Distributed set-valued estimation in sensor networks with limited communication data rate

This paper is concerned with a distributed set-valued estimation problem in noisy sensor networks with limited communication data rate. The sensors iterate a sample-quantize-exchange process: firstly, the sensors synchronously take noisy measurements of the plant; secondly, owing to the communication channel constraint, each sensor makes the manipulation of quantization on its measurement, estimate and performance bound by using a static logarithmic quantizer; thirdly, the quantized information is exchanged among the neighbors. By assuming hard bounds on the process noises and measurement noises, a distributed set-valued estimation strategy is proposed for each sensor to generate a set of estimates in state space which contains the true state of the plant. A sufficient condition for the existence of the distributed set-valued estimators is derived, and the estimator parameters are determined by solving a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.