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GPS Receivers
How GPS Receivers Work
BY MARSHALL BRAIN & TOM HARRIS
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.
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 satellits (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.
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 previous examples 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.
GPS Calculations
On the previous page, 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.
In
other words, there is only one value for the "current time" that the
receiver can use.
The
correct time value will cause all of the signals that the receiver is receiving
to align at a single point in space.
That
time value is the time value held by the atomic clocks in all of the
satellites.
So
the receiver sets its clock to that time value, and it then has the same time
value that all the atomic clocks in all of the satellites have. The GPS
receiver gets atomic clock accuracy "for free."
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.
In
the next section, we'll look at errors that may occur and see how the GPS
receiver corrects them.
Differential GPS
So far, we've learned how a GPS receiver calculates
its position on earth based on the information it receives from four located
satellites.
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.
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.
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
Marshall Brain, Founder
Marshall Brain is the founder of HowStuffWorks. He holds a bachelor's degree in electrical engineering from Rensselaer Polytechnic Institute and a master's degree in computer science from North Carolina State University. Before founding HowStuffWorks, Marshall taught in the computer science department at NCSU and ran a software training and consulting company. Learn more at his site.
Marshall Brain is the founder of HowStuffWorks. He holds a bachelor's degree in electrical engineering from Rensselaer Polytechnic Institute and a master's degree in computer science from North Carolina State University. Before founding HowStuffWorks, Marshall taught in the computer science department at NCSU and ran a software training and consulting company. Learn more at his site.
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