Estimation of covariance matrices satisfying sparsity priors

满足稀疏先验的协方差矩阵的估计

• 批准号: 273496688
• 负责人: Professor Götz Eduard Pfander, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Informationstechnik (LTI)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/273496688?language=en
• 关键词: Estimation; covariance; matrices; satisfying; sparsity

The success of Compressive Sensing (CS) is based on the observation that high-dimensional signals can often be described by a very small number of signal dependent active parameters.This project proposes a CS based approach to the estimation of second order statistics of stochastic vectors and sequences. These processes are assumed to satisfy a sparsity prior on the second order statistics, for example, small support area or low rank of the covariance matrix.Although the problem of estimating covariance matrices can be translated into a seemingly standard CS problem, the Kronecker product structure of the underlying measurement matrix prevents the application of standard results from the literature, for example, those based on coherence and the restricted isometry property. Alternative arguments and algorithms have to be developed, keeping in mind that sparsity conditions on the covariance matrix may become involved. Motivated by applications in communications, we study time-frequency structured measurement matrices in detail. On the stochastic side, this leads to questions on the the covariance estimation problem for WSSUS channels. With respect to communications, we consider Single-Input-Single-Output and Multiple-Input-Multiple-Output stochastic operators, with and without correlated subchannels. We will use CS techniques to estimate stationary stochastic processes based on a limited number of measurements and then turn to the identification problem for the covariance of non-stationary so-called underspread processes.

压缩感知（CS）的成功是基于观察到高维信号通常可以由非常少量的信号相关的主动参数来描述。 随机向量和序列的二阶统计量。假设这些过程满足a 二阶统计量的稀疏性先验，例如， 虽然估计协方差矩阵的问题可以转化为表面上标准的CS问题，但是底层测量矩阵的克罗内克乘积结构阻止了来自文献的标准结果的应用，例如， 基于相干性和限制等距性的那些。 必须开发替代的参数和算法，记住协方差矩阵上的稀疏条件可能会涉及。受通信中应用的启发，我们详细研究了时频结构测量矩阵。在随机方面，这导致问题的协方差估计问题WSSUS信道。关于通信，我们考虑单输入单输出和多输入多输出随机运营商，有和没有相关的子信道。 我们将使用CS技术估计平稳随机过程的基础上有限数量的测量，然后转向非平稳的所谓的underspread过程的协方差的识别问题。