A Novel Bayesian Filtering Method for Systems with Quantized Output Data

In this paper we develop a novel scheme for state estimation of discrete-time linear time-invariant systems with quantized output data. We take a Bayesian approach, therefore, we describe the behavior of the a posteriori probability density function of the state. The difficulty of this problem lies in the probability function of the measurable output given the state, which we approach through an approximation by a Gaussian sum, that naturally leads to a Gaussian sum for the a posteriori density function.