WGS-84 (World Geodetic System last updated in 1984) - defines the reference ellipsoid and the CTS used for GPS work. NGVD67 - (National Geodetic Vertical Datum) attempted to combine geoid and AMSL corrections; was an attempt to position the reference ellipsoid so that it best approximated the geoid. This datum is no longer used. NAVD88 - (North American Vertical Datum) an orthometric height datum. Based on a reference ellipsoid, the surface of which approximates the geoid over the region covered by the datum.