arXiv:2603.08158math.OCcs.LG2026-03

提出新算法提升卡尔曼滤波噪声估计鲁棒性,抗异常值能力显著增强。

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

  • 基于IRLS框架重构损失函数,用Huber准则替代传统最小二乘
  • 两阶段抗噪设计:先过滤异常数据,再迭代加权抑制残余异常
  • 实测噪声协方差估计误差降低超两个数量级,逼近理想下界

自相关最小二乘(ALS)方法是一种无需特定噪声模型即可高效估计卡尔曼滤波中噪声协方差的计算方法。然而,传统ALS及其变体依赖经典最小均方(LMS)准则,对测量异常值极为敏感,易导致性能严重下降。为此,本文提出一种基于迭代重加权最小二乘(IRLS)框架的新型抗异常值ALS算法——ALS-IRLS。该方法采用双层鲁棒化策略:首先在创新层面引入自适应阈值机制以剔除严重污染数据;其次,将异常污染的自相关协方差建模为ε-污染模型,用Huber损失函数替代标准LMS准则。通过IRLS迭代调整数据权重,有效缓解残余异常值影响。对比仿真结果表明,与标准ALS相比,ALS-IRLS使噪声协方差估计的均方根误差(RMSE)降低超过两个数量级,并显著提升下游状态估计精度,优于现有抗异常值卡尔曼滤波器,在存在噪声和异常数据时表现接近理想的Oracle下界。

原文摘要 · Abstract (English)

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.

卡尔曼滤波鲁棒估计异常值检测IRLS

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。