GPS, short for **Global Positioning System**, is a means for locating any point on the earth. It has many uses; navigation, surveying, vehicle tracking, hiking and outdoor recreation just to name a few.

In the 1970s the Department of Defense (DoD) conceived the idea of GPS. It was born from a need to accurately determine the position of ballistic missile submarines prior to launching missiles. All the old methods of determining position had their flaws. Those methods were affected by atmospheric conditions, limited in range, subject to enemy jamming, or degraded by interference.

The GPS system is made of 24 NAVSTAR satellites and five ground stations. The ground stations are responsible for keeping the satellites in precise orbit. The DoD placed each of the 24 satellites in a precise orbit at an altitude of 10,900 miles. Each satellite weighs two tons, is 18.5 feet long, and orbits the earth in a little less than 12 hours.

**The Trick: Measuring Distance With Time**

Each of the 24 satellites transmits its own unique signal. The GPS unit has stored in it those 24 separate “signatures” and therefor knows the postition of each satellite. By measuring the distance to at least four satellites, each in its distinct orbit, location of the GPS receiver can be pinpointed down to as little as 3 meters. Distance to each satellite is measured simply by the time it takes for a radio wave to reach the GPS unit.

To be able to lock onto four signals, a GPS unit needs to have at least four channels. Most units have 12 channels. Calculations were made for the orbits necessary for each of the 24 satellites so that at least five are “visible” to any one point on the earth at one time.

GPS can be used in any type of weather, and is used on land, in the air, and for marine applications. Some conditions limit its usefulness. Heavy tree cover and cliffs, steep hills, or tall buildings can interfere, but often in those situations one can move to a better location and still not be too far off the intended route.

The gps system consists of three pieces. There are the satellites that transmit the position information, there are the ground stations that are used to control the satellites and update the information, and finally there is the receiver that you purchased. It is the receiver that collects data from the satellites and computes its location anywhere in the world based on information it gets from the satellites. There is a popular misconception that a gps receiver somehow sends information to the satellites but this is not true, it only receives data. So, just how is it able to do compute its position?

**Geometric View**

Your gps receiver uses an elaboration of a technique that is tried and true and used by navigators and surveyors for centuries. Basically you use a known set of locations to compute your current location by taking fixes on the known sites. In the old days you took bearings (compass sightings) on existing locations and triangulated these on a chart to compute a fix on your location. Once you have a compass bearing you can draw a line through the known location and you know you are somewhere on that line. Do the same thing to a second point and the two lines will intersect. This is your position. If you try a third point it should intersect at the same place the other two lines intersect. Usually however, because of imprecise sightings, it intersects both lines at slightly different points thereby forming a small triangle. You are somewhere inside that triangle but you don’t know exactly where. If the triangle is small enough you consider it good enough, otherwise you need to take another sighting. Accuracy is determined primarily on your ability to get and plot an accurate bearing as well as the geometry of the known sites available. This means that if the sites are very close together you will get poorer results than if they are at some angular distance apart. What you would really like were two sites that were 90 degrees apart for best accuracy.

The gps receiver uses a slightly different approach. It measures its distance from the satellites and uses this information to compute a fix. How can it measure distance? Well it really measures the length of time the signal takes to arrive at your location and then based on knowing that the signal moves at the speed of light it can compute the distance based on the travel time. However, unlike the known sites of the olden days, these sites are moving. The solution to this problem is to have the satellite itself send enough information to calculate its current location relative to your receiver. Now, armed with the satellite location and the distance from the satellite we can expect that we are somewhere on a sphere that is described by the radius (distance) and centered at the satellite location.

By acquiring the same information from a second satellite we can compute a second sphere that cuts the first one at a plane. Now we know we are somewhere on the circle that is described by the intersection of the two spheres. If we acquire the same information from a third satellite we would notice that the new sphere would intersect the circle at only two points. If we know approximately where we are we can discard one of those points and we are left with our exact fix location in 3D space. Now, what would happen if we were to acquire the information from a fourth satellite? We should expect that it would show us to be at exactly the same point we just computed above. But what if it isn’t? Before we can answer that question we need a little more background.

A more basic question is, “How does the gps know the travel time so that it can compute the distance?” The satellite sends the current time along with the message so the gps can subtract its knowledge of the current time from the satellite time in the message (which is the time that the signal started its descent) and use this to compute the difference. For this to work the time in your gps must be pretty accurate – to a precision of well under a microsecond. The satellite itself has an atomic clock to keep the time very precisely, but your unit is probably not big enough nor expensive enough to have an atomic clock built in, so your clock is likely to be in error! For this reason our assumptions about the distance calculation are likely to have considerable error and the fourth satellite fix will reveal this to us. However, if we assume the error is caused by an error in our clock then we can adjust our clock a little and recompute all 4 fixes, continuing to do this iteratively until the error disappears! We will then have a good position fix and as a side effect we will also have the correct time to about 200 nanoseconds or so. One of the applications of gps technology is to provide the correct time even when we don’t care about our position.

Maintaining the fix means that we need to continuously recalculate the information based on the moving satellites. Once we have a number of fixes we can derive much more information than just location data. For example a gps can compute the travel direction (compass heading) by comparing current location to previous location. Similarly the gps can keep track of travel distance, compute speed, record travel time and other valuable data.

This view is simplified. In addition to the data already mentioned the unit uses Doppler data from the moving satellites, almanac data to figure out the approximate positions of all the satellites, and ephemeris data download directly from the satellite that can be used to compute its position in the sky. For a more detailed look at this information you should read the section on obtaining a fix. Similar to the geometry problem we had in the older system of taking bearings on fixed sites, the satellite geometry has a significant effect in the accuracy of our final position. A unitless number representing this geometry is called Dilution Of Position, DOP and is used by the gps in determining which of the satellites available represents the best ones to use. The smaller the number the better the geometry.