How does GPS work?

Mathematical Basis


Each of the GPS satellites transmits radio signals. GPS receivers pick up these signals and measure the distance to a satellite by multiplying the speed of the signal by the time it takes the signal to get there. The speed of the signal is the speed of light and the time is encoded within the signal. The satellites also send information on their exact location.

In order to find longitude, latitude, and altitude, four satellites are needed. If a measurment is taken using just one satellite, then all that is known is that the receiver is on the surface of a sphere with radius equal to the distance to the satellite. If two satellites are used, then the receiver must be on the surface of both spheres which is the intersection of the two spheres or the perimeter of a circle. If a third satellite is used, then the location of the user is narrowed down to the two points where the three spheres intersect. Three measurements are enough for land receivers since the lower of the two points would be selected. But when in the air or space, four satellites are needed: the intersection of all four spheres will be the receiver's location. When more than four satellites are used, greater accuracy can be achieved.


There are two types of GPS services. Precise Positioning Service (P-code) is more accurate and reserved for the U.S. military and select government agency users. The other service is the Standard Positioning Service which is freely available to all users. The SPS code (C/A code) has errors purposefully encoded into it for U.S. national security reasons and is used for non-military applications. One source of error is Selective Availability (SA) and is implenented into the signal in order to keep non U.S. military users from attaining high accuracy. The errors in the signal are constantly changing. SA affects signals concerning the satellite's clock and thereby gives false information on how far the satellite is from the user which makes the receiver give less accurate values. The following table compares PPS and SPS:

 Accuracy in:



 horizontal plane

 22 meters

100 meters 

 vertical plane

27.7 meters

156 meters

time transfer

200 nanoseconds

340 nanoseconds



We have learned how to improve the accuracy that can be attained using the freely available SPS signals.

A technique called differential GPS allows for greater accuracy of the civilian code by removing the error. This requires two receivers with one stationary knowing its exact location and the other probably roaming about. Both receivers calculate their positions and the stationary receiver takes the difference of the calculated position with that of its known position to calculate what the signal error is. Since the satellites are so far away, it can be assumed that both receivers are acquiring the same errors. Once the error is found the receivers can communicate with each other to find the location of the moving receiver. Differential position accuracies of 1-10 meters are possible with DGPS.



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