Global Positioning Systems (GPS) for Precision Farming
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Transcript of Global Positioning Systems (GPS) for Precision Farming
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
• Datums– Specifies a starting point for measurement– eg.: (NAD 1927 or NAD 1983)– Important to account for error between survey
reference and actual lat/lon
Computation of distance along Longitude
SLon=R
R
SLonR=6,433,000m
31.2 m/s
South
Computation of distance along Latitude
SLat=R40R40
R40=R cos
25.6 m/s
South
Error Budget
Typical Error in Meters (per satellite) Standard GPS Differential GPS
Satellite Clocks 1.5 0Orbit Errors 2.5 0Ionosphere 5 0.4Troposphere 0.5 0.2Receiver Noise 0.3 0.3Multipath 0.6 0.6SA 30 0
Typical Position Accuracy Horizontal 50 1.3Vertical 78 23-D 93 2.8
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