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GPS
Theory
Using the range from the satellite to the GPS receiver, the location of
the receiver is a point somewhere on the surface of a sphere. Adding a
third satellite to the equation creates two overlapping spheres placing
the location of the GPS receiver on a circle. A fourth satellite narrows
the location of the GPS receiver to two points. One location is on or
near the surface of the earth. The other position is in the opposite
direction in space and is discarded as a solution. The position
determined by four satellites provides latitude, longitude, altitude, and
time for a three-dimensional (3-D) location or fix.
The exact location of each satellite must be known at any given time.
Traveling in a high speed orbit, some satellites will "rise" and some will
"set" in relation to the location of the GPS receiver. A general almanac is
continuously transmitted from each satellite giving the approximate
location of each satellite. It takes about 12-1/2 minutes to acquire all of
the almanac data for the entire system. A given set of almanac data is
valid for about six months. So, it is possible for a GPS receiver that is
new or stored for a long time to take from 12 to 45 minutes to acquire all
of the required almanac information the first time it is turned on. If you
use your GPS receiver regularly, it should always have a current
almanac and you won't have to wait very long. The almanac only
provides an approximate location for each satellite so the receiver
knows where to begin to look. Information that pinpoints the exact
location of the satellite is also transmitted about every 30 seconds. This
data is called "ephemeris" data. The ephemeris data is used in the
calculation that determines the exact location the satellite.
Because four satellites are needed for a position fix and the satellites
are constantly moving, setting, and rising, the ideal receiver would
track at least five satellites with channels.
Accuracy, Error, and Limitations
GPS can be very accurate in defining a position fix. Accuracy can
however mean many things and depends upon how it is defined. If you
only want to know how accurate a system is in two dimensions, you
could use the Circular Error Probability (CEP) method. The CEP
method gives the diameter of a circle that the receiver will be located in
50% of the time. The Radial Normal Error (1 DRMS) method gives a
circle that is large enough that the receiver will be in it 63% to 68% of
the time. The 1 DRMS method is more restrictive than the CEP
method. A more common method of error measurement is the 2
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