Approximate Switched-Markov Filtering for Nonlinear Systems

The Kalman filter provides optimal state estimates for completely known linear systems. Unfortunately, many physical systems are neither exactly known, nonlinear. Numerous filtering schemes for nonlinear systems have been introduced over the years: general theories for nonlinear systems tend to be complex, and, due to their generality, are of little practical use to the design engineer. On the other hand, solutions for specific nonlinearites usually apply only to a single nonlinearity, and thus are limited in their applications. This paper, however, presents a methodology whereby the nonlinearity is first approximated by a piecewise linear model, and then a common filtering scheme is applied. The efficacy of this approach is that the same filtering algorithm may be applied to a broad class of nonlinear stochastic systems.