Power Constrained Dynamic Quantizer Design for Multisensor Estimation of HMMs with Unknown Parameters

This paper addresses an estimation problem for hidden Markov models (HMMs) with unknown parameters, where the underlying Markov chain is observed by multiple sensors. The sensors communicate their binary-quantized measurements to a remote fusion centre over noisy fading wireless channels under an average sum transmit power constraint. The fusion centre minimizes the expected state estimation error based on received (possibly erroneous) quantized measurements to determine the optimal quantizer thresholds and transmit powers for the sensors, called the optimal policy, while obtaining strongly consistent parameter estimates using a recursive maximum likelihood (ML) estimation algorithm. The problem is formulated as an adaptive Markov decision process (MDP) problem. To determine an optimal policy, a stationary policy is adapted to the estimated values of the true parameters. The adaptive policy based on the maximum likelihood estimator is shown to be average optimal. A nonstationary value iteration scheme is employed to obtain adaptive optimal policies which has the advantage that the policies are obtained recursively without the need to solve the Bellman optimality equation at each time step. We provide some numerical examples to illustrate the analytical results.