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Abstract: This paper is motivated by the filtering estimation for a class of nonlinear stochastic systems in the case that the measurements are randomly delayed by one sampling time. Through presenting Gaussian approximation about the one-step posterior predictive probability density functions (PDFs) of the state and delayed measurement, a novel Gaussian approximation (GA) filter is derived, which recursively operates by analytical computation and Gaussian weighted integrals. The proposed GA filter gives a general and common framework since: (1) it is applicable for both linear and nonlinear systems, (2) by setting the delay probability as zero, it automatically reduces to the standard Gaussian filter without the randomly delayed measurements, and (3) many variations of the proposed GA filter can be developed through utilizing different numerical technologies for computing such Gaussian weighted integrals, including the previously existing EKF and UKF methods, as well as the improved cubature Kalman filter (CKF) in our paper using the spherical–radial cubature rule. The performance of the new method is demonstrated with a simulation example of the high-dimensional GPS/INS integrated navigation. [Copyright &y& Elsevier]

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]

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]