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Department of Ag. Sci., Dairy Mgmt., and Ag. Bus., at SUNY Morrisville |
Bulletin #2/98:
Marshall 104,
Global Positioning System Technology (GPS) and its Use in Farming
(Adam Khan, Ph.D.)
The
crop production system that is environmentally sound yet profitable requires
precision. The use of GPS in precision farming is becoming more common. Its use
in measuring accurate acreage, locating less fertile areas in a field, and
application of variable rates of fertilizer in a field are already getting
attention. The following discussion describes GPS technology.
What is a GPS?
It is a satellite based navigation system. The Global Positioning System determines the accurate location of a point (in latitudes and longitudes) on earth. GPS is based on 24 space vehicles (SV's) or satellites orbiting the earth. It uses the following concepts:
Triangulation from satellites
To triangulate, the GPS measures the time it takes for a signal from satellite to a point on earth. Using this time, the distance from satellite to a point on earth is computed.
Distance = time (sec) x 186,000 miles/second
To measure time, GPS requires very accurate clocks. The clocks on satellites are based on atomic oscillations. There are four clocks on each satellite and each clock is worth $100,000.
We need to know where the satellite is in space.
As the GPS signal travels through ionosphere (80-120 miles) and atmosphere (water vapors), it is delayed.
Triangulation
GPS is based on satellite ranging where we determine our position on earth by measuring our distance from a group of satellites, about 10,900 miles away from earth. In order to understand triangulation, let us assume that a satellite is in the center of an imaginary sphere and is transmitting signals in all directions. Two imaginary spheres (of two satellites) will intersect at several points. Three imaginary spheres will intersect at two points, one of the points will be on earth and the other point will be in space. Four imaginary spheres of four satellites will intersect on only one point on earth. According to trigonometry, we really need four satellite ranges to unambiguously locate our self on earth.
Measuring Distance From a Satellite
To measure the distance from the satellite we multiply the velocity of light with the time it takes for the signal to reach earth.
Distance (miles) = 186,000 miles/sec x t(sec). For example, it will take 0.06 seconds for a signal to reach earth from a satellite at 12,000 miles away from earth. Very precise electronic clocks are nowadays relatively inexpensive. Most receivers can measure time with nanosecond accuracy.
In order to measure the length of time a signal would take to reach earth, we synchronize the satellites and receivers such that they generate the same code at exactly the same time. Once we receive the code, then we look back and see when the receiver generated the same code. The time difference will tell how long it took for the signal to reach earth. The signals are pseudo random codes which are complicated and repeated every millisecond.
Clocks in Satellites and in Receivers
The clocks in satellites are atomic clocks which run on oscillation of an atom. They are extremely precise. The clocks in receivers are not as precise. In order to offset this inaccuracy, we get an extra satellite range measurement. According to trigonometry: 3 perfect range measurements locate a point in three-dimensional space. Four imperfect measurements can eliminate any timing offset (as long as the offset is consistent). The ranges which contain timing errors are called pseudo ranges.. If the four spheres do not intersect at a single point, then the computer in the receiver pursues a series of trims from the ranges until they intersect at a single point. This is how the time offset is corrected. For real time position measurements, we need a four-channel receiver (at least) so that one channel is assigned each satellite.
Knowing Satellite Position in Space
High altitude (about 11,000 miles) of satellites keep them clear from earth's atmosphere and, therefore, the predictions of their orbits will be very accurate. The air force injects each satellite into a very precise orbit and some receivers have almanacs which precisely tell where the satellites will be. Each satellite goes around the earth once every 12 hours. The department of defense measures their altitude, position, and speed when they pass over a specific designated location on earth. The DOD looks for variations in position, speed, and altitude. These variations are called Ephemeris errors which are caused by gravitational pulls from moon, sun, and by the pressure of solar radiations. These variations (errors) which are minor are constantly relayed to satellites and the satellites relay back to earth along with their timing information. GPS satellites also transmit data about their health and orbital location.
Ionosphere and Atmosphere
Ionosphere and water vapors in atmosphere delay signals coming to earth from the satellites. Ionosphere is a blanket of charged particles 80-120 miles above earth. When light travels through ionosphere, its velocity decreases at a rate inversely proportional to its frequency squared (-Vtime = -1/ V2 time ) only the most advanced, dual frequency receivers have the ability to correct this type of error. They are called the "ionosphere-free solution."
Similarly, water vapors decrease the velocity of light (signal) but there is no way to correct this error. The magnitude of this error is equal to the width of a street.
Receiver Errors
The receivers sometimes may round off a mathematical operation or an electrical interference might cause an error in correlation of pseudo-random codes.
Multipath Errors
When the signals from satellites bound around from adjacent objects and then reach our antenna, they cause errors called multipath errors.
Geometric Dilution of Precision (GDOP)
The accuracy of data depends on which satellites we use. If two satellites are close to each other, then we get dilution of precisions and the error is magnified. The wider the angle between satellites, the better the measurement. Good receivers have the ability to choose four best satellites.
Selective Availability
Using an operational mode, SA (selective availability), the department of defense purposely degrades the accuracy of GPS. It is generally the largest component of error, if implemented.
Pseudo Random Codes
The pseudo random codes allow a receiver to figure out a time difference between itself and the satellites. GPS signals are very low power and can be received by antennas a few inches above earth. We know the patterns of Pseudo Random codes. If we divide the signals into time periods (chips) and compare our satellite signals with the inherent earth's background radio signals, or receivers signals with earth's background radio signals, only 50% of the time the chips will match and 50% of the time they would not. However, if we slide the satellite's codes back until they match with our receiver's codes, we will get a lot more matches. Further, the matches will amplify over a longer time span. There is very little information in GPS signals. They are simple timing marks.
C/A (Course Acquisition) Code and P (Precise or Protected) Code
There are two types of Pseudo Random codes:
C/A code: it is used by civilians and has lower frequency than P code.
P code: this code can be encrypted such that only military will have access to it. In addition, it is impossible to jam P code. Traditionally, the P code which is superimposed on a carrier that is ten times the frequency of a C/A carrier. Using S/A operational mode the DOD can even degrade the accuracy of S/A code. In case of S/A (selective availability) the DOD creates artificial clock error in the satellites. It is the largest source of error in the GPS system. Each satellite has its own distinct pseudo-random code.
Differential GPS
A receiver placed at a given (known) location (base station) calculates total error in satellite range. This error is then used to correct the locations measured by the other receivers (rover units) in the same locations. Since satellites are about 10,900 miles altitude, therefore, the error of base station will be identical to the errors of rover units.
Receivers
There are two types of receivers:
Sequencing receivers: these are one or two channels and are generally used for recreation purposes.
Continuous receivers: they are often used for surveying and scientific purposes. They generally have 4,6,8,10, & 12 channels. They eliminate the GDOP problems.
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This project was funded by UCT Alliance