A new nonlinear filter. (English) Zbl 1132.93045

Elliot, Robert J.; Haykin, Simon

Commun. Inf. Syst. 6, No. 3, 203-220 (2006).

Summary: A discrete time filter is constructed where both the observation and signal process have nonlinear dynamics with additive white Gaussian noise. Using the reference probably framework a convolution Zakai equation is obtained which updates the unnormalized conditional density. Our work obtains approximate solutions of this equation in terms of Gaussian sum when second order expansions are introduced for the non-linear terms.

MSC:

93E11	Filtering in stochastic control theory
93C10	Nonlinear systems in control theory

Keywords:

discrete time filter; convolution Zakai equation; Gaussian sum