Polynomial Filtering for Systems with Non-independent Uncertain Observations

The filtering problem for non-Gaussian, discrete-time, linear systems with correlated uncertainty in the observation equation is investigated in the present paper. A stochastic Markov sequence of correlated Bernoulli random variables is considered as a model for the uncertainty in the measurements. For this class of systems Hadidi-Schwartz defined a linear filter (giving the linear-optimal state estimate) assuming some structural properties of the system are satisfied. In the present paper similar conditions are shown to imply the existence of a polynomial filter (of any degree). Finally, the general polynomial filter equations are derived for the considered class of systems.