Distributed Robust State Estimation for Sensor Networks: A Risk-Sensitive Approach

In this paper, we investigate a distributed robust state estimation problem for linear Gaussian systems measured by a sensor network, where the sensors can communicate only with their neighbors and each sensor runs a local filter to estimate the state of the process based on the measurements from its neighbors. We present a distributed risk-sensitive filtering algorithm, where the high-gain dynamic consensus filter is utilized to compute the fused measurement data and the fused covariance-inverse matrices, based on which, the local filter is updated in a Riccati-based linear recursive form. For linear time-invariant systems, the asymptotic stability of local estimators in the proposed distributed risk-sensitive filtering algorithm is guaranteed if the value of the risk-sensitive parameter is chosen such that the centralized risk-sensitive filter is asymptotically stable. The robustness of the proposed risk-sensitive filtering algorithm to system uncertainty is verified by simulation results.