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Nonlinear Gaussian filter with the colored measurement noise

This paper is concerned with the Gaussian approximation (GA) filtering for a class of nonlinear stochastic systems in the case that the colored measurement noise is modeled as a first-order autoregressive process. First, through the augmentation of the standard measurements, the problem of designing the GA filter with the colored measurement noise is transformed into that of deriving the GA one with the delayed state in the augmented measurement function. Second, through presenting Gaussian approximation about the joint posterior probability density functions (PDF) of the present state, the delayed state and the augmented measurement, the novel GA filter with the delayed state are proposed, which recursively operate by analytical computation and nonlinear Gaussian integrals. The proposed GA filter provides a general and common framework, from which many variations can be developed by utilizing different numerical technologies for computing such nonlinear Gaussian integrals, for example the modified cubature Kalman filter (CKF) in this paper using the spherical-radial cubature rule. The performance of the new method is demonstrated with a simulation example.