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**Global Positioning Systems(GPS)for Precision Farming**An Introduction**The plan**• Introduction to GPS • What is GPS • How GPS works • Differential Correction • Integration and application of GPS into PF systems**Introduction to GPS**• What is GPS • The Global Positioning System (GPS) is a worldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations • GPS receivers use these satellites as reference points to calculate positions and time • Originally known as NAVigation System with Timing And Ranging (NAVSTAR)**How GPS Works (Six Steps)**1. Triangulation 2. Distance 3. Clocks 4. Satellite Position 5. Coordinate system 6. Errors**Triangulation**• Number of Satellites • One distance = sphere • Two distances = circle • Three distances = two points • Four distances = one point • Three distances + earths surface = one point • Locking • 1,2 satellites - No lock, course time • 3 Satellites - 2D positioning (Earth’s surface assumed) • 4 Satellites - 3D positioning (Lat/Lon/Alt)**Triangulation - critical points**• Position is calculated from distance measurements (ranges) to satellites. • Mathematically we need four satellite ranges to determine exact position. • Three ranges are enough if we reject ridiculous answers or use other tricks. • Another range is required for calculation of time.**Distance**• Distance = Speed x Time ? • 180 miles = 60 miles per hour x 3 hours • Speed of radio waves ? • 186 kmps • Time • 0.06 second • Distance = 186000 mps x 0.06 s • D = 11,160 miles (11Hr 58 Min period) • Accuracy (+/- 0.000,000,001 sec) = +/- 1 ns**Distance**• How does a receiver time the signal travel? • Satellites send a pseudo-random code • (each sends its own song of 1’s and 0’s) • Receiver matches its calculated sequence with the received signal by delaying more or less it’s signal • The amount of delay = the transit time! • How does the receiver separate the signals of each of the satellites? • Each satellite has it’s own sequence (song) calculated through a formula • Formula is conveyed in data from the satellites**Distance - critical points**• Distance to satellites is determined by measuring signal travel time. • Assume satellite and GPS receiver generate same pseudo-random codes at the same time. • By synchronizing the pseudo-random codes, the delay in receiving the code can be found. • Multiply delay time by the speed of light to get distance**Synchronization**• Satellites timing is extremely accurate. • precise atomic clocks on board. • All satellite clocks are synchronized and they send their codes at a known time • Ground GPS unit synchronizes its clock with the satellites • Four satellites with same time = only one correct solution for 1. time and 3. distances • (4 Equations, 4 unknowns)**Synchronization - critical points**• Accurate timing allows distance to satellites to be measured • Satellites achieve accurate timing with on-board atomic clocks. • Receiver clocks can be accurate because an extra satellite range measurement can remove errors.**Where are the satellites? (ephemeris)**• Satellites are launched into precise orbits • GPS receivers use an almanac to calculate accurate positions for the satellites (ephemeris) • Almanac is sent from satellites • US Airforce measures error in ephemeris (satellite position and speed) when they fly over C. Springs • Corrected ephemeris info is sent up to the satellite**ephemeris - critical points**• Satellite position (ephemeris) must be known as a reference for range measurements. • GPS satellite orbits are very predictable. • Minor variations in their orbits are measured by the Department of Defense. • The ephemeris error information is sent to the satellites, to be transmitted along with the timing signals.**Coordinate Systems**• ECEF Coordinates • Latitude/Longitude/Altitude • Degrees Minutes Seconds (Ag Hall, OSU USA) • Latitude 360 07’ 29” N • Longitude 970 04’ 21” W • Latitude = degrees from equator N or S • Longitude = degrees from Greenwitch E or W • Altitude = Meters above reference geoid • GPS uses WGS84 Ellipsoid (ECEF) • Can be transformed to others: NAD27, NAD83 • See: Peter Dana’s Web site**Coordinate Systems**• UTM • Cartesian positioning in meters • Abbreviation for “Universal Transverse Mercator” • Divided into cartesian zones • 60 wide, 840 North to 800 south • Reference • Specifies a starting point for measurement • eg.: (NAD 1927) • Important to account for error between survey reference and actual lat/lon**Error Budget**Trimble Navigation Limited