Information theoretic quantiser design for decentralised estimation of hidden Markov models

Quantiser design for a nonlinear filter is considered in the context of a decentralised estimation system with communication constraints. The filter is based on the quantised outputs of a discrete-time, two-state hidden Markov model (HMM) as measured by two remote sensor nodes. The optimal quantisation scheme is obtained by maximising the mutual information between the quantised measurements and the hidden Markov states. Filter performance is measured in terms of the probability of estimation error and is investigated through simulation for HMMs with both independent and correlated white Gaussian noise in the measurements. The performance of the filter based on continuous, unquantised signals provides a benchmark for the performance of the filter based on quantised measurements. Therefore, a method for computing the probability of estimation error directly for the continuous filter is also presented.