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

Trimble Navigation Limited