Critical Issues on Kalman Filter with Colored and Correlated System Noises. Issue 6 (22nd June 2017) - Zhou, Zebo; Wu, Jin; Li, Yong; Fu, Chen; Fourati, Hassen
Abstract: The Kalman filtering (KF) is optimal under the assumption that both process and observation noises are independent white Gaussian noise. However, this assumption is not always satisfied in real‐world navigation campaigns. In this paper, two types of KF methods are investigated, i.e. augmented KF (AKF) and the second moment information based KF (SMIKF) with colored system noises, including process and observation noises. As a popular noise‐whitening method, the principle of AKF is briefly reviewed for dealing with the colored system noises. The SMIKF method is developed for the colored and correlated system noises, which directly compensates for the covariance through stochastic model in the sense of minimum mean square error. To accurately implement the SMIKF, a refined SMIKF is further derived regarding the continuous‐time dynamic model rather than the discrete one. The computational burdens of the proposed SMIKF along with representative methods are analyzed and compared. The simulation results demonstrate the performances of proposed methods.