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HOW YOUR GPS WORKS
 The
gps system consists of three pieces. There are the satellites
that transmit the position information, there are the ground
stations that are used to control the satellites and update
the information, and finally there is the receiver that you
purchased. It is the receiver that collects data from the
satellites and computes its location anywhere in the world
based on information it gets from the satellites. There is
a popular misconception that a gps receiver somehow sends
information to the satellites but this is not true, it only
receives data. So, just how is it able to do compute its position?
GEOMETRIC VIEW
Your gps receiver uses an elaboration
of a technique that is tried and true and used by navigators
and surveyors for centuries. Basically you use a known set
of locations to compute your current location by taking fixes
on the known sites. In the old days you took bearings (compass
sightings) on existing locations and triangulated these on
a chart to compute a fix on your location. Once you have a
compass bearing you can draw a line through the known location
and you know you are somewhere on that line. Do the same thing
to a second point and the two lines will intersect. This is
your position. If you try a third point it should intersect
at the same place the other two lines intersect. Usually however,
because of imprecise sightings, it intersects both lines at
slightly different points thereby forming a small triangle.
You are somewhere inside that triangle but you don't know
exactly where. If the triangle is small enough you consider
it good enough, otherwise you need to take another sighting.
Accuracy is determined primarily on your ability to get and
plot an accurate bearing as well as the geometry of the known
sites available. This means that if the sites are very close
together you will get poorer results than if they are at some
angular distance apart. What you would really like were two
sites that were 90 degrees apart for best accuracy.
The gps receiver uses a slightly different
approach. It measures its distance from the satellites and
uses this information to compute a fix. How can it measure
distance? Well it really measures the length of time the signal
takes to arrive at your location and then based on knowing
that the signal moves at the speed of light it can compute
the distance based on the travel time. However, unlike the
known sites of the olden days, these sites are moving. The
solution to this problem is to have the satellite itself send
enough information to calculate its current location relative
to your receiver. Now, armed with the satellite location and
the distance from the satellite we can expect that we are
somewhere on a sphere that is described by the radius (distance)
and centered at the satellite location.
By acquiring the same information
from a second satellite we can compute a second sphere that
cuts the first one at a plane. Now we know we are somewhere
on the circle that is described by the intersection of the
two spheres. If we acquire the same information from a third
satellite we would notice that the new sphere would intersect
the circle at only two points. If we know approximately where
we are we can discard one of those points and we are left
with our exact fix location in 3D space. Now, what would happen
if we were to acquire the information from a fourth satellite?
We should expect that it would show us to be at exactly the
same point we just computed above. But what if it isn't? Before
we can answer that question we need a little more background.
A more basic question is, "How does
the gps know the travel time so that it can compute the distance?"
The satellite sends the current time along with the message
so the gps can subtract its knowledge of the current time
from the satellite time in the message (which is the time
that the signal started its descent) and use this to compute
the difference. For this to work the time in your gps must
be pretty accurate Ð to a precision of well under a microsecond.
The satellite itself has an atomic clock to keep the time
very precisely, but your unit is probably not big enough nor
expensive enough to have an atomic clock built in, so your
clock is likely to be in error! For this reason our assumptions
about the distance calculation are likely to have considerable
error and the fourth satellite fix will reveal this to us.
However, if we assume the error is caused by an error in our
clock then we can adjust our clock a little and recompute
all 4 fixes, continuing to do this iteratively until the error
disappears! We will then have a good position fix and as a
side effect we will also have the correct time to about 200
nanoseconds or so. One of the applications of gps technology
is to provide the correct time even when we don't care about
our position.
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