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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. [Copyright &y& Elsevier]

This paper proposes a general framework solution of Gaussian filter (GF) for both linear and nonlinear dynamic systems with correlated noises at the same epoch. Detailed discussions and simulation comparisons with existing Gaussian approximation recursive filter and existing de-correlating GF are provided, which show advantages of estimation accuracy of the proposed method in some applications. [ABSTRACT FROM AUTHOR]