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This paper addresses state estimation of linear systems with specialattention on unknown process and measurement noise covariances, aiming toenhance estimation accuracy while preserving the stability guarantee of theKalman filter. To this end, the full information estimation problem over afinite interval is firstly addressed. Then, a novel adaptive variationalBayesian (VB) moving horizon estimation (MHE) method is proposed, exploiting VBinference, MHE and Monte Carlo integration with importance sampling for jointestimation of the unknown process and measurement noise covariances, along withthe state trajectory over a moving window of fixed length. Further, it isproved that the proposed adaptive VB MHE filter ensures mean-square boundednessof the estimation error with any number of importance samples and VBiterations, as well as for any window length. Finally, simulation results on atarget tracking example demonstrate the effectiveness of the VB MHE filter withenhanced estimation accuracy and convergence properties compared to theconventional non-adaptive Kalman filter and other existing adaptive filters.

A Variational Bayes Moving Horizon Estimation Adaptive Filter with Guaranteed Stability