Communications in Information and Systems
Volume 6 (2006)
A new nonlinear filter
Pages: 203 – 220
A discrete time filter is constructed where both the observation and signal process have non-linear dynamics with additive white Gaussian noise. Using the reference probably frame- work 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.