Distributed Filtering Under Constrained Bit Rate Over Wireless Sensor Networks: Dealing With Bit Rate Allocation Protocol

This article is concerned with the distributed filtering issue for linear discrete-time systems under bounded noises and constrained bit rate over wireless sensor networks. The communication between different sensor nodes is implemented via a wireless digital communication network with limited bandwidth. A bit rate constraint, which is subject to the so-called bandwidth allocation strategy, is placed to quantify the effect of the network bandwidth on the distributed filtering performance. An improved coding-decoding procedure is proposed to enable each node to decode messages from its neighbor nodes. Based on this procedure, a decoded-innovation-based distributed filtering scheme is put forward and a sufficient condition is established to ensure that the filtering error dynamics is ultimately bounded. Subsequently, a relationship between the bit rate and certain specific filtering performance is discovered. The desired parameters of the distributed filter are determined via solving two optimization problems whose objectives are actually the filtering performance indices including the smallest ultimate bound and the fastest decay rate. Furthermore, the codesign issue of the bit rate allocation protocol and the filter gain is converted into the mixed integer nonlinear programming problem, which is solved by means of the particle swarm optimization algorithm and the linear matrix inequality technique. Finally, numerical simulations on three scenarios are provided to verify the validity of the proposed distributed filtering approach.