State estimation for jump markov nonlinear systems of unknown measurement data covariance |
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| Authors: | Ke Li Shunyi Zhao Choon Ki Ahn Fei Liu |
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| Institution: | 1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China;2. Choon Ki Ahn is with the School of Electrical Engineering, Korea University, Seoul 136–701, Korea;1. School of Automation, Nanjing University of Science &Technology, No. 200 Xiaolingwei, Nanjing, China;2. School of Science, Nanjing University of Science &Technology, No. 200 Xiaolingwei, Nanjing, China;3. Shanghai Institute of Mechanical and Electrical Engineering, No.421 Guilin Road, Shanghai, China;1. School of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China;2. Key Laboratory of Information Fusion Technology, Ministry of Education, Xi’an, Shaanxi, 710072, China;3. School of Electronic Engineering, Xidian University, Xi’an, Shaanxi, 710071, China;4. National Lab of Radar Signal Processing, Xi’an, Shaanxi, 710071, China;5. Southwest China Institute of Electronic Technology, Chengdu, Sichuan, 610036, China |
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| Abstract: | For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable. |
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