Adaptive Kalman Filtering With Uncertain System Noises Based on Variance Component Estimation Theory

This article proposes an adaptive Kalman filtering method with uncertain system noises based on variance component estimation (VCE) to adaptively tune the variances of system noises, i.e., process and measurement noises. A unified system noises contained model is constructed for estimating the variance components of both process and measurement noises in a moving window of multiple historical epochs. To establish a standard linear mixed effects model, the self-correlated process noises in the time window are replaced by a new series of uncorrelated noises in the sense of distribution equivalence. Then, the variance components of system noises are estimated based on a maximum likelihood method. Both simulations and experiments were carried out to evaluate the performances of the proposed method. The results show the efficiency of the proposed method, outperforming other state-of-the-art adaptive filtering methods in scenarios of time-variant and uncertain system noises.