Adaptive Decentralized Kalman Filters with Non-Common States for Nonlinear Systems

Abstract This paper presents two fault tolerance methods for decentralized Kalman filter with non-common states (DKF-NCS) for nonlinear systems. The DKF-NCS is used in a sensor network, where states are not uniform across all nodes. To detect and isolate faulty measurements, the χ 2 test has been quite useful, where faulty measurements are detected based on the innovation error and innovation error covariance matrix. However, the innovation error and innovation error covariance matrix are dependent on the predicted state vector and its error covariance along with measurement model. The χ 2 distribution test fails, if the predicted state vector is not consistent with its predicted error covariance matrix. Also, due to processing of set of measurements independently, fault detection happens more often in decentralized estimation compared to centralized estimation. Therefore, discarding the valid measurements based on χ 2 detector may impact the performance of decentralized estimators significantly. To overcome this problem, we propose two adaptive fault tolerance methods. The first method handles faulty measurements at the assimilation step by applying weighted correction of the information and information matrix. The second method modifies the measurement noise matrix based on a closed-form solution, if fault is detected. These methods are validated using 100 simulation runs for a tracking problem. Overall, the proposed methods are demonstrated to be superior compared to the χ 2 test and an existing adaptive extended Kalman filter.