Fundamentals of Kalman Filtering: A Practical Approach, Second Edition

In this chapter we have investigated various filtering options, including no filtering at all, for determining the location of a receiver based on noisy range measurements from a satellite pair. The importance of satellite geometry was demonstrated, and it was shown why an extended Kalman filter is better than a simple second-order recursive least-squares filter for this problem. The value of adding process noise to the extended Kalman filter in tracking a receiver traveling along an erratic path also was demonstrated. It also was shown that an extended Kalman filter could be built that could track a stationary or constant velocity receiver based on one satellite only if enough time were available. However, if the receiver velocity was varying, one satellite was not sufficient for maintaining track.