Projection filters and matched moment filters in tracking

Abstract

In problems in tracking, the natural stochastic model for the measurements and the dynamics of target and observer often contain nonlinear elements, and the design of a recursive tracking algorithm has to be treated as a problem of approximation in nonlinear filtering. The extended Kalman filter has proved to be a surprisingly effective algorithm, producing good estimates for many problems, but it is susceptible to sudden loss of track. Consequently, as the demands on the performance of tracking algorithms have increased, new methods of tracker design have emerged, notably the particle filter and the unscented Kalman filter of Julier, Uhlman and Durrant-Whyte. These are general methods in nonlinear filter design, that have enabled the class of problems for which there are effective algorithms to be greatly extended. But they, too, have their limitations: the particle filter, though highly flexible, is computationally expensive; the unscented Kalman filter, though it is widely applicable and much more 'robust' than the extended Kalman filter, can still lose accuracy in some extreme situations.To achieve both computational efficiency and accuracy in tracking appears to require the design of algorithms that are more closely tailored to the problem in hand.