SetMembership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty This paper presents a new setmembership based hybrid Kalman filter (SMHKF) by combining the Kalman filtering (KF) framework with the setmembership concept for nonlinear state estimation under systematic uncertainty consisted of both stochastic error and unknown but bounded (UBB) error. Upon the linearization of the nonlinear system model via a Taylor series expansion, this method introduces a new UBB error term by combining the linearization error with systematic UBB error through the Minkowski sum. Subsequently, an optimal Kalman gain is derived to minimize the mean squared error of the state estimate in the KF framework by taking both stochastic and UBB errors into account. The proposed SMHKF handles the systematic UBB error, stochastic error as well as the linearization error simultaneously, thus overcoming the limitations of the extended Kalman filter (EKF). The effectiveness and superiority of the proposed SMHKF have been verified through simulations and comparison analysis with EKF. It is shown that the SMHKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.

Distributed filtering for uncertain systems under switching sensor networks and quantized communications Abstract   This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and intervalquantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an eventtriggered update based DKF is presented with a tighter mean square error (MSE) bound than that of the timedriven one by designing a proper threshold. Both the two DKFs are shown to provide the upper bounds of MSE online for each sensor. Under mild conditions on systems and networks, the MSE boundedness and asymptotic unbiasedness for the proposed two DKFs are proved. Finally, numerical simulations demonstrate the effectiveness of the developed filters.