Outlier-robust Autocovariance Least Square Estimation via Iteratively Reweighted Least Square
This work provides a more robust method for estimating noise covariances in Kalman filters, which is crucial for applications where measurement outliers are common and can severely degrade filter performance.
The paper addresses the sensitivity of the Autocovariance Least Squares (ALS) method to measurement outliers in Kalman filter noise covariance estimation. The proposed ALS-IRLS algorithm, using a two-tier robustification strategy and iteratively reweighted least squares, reduces the RMSE of noise covariance estimates by over two orders of magnitude compared to standard ALS and significantly improves state estimation accuracy.
The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic least mean squares (LMS) criterion, making them highly sensitive to measurement outliers and prone to severe performance degradation. To overcome this limitation, this paper proposes a novel outlier-robust ALS algorithm, termed ALS-IRLS, based on the iteratively reweighted least squares (IRLS) framework. Specifically, the proposed approach introduces a two-tier robustification strategy. First, an innovation-level adaptive thresholding mechanism is employed to filter out heavily contaminated data. Second, the outlier-contaminated autocovariance is formulated using an $ε$-contamination model, where the standard LMS criterion is replaced by the Huber cost function. The IRLS method is then utilized to iteratively adjust data weights based on estimation deviations, effectively mitigating the influence of residual outliers. Comparative simulations demonstrate that ALS-IRLS reduces the root-mean-square error (RMSE) of noise covariance estimates by over two orders of magnitude compared to standard ALS. Furthermore, it significantly enhances downstream state estimation accuracy, outperforming existing outlier-robust Kalman filters and achieving performance nearly equivalent to the ideal Oracle lower bound in the presence of noisy and anomalous data.