Abstract
This paper presents a new set-membership based hybrid Kalman filter (SM-HKF) by combining the Kalman filtering (KF) framework with the set-membership 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 SM-HKF 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 SM-HKF have been verified through simulations and comparison analysis with EKF. It is shown that the SM-HKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.
Highlights
The nonlinear state estimation problem has received significant attention in the fields of process control [1], tracking guidance [2], system identification [3], sensor networks [4], navigation [5,6] and so on
Motivated by the techniques reported in References [11] and [21], this paper proposes a set-membership based hybrid Kalman filter (SM-HKF) for nonlinear system state estimation in the presence of both unknown but bounded (UBB) error and stochastic error
This paper presents a new SM-HKF to address the issue of nonlinear state estimation with systematic uncertainty
Summary
The nonlinear state estimation problem has received significant attention in the fields of process control [1], tracking guidance [2], system identification [3], sensor networks [4], navigation [5,6] and so on. Motivated by the techniques reported in References [11] and [21], this paper proposes a set-membership based hybrid Kalman filter (SM-HKF) for nonlinear system state estimation in the presence of both UBB error and stochastic error. This method linearizes the nonlinear system model by a Taylor series expansion and combines the linearization error with the systematic UBB error to generate a new UBB error term through the Minkowski sum. Simulations and comparison analysis have been conducted to evaluate the effectiveness of the proposed method
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