Nonlinear Gaussian Filter with Multi-Step Colored Noise

Abstract

Color noise is a special kind of noise often occurring in localization systems, and it is more suitable than the general Gaussian white noise to model time dependence due to time delay or high-frequency sampling. This paper derives a nonlinear Gaussian filtering framework for multi-step colored noise systems using noise whitening techniques and Bayes rule. Meanwhile, the cubature rule is used to solve the Gaussian-weighted integral in the proposed Gaussian filtering framework, resulting in an analytic form of posterior state estimate. Compared with the existing nonlinear filtering algorithms, the proposed method has obvious advantages in colored noise systems because it fully takes into account the time dependence of colored noise. Finally, the effectiveness and advantages of the proposed algorithm are verified with a classical target tracking system.