On Filtering Methods for State-Space Systems having Binary Output Measurements

Abstract In this paper we develop two filtering algorithms for state-space systems with binary outputs. We approximate the conditional probability mass function of the output signal given the state by using a Gaussian quadrature rule. This approximation naturally leads to a Gaussian Sum structure for the a posteriori density function. Our first algorithm is based on Gaussian Mixture models, and the second algorithm is based on Particle Filtering. Finally, we present numerical examples to illustrate the effectiveness of our proposal.