Distributed Kalman filtering for uncertain dynamic systems with state constraints

This article addresses the distributed state estimation problem for uncertain time-varying dynamic systems with state constraints over a sensor network. By using a null space method, the distributed state estimation problem for uncertain dynamic systems with state constraints can be cast into a new unconstrained distributed state estimation problem for reduced uncertain dynamic systems. A constrained distributed Kalman filter is proposed, and it is shown that the full state estimates can be recovered at any time and satisfy the constraints. An optimized upper bound of the estimation error covariance of each sensor is obtained, and the corresponding gains are designed. The application conditions of the proposed algorithm are mild, and they can be off-line checked. Furthermore, the computational requirements in this article are also reduced compared with the existing results. Finally, the performance of the proposed filter algorithm is demonstrated through numerical simulations.