# 5.3.1 How GPS Works: An Introduction

available and reasonably priced, thanks to the Global Positioning
System (GPS). How do these little wonders figure out exactly where
you are?

The basic principle behind GPS is simple, and it's one that you may
have used many times while doing coastal navigation: if you know where
a landmark is located, and you know how far you are from it, you can
plot a line of position. (In reality, it's a circle or sphere of
position, but it can * *be treated as a line if the circle is very
large.) If you can plot two or more lines of position, you know that
you are at the point where the lines cross. With GPS, the landmarks
are a couple of dozen satellites flying about 12,000 miles above the
earth. Although they are moving very rapidly, their positions and
orbits are known with great precision at all times.

Part of every GPS receiver is a radio listening for the signals being
broadcast by these satellites. Each spacecraft continuously sends a data
stream that contains orbit information, equipment status, and the exact
time. All of the information is useful, but the exact time is crucial. GPS
receivers have computers that can calculate the difference between the
time a satellite sends a signal and the time it is received. The computer
multiplies this time of signal travel by the speed of travel (almost a billion
feet per second!) to get the distance between the GPS receiver and the
satellite (TIME x SPEED = DISTANCE); it then works out a line of
position based on the satellite's known location in space.

Even with two lines of position, though, the resulting fix may not be very
good due to receiver clock error. The orbiting satellites have extremely
accurate (and expensive!) clocks that use the vibrations of an atom as the
fundamental unit of time, but it would cost far too much to put similar
atomic clocks in GPS receivers as well. Since precise measurement of time
is critical to the system - a clock error of only one thousandth of a second
would create a position error of almost 200 miles - the system designers
were faced with a dilemma.

Geometry to the rescue! It turns out that GPS receivers can use
inexpensive quartz clocks (like the ones used in wristwatches) and still
come up with extremely accurate position fixes as long as one extra line of
position is calculated. How does this work? First, imagine two
earthbound landmarks with known positions - for example, Honolulu and
Los Angeles. If we measure the travel time of radio waves from each of
these cities to San Francisco, we can use the known speed of the radio
waves to compute two lines of position that cross. If our clock is a little
fast, our position lines will show us to be closer to both cities than we
really are; the lines will cross, but that crossing point might be somewhere
out in the ocean southwest of San Francisco. On the other hand, if our
clock is too slow, we will appear to be farther away from the chosen
landmarks than we really are, and our position lines might cross to the
northeast of us, near Sacramento.

Now, if we get just one more position line - from Seattle, let's say - the
three lines would form a triangle, and the center of the area in this triangle
is our REAL position. The clock error is the same for all three lines, just
in different directions, so moving them together until they converge on a
point eliminates the error. Therefore, it's OK if our GPS receiver's clock
is a little off, as long as the clocks on the satellites are keeping exact time
and we have a computer that can pinpoint the center of a triangular area.

For accurate two-dimensional (latitude and longitude) position fixes, then,
we always need to get signals from at least three satellites. There are now
enough GPS satellites orbiting the earth to allow even three-dimensional
position determination (latitude, longitude, and altitude, which requires
signals from at least FOUR satellites) anytime, from anywhere in the
world. The more satellites your receiver can "see" at one time, the more
accurate your position fix will be, up to the system's standard accuracy
limit of a few hundred feet.

The U.S. Department of Defense is responsible for the GPS system, and
they reserve increased accuracy for military users. For this reason, the
satellites broadcast a coded signal ("encrypted P-code") that only special
random errors are put into the satellite clock signals that the civilian GPS
accuracy, though, including the U.S. Coast Guard.

To get around the DoD-imposed accuracy limitation, the Coast Guard is
setting up "differential beacons" around the U.S. A differential beacon
picks up GPS satellite signals, determines the difference between the
computed position from the satellite and the beacon's own exactly-known
location, then broadcasts the error information over a radio channel for all
nearby differential-equipped receivers to use. With this method,
inexpensive GPS receivers can produce position information accurate to
within a few inches using the standard, uncoded civilian signal. GPS
becoming quite common, although a separate differential beacon receiver
usually must be purchased.

The way GPS receivers pick up the satellite signals is pretty interesting:
all of the satellites broadcast their messages on the same frequency, but
they each include a unique identification number. The receiver determines
which message is from which satellite by matching the identification
number with the ones stored in its memory. This is sort of like standing in
a room with many people speaking at the same time - you can listen to
what just one person is saying among all of the conversations taking place
simultaneously, and you can identify a person's voice by its particular
sound. In the same way, a GPS receiver picks up signals from all of the
satellites in view and matches them with patterns in memory until it
figures out which ones are "talking" and what they are saying. This
technique allows GPS receivers without backyard-sized dish antennas to
reliably use the extremely weak signals that the satellites transmit
towards the earth.

Ten years ago, it would have been hard to believe that you could buy a
device capable of providing your precise location anywhere on the globe,
much less that it would be smaller than a frozen waffle and cost less than
a new winch. In just a few years, I suspect that these technological
marvels will be just about everywhere, and much cheaper - at this writing
(May 1994), there are terrific handheld units with basic course plotters
selling for under \$500, and the prices keep going down.

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