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 edition of HowStuffWorks,
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, but 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.
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.
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.
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 in to 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.
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.
Most receivers have a certain amount of memory available
for you to store your own navigation data. This greatly
expands the functionality of the receiver, because it
essentially lets you make a record of specific points on
Earth. The basic unit of user input is the waypoint. A
waypoint is simply the coordinates for a particular location.
You can save this in your receiver's memory in two ways:
You can tell the receiver to record its coordinates when
you are at that location.
You can find the location on a map (the internal map or
another one) and enter its coordinates as a waypoint.
This capability lets you use your GPS receiver in a
number of different ways. You can record any specific location
that interests you so you'll be able to find it again at a
later time. This might include:
Good camp sites
Favorite road-side shops
Excellent fishing spots
Scenic overlooks
Where you left your car
You can also combine a series of different waypoints to
form a route. One way to use this function is to
periodically record waypoints as you make a trip so that you
can backtrack, or follow the same route again in the future.
Route-mapping also lets you plan ahead: When you have time to
examine a map at home, you can record a series of waypoints
along the roads or trails that lead to your destination. Then,
when you're traveling, all you'll need to find your way is
your GPS receiver.
If the receiver has a data port, you can also
download your routes to a computer, which has much more
storage space, and then upload them again when you plan to
follow those routes. Computers can do a lot more with GPS
location data than your average receiver, because computers
have much more memory and much faster processing capabilities.
You can also update your computer maps easily, so you can
include any surveying adjustments or changes in an area.
At its heart, a GPS receiver is just an accurate way to get
raw positional data, which can then be applied to geographic
information that has been accumulated over the years. This
idea is incredibly simple, but it has seemingly endless
applications. The considerable contributions of GPS to
aviation, maritime navigation, military operation, surveying
and recreation have already secured its place among the most
revolutionary inventions of all time.
For much more information on GPS and GPS receivers, check
out the links on the next page.
