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Global
Positioning System Technology (GPS) and its Use in Farming
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| What
is a GPS? |
| The
Global Positioning System (GPS) determines the accurate location
of a point (the latitude and longitude) on earth. GPS is based
on 24 space vehicles (SV's), or satellites, orbiting the earth.
It uses the following concepts: |
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| Triangulation
from satellites: |
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To
triangulate, the GPS measures the time it takes a radio signal
from a satellite to reach a point on earth. Using this time, the
distance from satellite to a point on earth is computed. |
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| Distance
= time (sec) x 186,000 miles/second |
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To
measure time, GPS requires very accurate clocks. The clocks on
satellites are based on atomic oscillations. There are four
clocks on each satellite. Each clock is worth $100,000. We
need to know where the satellite is in space to determine
distance. |
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As
the GPS signal travels through the ionosphere (80-120 miles) and
troposphere
(water vapors), it is delayed. |
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| Triangulation |
| GPS
is based on satellite ranging where we determine our position on
the 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 a point. |
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| 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. 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 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
complicated pseudo-random codes that are repeated every
millisecond. |
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| Clocks
in Satellites and Receivers |
| The
clocks in satellites are atomic clocks which run on the
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, three perfect range measurements
locate a point in three-dimensional space while 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. |
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| Knowing
Satellite Position in Space |
| High
altitude (about 11,000 miles) of satellites keep them clear from
earth's atmosphere. Therefore, the predictions of the
orbits of these satellites will be very accurate. The Air Force
injects each satellite into a very precise orbit and some
receivers have almanacs that precisely tell where the satellites
will be. Each satellite goes around the earth once every 12
hours. The Department of Defense (DoD) measures their
altitude, position, and speed when they pass over
specifically-designated locations on earth. The DOD looks for
variations in position, speed, and altitude. These
variations are called ephemeral errors which are caused by
gravitational pulls from the moon, sun, and by the pressure of
solar radiation. These variations (errors) which are minor
are constantly relayed to satellites. In turn, the
satellites relay these back to earth along with their timing
information. GPS satellites also transmit data about their
health and orbital locations. |
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| Ionosphere
and Troposphere |
| The
earth's atmosphere delays radio signals from satellites.
The ions in the outer atmosphere (ionosphere) and the water
vapor in the troposphere cause these delays. The
ionosphere is a blanket of charged particles 80-120 miles above
earth. When light travels through the ionosphere, its velocity
decreases at a rate inversely proportional to its frequency
squared. 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 vapor decrease the velocity of radio signal that travels
at the speed of light. However, there is no way to correct
this error which is relatively small in magnitude (in most cases
resulting in inaccuracies less than the width of an average
street). |
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| Receiver
Errors |
| The
receivers sometimes may round off a mathematical operation or an
electrical interference might cause an error in correlating the
pseudo-random codes. |
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| Multipath
Errors |
| When
the signals from satellites bounce around from adjacent objects
and then reach our antenna, they cause errors called multipath
errors. |
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| 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
precision and the error is magnified. The wider the angle
between the satellites, the better the measurement. Good
receivers have the ability to choose the four best satellites. |
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| 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. |
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| 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 but 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. |
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| C/A
(Course Acquisition) Code and P (Precise or Protected) Code |
| There
are two types of pseudo-random codes: |
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C/A
code: This code is used by civilians and has lower
frequency than P code. |
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P
code: This code can be encrypted such that only
military receivers will have access to it. In addition, it is
impossible to jam P code. Traditionally, the P code is
superimposed on a carrier that is ten times the frequency of a
C/A carrier. Using the Selective Availability (S/A)
operational mode the DOD can even degrade the accuracy of C/A
code. In the case of S/A, the DOD creates artificial clock
errors in the satellites. It is the largest source of error in
the GPS system. However, starting from 2 May 2000, the S/A
operational mode was suspended by the U.S. Government thereby
eliminating the errors in GPS measurements associated with this
tactical mode. |
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| Differential
GPS |
| A
receiver placed at a given (known) location (base station)
calculates the 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 at altitudes of about 11,000 miles, the error of the base
station will be identical to the errors of rover units. |
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| Receivers |
| There
are two types of receivers: |
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Sequencing
receivers: These are one-or two-channel receivers and
are generally used for recreational purposes. |
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Continuous
receivers: These receivers are often used for
surveying and scientific purposes. They generally have 4,
6, 8, 10, or 12 channels. They eliminate the inaccuracies
associated with geometric dilution of precision. |
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