Distributed Recursive Filtering for Time-Varying Systems with Dynamic Bias over Sensor Networks: Tackling Packet Disorders

In this paper, a distributed filter is designed for time-varying systems corrupted by dynamic bias and packet disorders over sensor networks, where the plant under consideration includes stochastic bias which is governed by a dynamical equation. Moreover, the transmission delays are present in all sensor-to-filter communication channels, and such delays are described by using random variables that have known probability distributions. We focus on constructing a distributed yet recursive filter under the corruption of dynamic bias plus packet disorders. By means of the inductive method, upper bounds (on attained error covariances of the distributed filter) are first given and later minimized by properly parameterizing filter gains. Subsequently, a sufficient condition is presented to rigorously ensure the mean-square boundedness with respect to attained filtering errors. Finally, an example is given for effectiveness validation. This work was supported by National Natural Science Foundation of China under Grants 61933007, 62103359, 62173292 and 12071409, the Natural Science Foundation of Universities in Jiangsu Province of China under Grant 21KJB120011, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany.