Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.