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.

翻译：自协方差最小二乘（ALS）方法是一种计算高效的噪声协方差估计方法，无需特定的噪声模型即可用于卡尔曼滤波器。然而，传统的ALS方法及其变体均基于经典的最小均方（LMS）准则，导致其对测量离群值高度敏感，性能极易严重退化。为克服这一局限，本文提出一种基于迭代重加权最小二乘（IRLS）框架的新型离群值鲁棒ALS算法，称为ALS-IRLS。具体而言，所提方法引入了一种双层鲁棒化策略。首先，采用创新序列层面的自适应阈值机制以滤除严重受污染的数据。其次，使用$ε$-污染模型对受离群值污染的自协方差进行建模，并以Huber代价函数替代标准的LMS准则。随后，利用IRLS方法根据估计偏差迭代调整数据权重，从而有效减轻残余离群值的影响。对比仿真实验表明，与标准ALS相比，ALS-IRLS将噪声协方差估计的均方根误差（RMSE）降低了超过两个数量级。此外，该算法显著提升了后续状态估计的精度，其表现优于现有的离群值鲁棒卡尔曼滤波器，在存在噪声和异常数据的情况下，性能几乎达到了理想Oracle下界的水平。