Kalman filter with recursive covariance estimation for protection against system uncertainty

This study is intended to design a novel adaptive Kalman filter (KF) that can solve the filtering problem with unknown noise statistics. The proposed method named as measurement sequence adaptive KF (MSAKF) can adaptively estimate the unknown parameters of noise statistics via the information from measurement sequences. In order to enhance the computational efficiency, algorithm optimisation via recursive covariance estimation is introduced. In addition, stability analysis of the MSAKF is also made under some given conditions. The estimation process is proved to be stable and its filtering results converge to the ones of the ideal KF with exact system parameters. To demonstrate the effectiveness of the MSAKF algorithm, the simulation based on a navigation signal-tracking model is presented, and the results show that the MSAKF algorithm possesses low calculation complexity, fast convergence, high-precision and adaptability in complex application environments.