An Improved Sage-Husa Variational Robust Adaptive Kalman Filter With Uncertain Noise Covariances

The time-varying noise covariance matrices with respect to a linear Gaussian system are inaccurate, which may make the estimation accuracy of some filtering algorithms less than expected. To tackle the aforementioned issue, a modified variational robust filter is presented. In this algorithm, a sliding-window-based variational filter is employed, which improves the algorithm's accuracy and efficiency via the latter state to adjust the previous state and avoids the iterations of fixed point. The inverse-Wishart distribution is considered as the observation noise covariance's prior distribution and is capable of estimating the observation noise covariance and the system state via the variational Bayesian technique. The Sage-Husa filter is employed for estimating the state noise covariance, and a modified monitoring strategy for real-time adjustment of the state noise covariance is developed to ensure the matrix's positive semidefinite. An adaptive factor is constructed for balancing the predicted and observation states to improve the algorithm's robustness. Simulation and experiment results show that the proposed filtering algorithm performs better than some existing filtering algorithms with regards to convergence and accuracy.