Classical signal from noise separation problems assume that the signal is a trajectory of a low-complexity linear time-invariant system and that the noise is a random process. In this paper, we generalize this classical setup to what we call data-driven structured noise filtering. In the new setup, the noise has two components: structured noise, which is also a trajectory of a low-complexity linear time-invariant system, and unstructured noise, which is a zero-mean white Gaussian process. The key assumption that makes the separation problem in the new setup well posed is that among several experiments, the signal's dynamics remains the same while the structured noise's dynamics varies. The data-driven structured noise filtering problem then becomes a problem of estimation of common linear time-invariant dynamics among several observed signals. We show that this latter problem is a structured low-rank approximation problem with multiple rank constraints and use a subspace identification approach for solving it. The resulting methods allow computationally efficient and numerically robust implementation and have the system theoretic interpretation of finding the intersection of autonomous linear time-invariant behaviors. Statistical analysis providing confidence bounds is a topic for future research.

中文翻译：

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通过常见动态估计进行数据驱动的结构化噪声过滤

来自噪声分离问题的经典信号假设信号是低复杂度线性时不变系统的轨迹，并且噪声是随机过程。在本文中，我们将这种经典设置推广到我们所说的数据驱动结构化噪声过滤。在新设置中，噪声有两个组成部分：结构化噪声，它也是一个低复杂度线性时不变系统的轨迹，以及非结构化噪声，它是一个零均值白高斯过程。使新设置中的分离问题很好地提出的关键假设是，在几个实验中，信号的动态保持不变，而结构化噪声的动态变化。然后，数据驱动的结构化噪声过滤问题变成了在几个观察到的信号中估计公共线性时不变动态的问题。我们表明后一个问题是具有多个秩约束的结构化低秩逼近问题，并使用子空间识别方法来解决它。由此产生的方法允许计算高效和数值鲁棒的实现，并具有寻找自主线性时不变行为的交集的系统理论解释。提供置信界限的统计分析是未来研究的主题。由此产生的方法允许计算高效和数值鲁棒的实现，并具有寻找自主线性时不变行为的交集的系统理论解释。提供置信界限的统计分析是未来研究的主题。由此产生的方法允许计算高效和数值鲁棒的实现，并具有寻找自主线性时不变行为的交集的系统理论解释。提供置信界限的统计分析是未来研究的主题。