Global Positioning System Reference
In-Depth Information
the distance to each satellite, r 1,2,3. Let us say that satellite B is the first
to move into range of the receiver. From this data, the receiver knows
something of its own location: it must lie on a circle of radius r 2 centered
on B . Next, satellite C moves into range and transmits its data. The re-
ceiver now knows it is a distance r 3 away from C and so must lie at one of
two positions (labeled 1 and 3 in fig. 3.21a). To fix its position without am-
biguity, the receiver needs a third satellite. When A appears and transmits
data, the receiver can finally conclude that it is at position 3. (Here for
ease of explanation I have assumed that the three satellites appear se-
quentially to the receiver; in practice their transmissions are monitored
simultaneously.)
Thus, for the two-dimensional case, we see that three satellites are
needed. The real world is three-dimensional, however, 18 and in this case
four satellites are required to uniquely fix receiver position. You can see
why this is the case from figure 3.21b. A receiver knows that it lies a certain
distance from a satellite, so it lies somewhere on the surface of a sphere
centered on the satellite. For two such satellites, the receiver knows that its
position must lie on the circle of intersection, shown in the illustration.
From a circle we know already that it takes two more satellites to fix the
position; thus, a total of four satellites are needed in the real world.
For a receiver on the surface of the earth, we already know one of the
spheres, the earth itself (OK, so it is not quite a sphere, but the idea still
works), and so you might think that we need only three satellites to fix
position on the earth's surface. Technically true, but in practice the fourth
satellite is used to eliminate clock error in the receiver, as discussed ear-
lier. In fact, the more satellites that a receiver can detect, the better, so far
as positioning accuracy is concerned. The estimated position of the re-
ceiver becomes more accurate with each additional satellite it sees because
various errors are canceled or partially canceled by the di√erential GPS
technique.
18. Einstein may disagree.
 
Search WWH ::




Custom Search