1. Global Positioning Systems (GPS) for Precision Farming
An Introduction

2. The plan Introduction to GPS What is GPS How GPS works
Differential Correction
Integration and application of GPS into PF systems

3. 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)

4. How GPS Works (Six Steps)
1. Triangulation
2. Distance
3. Clocks
4. Satellite Position
5. Coordinate system
6. Errors

5. Triangulation Number of Satellites Locking 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)

6. 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.

7. Distance Distance = Speed x Time ? Speed of radio waves ? Time
180 miles = 60 miles per hour x 3 hours
Speed of radio waves ?
186 kmps
Time
0.06 second
Distance = mps x 0.06 s
D = 11,160 miles (11Hr 58 Min period)
Accuracy (+/ ,000,001 sec) = +/- 1 ns

8. 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

9. 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

10. 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)

11. 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.

12. 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

13. 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.

14. Coordinate Systems ECEF Coordinates See: Peter Dana’s Web site
Latitude/Longitude/Altitude
Degrees Minutes Seconds (Ag Hall, OSU USA)
Latitude ’ 29” N
Longitude ’ 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

15. Coordinate Systems UTM Reference 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

16. Computation of distance along Longitude
South

17. Computation of distance along Latitude
South

18. Error Budget
Trimble Navigation Limited