提出高效算法求解任意矩阵的Hankel和Toeplitz秩1逼近，用于少样本方向估计算法。
Hankel and Toeplitz Rank-1 Decomposition of Arbitrary Matrices with Applications to Signal Direction-of-Arrival Estimation
- 基于L2和L1范数设计结构化矩阵分解算法，适配信号处理场景。
- 在白高斯与拉普拉斯噪声下，所提估计器达到最大似然最优性能。
- 适用于少样本、实时部署的自主系统方向估计任务。
我们研究在L2和L1范数误差下，对任意矩阵进行最优秩1 Hankel和Toeplitz结构逼近的问题。这类问题自然出现在工程系统中，尤其是现代自主系统应用中关键的少样本方向估计算法。本文提出高效且精确的结构化矩阵分解算法，并推导出适用于实际传感系统部署的小样本支持方向估计算法。在白高斯噪声下，L2范数估计器被严格证明为最大似然最优；在拉普拉斯噪声下，L1范数估计器也具备最大似然最优性。通过大量仿真及真实数据实验，验证了所提方法在少样本方向估计中的有效性。
原文摘要 · Abstract (English)
We consider the problems of computing the optimal rank-1 Hankel and Toeplitz-structured approximation of arbitrary matrices under L2 and L1-norm error. Such problems arise naturally in engineered systems, including the basic few-shot signal Direction-of-Arrival (DoA) estimation problem that is of importance to modern autonomous systems applications. We develop accurate and computationally efficient structured matrix decomposition algorithms for both formulations and then derive analytically grounded small-sample-support DoA estimators for practical sensing system deployments. The resulting estimators under the L2 and L1 norms are formally shown to be maximum-likelihood optimal under white Gaussian and Laplace noise, respectively. The estimators are further validated through extensive simulation studies and real-world data experiments in few-shot DoA inference.
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