The optimal robust finite-horizon Kalman filtering for multiple sensors with different stochastic failure rates

This work deals with the filtering problem for norm-bounded uncertain discrete dynamic systems with multiple sensors having different stochastic failure rates. For tackling the uncertainties of the covariance matrices of state and state estimation error simultaneously, their upper bounds containing a scaling parameter are derived, and then a robust finite-horizon filtering minimizing the upper bound of the estimation error covariance is proposed. Furthermore, an optimal scaling parameter is exploited to reduce the conservativeness of the upper bounds of the state and estimation error covariances, which leads to an optimal robust filtering for all possible missing measurements and all admissible parameter uncertainties. A numerical example illustrates the performance improvement over the traditional Kalman filtering method.