A Gaussian approximation recursive filter for nonlinear systems with correlated noises |
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| Authors: | Xiaoxu Wang Yan Liang Quan Pan Feng Yang |
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| Affiliation: | 1. Department of Control Science and Engineering, Zhejiang University, Hangzhou, 310013, China;2. Department of Automation, Tsinghua University, Beijing, 100084, China;3. School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia;1. Shanghai Key Lab of Modern Optical System, Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China;3. Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | This paper proposes a Gaussian approximation recursive filter (GASF) for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other. Through presenting the Gaussian approximations about the two-step state posterior predictive probability density function (PDF) and the one-step measurement posterior predictive PDF, a general GASF framework in the minimum mean square error (MMSE) sense is derived. Based on the framework, the GASF implementation is transformed into computing the multi-dimensional integrals, which is solved by developing a new divided difference filter (DDF) with correlated noises. Simulation results demonstrate the superior performance of the proposed DDF as compared to the standard DDF, the existing UKF and EKF with correlated noises. |
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