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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]

A recent comment (Chang, 2014) theoretically demonstrated that for the linear system with the correlated process and measurement noises, the GASF framework proposed in the paper Wang et al. (2012) was equivalent to the conventional de-coupling filtering framework. In this note, we would further show that such equivalence between the two frameworks can be justified in a more general way, even for the nonlinear system. [ABSTRACT FROM AUTHOR]