Nonlinear filtering of continuous systems: foundational problems and new results |
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| Authors: | Peiliang Xu |
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| Institution: | (1) Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, 611-0011, Japan |
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| Abstract: | The previous work of Xu on discrete nonlinear filtering is extended to continuous systems. The new results are summarized as follows: (1) a second-order unbiased prediction of the true state governed by a vector stochastic differential equation is worked out; (2) a set of coupled differential equations for a new truncated second-order nonlinear filter and its variance–covariance matrix are derived from the frequentist point of view. The new filter is proved to be unbiased to the second-order approximation; and, most importantly, (3) comparison of the new filtering and accuracy results with the literature on nonlinear filtering has indicated that more than 40 years of nonlinear filtering of continuous systems may have foundational problems.Acknowledgments. This work is supported by a Grant-in-Aid for Scientific Research (C13640422). The author thanks Prof J.A.R. Blais, Prof A. Dermanis and Prof B. Schaffrin for their constructive comments. |
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| Keywords: | Nonlinear stochastic differential equation – Nonlinear filtering – Continuous nonlinear systems – Bayesian approach – Frequentist approach |
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