### How GPS works

Over the past few years, at a cost of about \$20 billion, the United States Department of Defense has launched a series of satellites into orbit about 10,900 miles above the earth. Eventually there will be 24 total satellites in orbit. These satellites broadcast signals which, in effect, tell your GPS receiver the location of the satellite, and what time it is. These signals are very accurate (the position is accurate to centimeters, and the time is accurate to millionths of a second per year). A GPS receiver uses these signals, and by a series of calculations, can determine where the receiver is, in theory to fractions of an inch. This all sounds pretty easy, but there are a lot of tricky parts to the problem. These satellites are moving pretty fast (more than 10,000 miles per hour), so during the second, or so, that it takes the receiver to compute your position, the satellite has moved about 3 miles.

A GPS receiver triangulates using the signals from at least 3 satellites, simultaneously, to determine your latitude and longitude (called a 2D fix). With four or more satellites, you can determine your altitude as well (called a 3D fix). Normally, there are more satellites visible, so the receiver can use their signals to improve the accuracy of your position. If you are in a location where you can't see very much of the sky, you won't be able to see enough satellites. A very narrow canyon (like standing at street level among skyscrapers) might cause this sort of problem, and your receiver will tell you about it if it occurs.

### Accuracy

In general, virtually every receiver has a basic accuracy of about 10 meters, which in practice is "diluted" by geometry and other errors to about 2 or 3 times that. Vertical acccuracy is usually about twice as bad as horizontal accuracy. If you figure that your GPS position is within a hundred feet, you won't go wrong most of the time. The inaccuracies take the form of random variations in the calculated position varying from measurement to measurement and cause the displayed position to vary slightly, even when you are standing still.

No, it's not the math class where Michael Jackson teaches you how to use straightedge and compass. Your GPS receiver calculates where you are by triangulating (there's the geometry) the signals it gets from the satellites. If the satellites are distributed around the sky evenly, you can calculate an accurate position. However, if all the satellites are in a clump, you can't calculate as closely. Also, if the signals are weak (say from going through trees, etc.), you might not be able to calculate an accurate position.

All of these factors are combined in a single number called the Dilution of Precision or DOP, which can be displayed on your receiver. The DOP is a multiplier which tells you how much worse your accuracy is than the best possible. A DOP of 2 is really good, a DOP of 20 is really bad. The receivers have some way of telling you how accurate the position display is, usually telling you that you have a 95% chance of being within some distance (like 100 feet) from the displayed position.

#### Selective Availability

If you look at the spec sheet for any of the GPS receivers, you will see some sort of disclaimer which says something like:

The Global Positioning System is operated by the Department of Defense. All GPS systems are subject to accuracy degradation to 100m 2DRMS under the DoD imposed Selective Availability program.

When the GPS system was first designed some 20 years ago, they set things up so that there were two basic accuracies available. The first was called the Standard Positioning Service (SPS, also called C/A ), with an accuracy of about 300 meters, and was available to everyone. The other was called the Precise Positioning Service (PPS, also called P or Y code) with 30 meter accuracy, and was encrypted, and only available for military users (and other special people). GPS was originally designed to help target ICBM's, and it wasn't considered a good strategic idea to allow just anyone to have the 30 meter accuracies available. As it turns out, the accuracy you can get from the SPS signal with modern technology is substantially better than the original designers expected, with a few meters not out of the question. Clever equipment designers have figured out ways to use the precise signal, without needing to decode it, to get relative positions that are accurate to millimeters.

GPS has made big inroads in the surveying business, since it works between spots which can't be seen from each other, unlike conventional optical techniques (like transits and lasers). With suitable GPS equipment, costing less than \$20,000, you can measure the distance between two points 100 km apart to an accuracy of about a centimeter in a few seconds. What a boon for surveying in rolling hills or forest!

This put the Department of Defense in a bit of a quandary. They had already determined as a policy that it wasn't a good idea for high accuracy to be available to just everyone. So they came up with the idea of injecting artificial errors into the standard signals to reduce the accuracy back to around 200 meters. This is known as "Selective Availability". Selective Availability is currently turned on intermittently, but the increasingly wide spread use of GPS has prompted a lot of discussion about a policy that, in effect, was formulated 20 years ago. However, the manufacturers have to cover themselves, hence the disclaimer.

Copyright 1997, Jim Lux / gpsside.htm / Back to the article / Back to home page / Mail to Jim