24. GPS Errors, Initialization, and Calibration

GPS Summary

GPS (Global Positioning System) is an amazing but complex system which provides unbiased but noisy measurements of absolute position. These measurements are used in conjunction with accelerometers (which are low noise but susceptible to drift) to infer vehicle position.

One of the truly remarkable properties of GPS is its infinite scalability. Since satellites only transmit information and don't have to receive any external data, one satellite can serve an unlimited number of GPS receivers.

How it works

A GPS receiver needs a line-of-sight to four GPS satellites. With this established, it can calculate the time of flight from each satellite to the receiver and then perform trilateration to infer its position. We can also use GPS to directly measure velocity by measuring Doppler shift.

Each time of flight measurement defines a "pseudorange" from the receiver to the corresponding satellite. In an ideal world, each "pseudorange" would be exact "range" from receiver to satellite. If this were the case, we would only need three satellites to localize a receiver on (or near) the surface of the Earth.

The fourth satellite is necessary to account for the "clock error" of the receiver.

Sources of Errror

Error is introduced anytime the signal from satellite to receiver is delayed. Light moves quickly and a delay of only 1 nanosecond corresponds to about 1 foot (30 cm) of error in calculated distance. There are a few ways that these errors tend occur:

1. Atmospheric Effects: electrons in the ionosphere can interfere with and delay the signal.
2. Multipath Errors: these occur when the satellite signal reflects off of some surface before reaching the receiver.