Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises, 4th Edition

7

Linearization, Nonlinear Filtering, and Sampling Bayesian Filters

Many of the early applications of Kalman filtering were in navigation where the measurements were nonlinear. Thus, linearization has been an important consideration in applied Kalman filtering right from the start, and it continues to be so to this very day. Linearization is the main topic of Sections 7.1 and 7.2, and it is the authors' recommendation that the student just new to Kalman filtering should begin with these sections, because they are very basic. In particular, the extended Kalman filter that is discussed in Section 7.2 was one of the early means of coping with nonlinear measurements, and it is still the method of choice in many applications. However, there are some newer extensions of basic Kalman filtering that have been introduced in recent years that are also important. Three of these, namely the ensemble, unscented, and particle filters have been selected for discussion here in Sections 7.4, 7.5, and 7.6. Research in Kalman filtering is still quite active, so it is reasonable to expect to see further extensions and variations on the basic filter in the years ahead.

7.1 LINEARIZATION

Some of the most successful applications of Kalman filtering have been in situations with nonlinear dynamics and/or nonlinear measurement relationships. We now examine two basic ways of linearizing the problem. One is to linearize about some nominal trajectory in state space that does not depend on the measurement data. ...