Power-efficient dynamic quantization for multisensor HMM state estimation over fading channels

In this paper, we address the problem of designing power efficient quantizers for state estimation of hidden Markov models using multiple sensors communicating to a fusion centre via error-prone randomly time-varying flat fading channels modelled by finite state Markov chains. Our objective is to minimize a tradeoff between the long term average of mean square estimation error and expected total power consumption. We formulate the problem as a stochastic control problem by using Markov decision processes. Under some mild assumption on the measurement noise at the sensors, the discretized action space (quantization thresholds and transmission power levels) version of the optimization problem forms a unichain Markov decision process for stationary policies. The solution to the discretized problem provides optimal quantization thresholds and power levels to be communicated back to the sensors via a feedback channel. Moreover, in order to improve the performance of the quantization system, we employ a gradient- free stochastic optimization technique to determine the optimal set of quantization thresholds from which optimal quantization levels are determined. The performance results for estimation error/total transmission power tradeoff are studied under various channel conditions and sensor measurement qualities.