M-estimation based sparse grid quadrature filter and stochastic stability analysis |
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| Institution: | 1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, PR China;2. State Key Laboratory of Synthetical Automation of Process Industries, Northeastern University, Shenyang 110819, PR China;1. School of Measurement and Communication, Harbin University of Science and Technology, Harbin 150080, China;2. School of Science, Harbin University of Science and Technology, Harbin 150080, China;3. School of Automation, Harbin University of Science and Technology, Harbin 150080, China;4. Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin 150080, China;1. Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, Department of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China;2. Department of Electrical and Computer Engineering, University of Calgary, 2500 University Drive NW Calgary, Alberta, T2N 1N4, Canada |
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| Abstract: | In this study, a novel M-estimation based sparse grid quadrature filter (MSGQF) is proposed to improve the robust performance of the nonlinear system. We present a systematic formulation of the sparse grid quadrature filter (SGQF), and extend it to the discrete-time nonlinear system with abnormal measurement values. The M-estimation method is introduced in the SGQF, which uses the Huber’s cost function to update the measurement covariance. Convergence on the modified robust SGQF is established and proved. The sufficient conditions are shown to ensure stochastic stability of the MSGQF. A target tracking problem has been conducted to demonstrate the accuracy of the MSGQF. When measurement abnormal values appear, it outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the MSGQF provides significant performance improvement in the robustness of the nonlinear system. |
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