Finite fast fourier transform filter for discrete linear systems with Markov jump parameters

Linear discrete time stochastic dynamical systems with switching parameters may represent a wide class of physical processes. Given the fact that, for non linear systems, the conditional density has no finite parametrization, optimal filters for this class of models are generally infinite dimensional. An exact recursive hybrid filter form has been recently found by Elliott and al [3]. The purpose of this note is to present a new simple approximation scheme of this exact version, which avoids the exponential growth memory problem of the original form. This new numerical scheme is shown to be computationnally efficient. Its implementation is discussed and a comparison of its performances with the Interacting Multiple Models (IMM) algorithm [2] shows its efficiency.