Recursive Least-Squares Wiener Consensus Filter and Fixed-Point Smoother in Distributed Sensor Networks

Abstract

Distributed Kalman filter (DKF) is classified into the information fusion Kalman filter (IFKF), i. e. the centralized Kalman filter (CKF), and the Kalman consensus filter (KCF) in distributed sensor networks. The KCF has the advantage to improve the estimate of the state at the sensor node uniformly by incorporating the information of the observations and the filtering estimates at the neighbor nodes. In the first devised KCF, a user adjusts the consensus gain. This paper designs the recursive least-squares (RLS) Wiener consensus filter and fixed-point smoother that do not need to be adjusted in linear discrete-time stochastic systems. In addition to the observation equation at the sensor node, an observation equation is introduced excessively. Here, the new observation is the sum of the filtering estimates of the signals at the neighbor nodes of the sensor node. Thus, it is interpreted that the RLS Wiener consensus estimators incorporate the information of the observations at the neighbor nodes indirectly because the observations are used in the calculations of the filtering estimates. A numerical simulation example shows that the proposed RLS Wiener consensus filter and fixed-point smoother are superior in estimation accuracy to the RLS Wiener estimators.