A Novel Adaptive Kalman Filter With Colored Measurement Noise

In this paper, a novel variational Bayesian-based adaptive Kalman filter (VBAKF) is proposed to solve the problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices. The filter problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices is transformed into the filtering problem of a linear state-space model with white measurement noise and inaccurate noise covariance matrices using measurement differencing method and state augmentation approach. The augmentation state vector, corresponding predicted error covariance matrix and covariance matrix of white measurement noise are jointly estimated based on the variational Bayesian approach. The ability of addressing the colored measurement and inaccurate noise covariance matrices is demonstrated in the simulation of a target tracking example.