Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks

This paper investigates the problem of designing decentralized robust Kalman filters for sensor networks observing a physical process with parametric uncertainty. A sensor network consists of distributed collection of nodes, each of which has sensing, communication and computation capabilities. We consider a heterogeneous sensor network consisting of two types of nodes (type A and type B) and central base station. Type A nodes undertake the sensing and make noisy observations of the same physical process while type B nodes play the role of cluster-heads. We derive the information form of robust Kalman filter by using the Krein space approach which proves to be useful to fuse the cluster state estimates. We obtain the decentralized robust Kalman filter for each type B node for the state estimation of uncertain stochastic system by taking into consideration the sensing model of each cluster and the information form of robust Kalman filter. The type B nodes transmit their state estimates along with the inverse of error covariance matrix to the central base station which fuses the cluster state estimates to generate the overall global state estimate. Simulation results demonstrate that the performance of the centralized state estimate is comparable to the performance of the global state estimate and this suggests that they are identical.