标题： 联合协方差估计与相互线性结构 显示英文标题

标题： Joint Covariance Estimation with Mutual Linear Structure

摘要： 我们研究了联合估计结构化协方差矩阵的问题。假设结构未知，使用异构训练集实现估计。也就是说，给定来自均值为零且协方差不同的总体的测量分组，我们的目标是确定这些协方差矩阵的共同结构并对其进行估计。假设协方差在对称矩阵空间中张成一个低维仿射子空间，我们开发了一种新的高效算法来发现该结构并利用它改进估计。我们的方法基于在矩阵空间中应用主成分分析。我们还在高斯场景下推导出所提出算法的性能上限，并将其与克拉美-罗下界进行比较。数值模拟被展示以说明所提出方法的性能优势。 显示英文摘要

摘要： We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method.