Outlier-robust Autocovariance Least Square Estimation via Iteratively Reweighted Least Square

TL;DR

This paper introduces ALS-IRLS, a robust autocovariance least squares method that effectively mitigates measurement outliers, significantly improving noise covariance estimation and state estimation accuracy in Kalman filtering.

Contribution

The paper presents a novel outlier-robust ALS algorithm using IRLS with a two-tier strategy, including adaptive thresholding and Huber cost, to enhance robustness against measurement outliers.

Findings

Reduces RMSE of noise covariance estimates by over 100x.

Improves downstream state estimation accuracy significantly.

Outperforms existing outlier-robust Kalman filters, nearing Oracle performance.

Abstract

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 $\epsilon$-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.