Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Yangtianze Tao

Friday, February 16, 2024 9:00 PM - 9:30 PM

Online

The autocovariance least squares estimation (ALS) method is an effective approach to solving the noise covariance estimation problem of Kalman filter based on the autocovariance of the innovations with acceptable computational complexity and no specific noise model requirements. The conventional ALS method and its variants employ the classic least mean squares (LMS) of the deviation between the predicted autocovariance and the observed one as the optimality criterion, which however are notably sensitive to outliers and severely degrade the performance. To address the limitation, a novel outlier-robust ALS algorithm based on the iteratively reweighted least squares (IRLS) method is proposed, termed the ALS-IRLS algorithm. In the algorithm, the observation of the autocovariance contaminated with outliers is modeled as the ϵ-contamination model, and the Huber cost function is utilized to substitute the LMS criterion to enhance the robustness against outliers. The solution is obtained using the IRLS method which iteratively updates the weights assigned to each data based on the deviation from the previous iteration, effectively mitigating the influence of the outliers on the parameter estimation process. Comparative simulations on the target tracking application and experimental results demonstrate that the proposed approach significantly improves the robustness of the noise covariance estimate against outliers, ensuring more accurate and reliable parameter estimation in the presence of noisy and anomalous data.