In this article, we propose a novel algorithm, namely PETRELS-ADMM, to deal with subspace tracking in the presence of outliers and missing data. The proposed approach consists of two main stages: outlier rejection and subspace estimation. In the first stage, alternating direction method of multipliers (ADMM) is effectively exploited to detect outliers affecting the observed data. In the second stage, we propose an improved version of the parallel estimation and tracking by recursive least squares (PETRELS) algorithm to update the underlying subspace in the missing data context. We then present a theoretical convergence analysis of PETRELS-ADMM which shows that it generates a sequence of subspace solutions converging to the optimum of its batch counterpart. The effectiveness of the proposed algorithm, as compared to state-of-the-art algorithms, is illustrated on both simulated and real data.

中文翻译：

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具有缺失数据和离群值的鲁棒子空间跟踪：具有收敛保证的新算法

在本文中，我们提出了一种新颖的算法，即PETRELS-ADMM，用于在存在异常值和丢失数据的情况下处理子空间跟踪。所提出的方法包括两个主要阶段：离群值拒绝和子空间估计。在第一阶段，有效利用乘数交替方向法（ADMM）来检测影响观察数据的离群值。在第二阶段，我们提出了一种改进的并行估计和递归最小二乘跟踪（PETRELS）算法版本，以更新丢失数据上下文中的基础子空间。然后，我们提出PETRELS-ADMM的理论收敛性分析，结果表明它生成了一系列子空间解，收敛到其批次对应物的最优值。与最新算法相比，该算法的有效性，