Distributed reduced-order Kalman consensus filter for multisensor networked descriptor systems

Abstract

In the context of multisensor linear discrete networked descriptor systems, an equivalence transformation, achieved via singular value decomposition, leads to the derivation of two lower-dimensional non-descriptor subsystems. Each network node can perform state estimation based on data of its own and its neighboring nodes. Applying the Kalman consensus filter (KCF) framework, wherein one-step prediction estimates of a reduced-order subsystem are exchanged among network nodes, a distributed reduced-order KCF is designed for each sensor node, incorporating multiple consensus gains. This design facilitates collaborative state estimation by enabling nodes to leverage both their own measurements and the prediction estimates received from their neighbors. The optimal Kalman filtering gains and the optimal consensus filtering gains are determined by minimizing the trace of the filtering error covariance matrix. The investigation delves into the stability and steady-state characteristics of the tailored distributed reducer-order filtering systems. The performance of the algorithms is confirmed through illustrative simulation cases.