Filtering for nonlinear systems driven by nonwhite noises:an approximation scheme

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Abstract
The filtering problem is considered for a nonlinear model with state and observation equations driven by noise processes having a Markovian representation; this includes the case of systems driven by Gaussian noise processes with stationary increments having rational spectral densities. Under some natural regularity conditions the model is shown to be equivalent to one in which the observation has a noisy as well as a noiseless component. For the model in this latter equivalent form and where the coefficients are supposed to depend causally on the observations, we study an approximation scheme, based on periodic sampling. An error bound for the approximation is derived in the case when there are only noisy observations. In this latter case we consider also the situation when the system depends on an unknown random parameter and derive a robustness result in terms of the probability distribution of this parameter.