You ask somebody else where you are, and she says, "You are 690 km from Emerald." Now you're getting somewhere. If you combine this information with the Mt. Isa 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 km from Mt. Isa and 690 km from Emerald.

If a third person tells you that you are 615 km from Dirranbandi, 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 -- near Windorah, Qld. ( if you have a map.)

This same concept works in three-dimensional space, as well, but we are dealing with spheres instead of circles.

3-D Trilateration.
Imagine each satellite to be the centre of an imaginary sphere. If we know our exact distance from a satellite in space, we know we are somewhere on the surface of an imaginary sphere with a radius equal to the distance to the satellite. If we know our exact distance from a second satellite, the same fact will apply.The intersecting plane of the spheres forms a perfect circle, and the observer will be at some point on the circumference of that circle. If we take a third and a fourth measurement from two more satellites, similar circular intercepts will give a precise point of observation on the Earth surface. Receivers generally look to four or more satellites, to improve accuracy and provide precise altitude information.

In order to make this calculation, the GPS receiver has to know two things:

• The location of at least three satellites in " line of sight ".
• 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. They transmit on several low power ( 20 - 25 watts ) radio frequencies in the UHF range. The civilain frequency is designated L1, 1575.42 mhz. 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 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.

Measuring Distance.
We have seen 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 master control station 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.