Our
ancestors had to go to pretty extreme measures to keep from
getting lost. They erected monumental landmarks, laboriously
drafted detailed maps and learned to read the stars
in the night sky.
Things are much, much easier today. For less than $100, you
can get a pocket-sized gadget that will tell you exactly where
you are on Earth at any moment. As long as you have a GPS
receiver and a clear view of the sky, you'll never be lost
again.
In this article, we'll find out how these handy guides pull
off this amazing trick. As we'll see, the Global Positioning
System is vast, expensive and involves a lot of technical
ingenuity, but the fundamental concepts at work are quite
simple and intuitive.
Trilateration Basics When people talk about
"a GPS," they usually mean a GPS receiver. The
Global Positioning System (GPS) is actually a
constellation of 27 Earth-orbiting satellites
(24 in operation and three extras in case one fails). The U.S.
military developed and implemented this satellite network as a
military navigation system, but soon opened it up to everybody
else.
Photo courtesy NASA NAVSTAR GPS
satellite
Each of these 3,000- to 4,000-pound solar-powered
satellites circles the globe at about 12,000 miles (19,300
km), making two complete rotations every day. The orbits are
arranged so that at any time, anywhere on Earth, there are at
least four satellites "visible" in the sky.
A GPS receiver's job is to locate four or more of these
satellites, figure out the distance to each, and use this
information to deduce its own location. This operation is
based on a simple mathematical principle called
trilateration. Trilateration in three-dimensional space
can be a little tricky, so we'll start with an explanation of
simple two-dimensional trilateration.
2-D Trilateration Imagine you are somewhere
in the United States and you are TOTALLY lost -- for whatever
reason, you have absolutely no clue where you are. You find a
friendly local and ask, "Where am I?" He says, "You are 625
miles from Boise, Idaho."
This is a nice, hard fact, but it is not particularly
useful by itself. You could be anywhere on a circle around
Boise that has a radius of 625 miles, like this:
You ask somebody else where you are, and she says, "You are
690 miles from Minneapolis, Minnesota." Now you're getting
somewhere. If you combine this information with the Boise
information, you have two circles that intersect. You now know
that you must be at one of these two intersection points, if
you are 625 miles from Boise and 690 miles from Minneapolis.
If a third person tells you that you are 615 miles from
Tucson, Arizona, you can eliminate one of the possibilities,
because the third circle will only intersect with one of these
points. You now know exactly where you are -- Denver,
Colorado.
This same concept works in three-dimensional space, as
well, but you're dealing with spheres instead of
circles. In the next section, we'll look at this type of
trilateration.
3-D Trilateration Fundamentally,
three-dimensional trilateration isn't much different from
two-dimensional trilateration, but it's a little trickier to
visualize. Imagine the radii from the examples in the last
section going off in all directions. So instead of a series of
circles, you get a series of spheres.
If you know you are 10 miles from satellite A in the sky,
you could be anywhere on the surface of a huge, imaginary
sphere with a 10-mile radius. If you also know you are 15
miles from satellite B, you can overlap the first sphere with
another, larger sphere. The spheres intersect in a perfect
circle. If you know the distance to a third satellite, you get
a third sphere, which intersects with this circle at two
points.
The Earth itself can act as a fourth sphere -- only one of
the two possible points will actually be on the surface of the
planet, so you can eliminate the one in space. Receivers
generally look to four or more satellites, however, to improve
accuracy and provide precise altitude information.
In order to make this simple calculation, then, the GPS
receiver has to know two things:
The location of at least three satellites above you
The distance between you and each of those satellites
The GPS receiver figures both of these things out by
analyzing high-frequency, low-power radio signals from
the GPS satellites. Better units have multiple receivers, so
they can pick up signals from several satellites
simultaneously.
Radio
waves are electromagnetic energy, which means they travel
at the speed of light (about 186,000 miles per second, 300,000
km per second in a vacuum). The receiver can figure out how
far the signal has traveled by timing how long it took the
signal to arrive. In the next section, we'll see how the
receiver and satellite work together to make this measurement.
Measuring Distance In the last section, we
saw that a GPS receiver calculates the distance to GPS
satellites by timing a signal's journey from satellite to
receiver. As it turns out, this is a fairly elaborate process.
At a particular time (let's say midnight), the satellite
begins transmitting a long, digital pattern called a pseudo-random
code. The receiver begins running the same digital
pattern also exactly at midnight. When the satellite's signal
reaches the receiver, its transmission of the pattern will lag
a bit behind the receiver's playing of the pattern.
The length of the delay is equal to the signal's travel
time. The receiver multiplies this time by the speed of light
to determine how far the signal traveled. Assuming the signal
traveled in a straight line, this is the distance from
receiver to satellite.
In order to make this measurement, the receiver and
satellite both need clocks that can be synchronized down to
the nanosecond. To make a satellite positioning system using
only synchronized clocks, you would need to have atomic
clocks not only on all the satellites, but also in the
receiver itself. But atomic clocks cost somewhere between
$50,000 and $100,000, which makes them a just a bit too
expensive for everyday consumer use.
The Global Positioning System has a clever, effective
solution to this problem. Every satellite contains an
expensive atomic clock, but the receiver itself uses an
ordinary quartz
clock, which it constantly resets. In a nutshell, the
receiver looks at incoming signals from four or more
satellites and gauges its own inaccuracy.
Differential GPS When you measure the
distance to four located satellites, you can draw four spheres
that all intersect at one point. Three spheres will intersect
even if your numbers are way off, but four spheres will
not intersect at one point if you've measured incorrectly.
Since the receiver makes all its distance measurements using
its own built-in clock, the distances will all be
proportionally incorrect.
The receiver can easily calculate the necessary adjustment
that will cause the four spheres to intersect at one point.
Based on this, it resets its clock to be in sync with the
satellite's atomic clock. The receiver does this constantly
whenever it's on, which means it is nearly as accurate as the
expensive atomic clocks in the satellites.
In order for the distance information to be of any use, the
receiver also has to know where the satellites actually are.
This isn't particularly difficult because the satellites
travel in very high and predictable orbits. The GPS receiver
simply stores an almanac that tells it where every
satellite should be at any given time. Things like the pull of
the moon and the sun do
change the satellites' orbits very slightly, but the
Department of Defense constantly monitors their exact
positions and transmits any adjustments to all GPS receivers
as part of the satellites' signals.
This system works pretty well, but inaccuracies do pop up.
For one thing, this method assumes the radio signals will make
their way through the atmosphere at a consistent speed (the
speed of light). In fact, the Earth's atmosphere slows the
electromagnetic energy down somewhat, particularly as it goes
through the ionosphere and troposphere. The delay varies
depending on where you are on Earth, which means it's
difficult to accurately factor this into the distance
calculations. Problems can also occur when radio signals
bounce off large objects, such as skyscrapers,
giving a receiver the impression that a satellite is farther
away than it actually is. On top of all that, satellites
sometimes just send out bad almanac data, misreporting their
own position.
Differential GPS (DGPS) helps correct these errors.
The basic idea is to gauge GPS inaccuracy at a stationary
receiver station with a known location. Since the DGPS
hardware at the station already knows its own position, it can
easily calculate its receiver's inaccuracy. The station then
broadcasts a radio signal to all DGPS-equipped receivers in
the area, providing signal correction information for that
area. In general, access to this correction information makes
DGPS receivers much more accurate than ordinary receivers. For
additional information on DGPS, check out Starlink's DGPS
Explained.
Using the Data In the last couple of
sections, we saw that the most essential function of a GPS
receiver is to pick up the transmissions of at least four
satellites and combine the information in those transmissions
with information in an electronic almanac, all in order to
figure out the receiver's position on Earth.
Once the receiver makes this calculation, it can tell you
the latitude, longitude and altitude (or some similar
measurement) of its current position. To make the navigation
more user-friendly, most receivers plug this raw data into map
files stored in memory.
Photo courtesy Garmin The StreetPilot II, a GPS receiver with
built-in maps for
drivers
You can use maps stored in the receiver's memory, connect
the receiver to a computer
that can hold more detailed maps in its memory, or simply buy
a detailed map of your area and find your way using the
receiver's latitude and longitude readouts. Some receivers let
you download detailed maps into memory or supply detailed maps
with plug-in map cartridges.
A standard GPS receiver will not only place you on a map at
any particular location, but will also trace your path across
a map as you move. If you leave your receiver on, it can stay
in constant communication with GPS satellites to see how your
location is changing. With this information and its built-in
clock, the receiver can give you several pieces of valuable
information:
How far you've traveled (odometer)
How long you've been traveling
Your current speed (speedometer)
Your average speed
A "bread crumb" trail showing you exactly where you have
traveled on the map
The estimated time of arrival at your destination if you
maintain your current speed
To obtain this last piece of information, you would have to
have given the receiver the coordinates of your destination,
which brings us to another GPS receiver capability: inputting
location data.
