Distributed Kalman Filters With Random Sensor Activation and Noisy Channels

This paper studies distributed Kalman filtering problems for sensor networks with random sensor activation and noisy channels. Each sensor measures the target state with a random activation and receives state estimates of its neighbor nodes. Communication noises are considered in communication links between sensors and their neighbor nodes. Considering cross-covariance matrices between sensors, an optimal distributed Kalman filter (ODKF) with a given recursive structure is proposed for each sensor, which depends on the knowledge whether a sensor itself is activated to measure the target state or not and whose filter gains and covariance matrices depend on random activation rate of the sensor. In the ODKF algorithm, optimal Kalman filter gain for each sensor and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. To reduce computational cost, a suboptimal distributed Kalman filter (SDKF) is also presented by considering a locally minimum upper bound of the filtering error covariance matrix, where the calculation of cross-covariance matrices among sensor nodes is avoided. The stability and steady-state property of the proposed ODKF and SDKF algorithms are explored. Finally, the proposed methods are also extended to the nonlinear scenarios. Simulation examples show the effectiveness of the proposed algorithms.