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A Gaussian approximation recursive filter for nonlinear systems with correlated noises. (English) Zbl 1257.93102
Summary: 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.

MSC:
93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
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