基于绝对特征值的稀疏阵列协方差矩阵估计
Absolute Eigenvalues-Based Covariance Matrix Estimation for a Sparse Array
摘要：
广义平稳信号经满线阵空间采样后的总体协方差矩阵是半正定的，且满足Toeplitz条件。然而，增广稀疏阵列的直接增广协方差矩阵是Toeplitz的，但不是半正定的，导致负特征值，这给其应用带来了固有的挑战，包括模型阶估计和源定位。基于正特征值的增广稀疏阵列协方差矩阵是鲁棒的，但是当直接增广矩阵的所有噪声特征值都为负时，该矩阵是不可获得的，这是一种可能的情况。为了解决这个问题，我们提出了一个强大的协方差矩阵的可扩展稀疏阵列，利用正负噪声特征值。所提出的协方差矩阵估计可以与基于子空间的算法和自适应波束形成器结合使用，以产生准确的信号方向估计。
英文摘要：
The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but not positive semi-definite, resulting in negative eigenvalues that pose inherent challenges in its applications, including model order estimation and source localization. The positive eigenvalues-based covariance matrix for augmentable sparse arrays is robust but the matrix is unobtainable when all noise eigenvalues of the direct augmented matrix are negative, which is a possible case. To address this problem, we propose a robust covariance matrix for augmentable sparse arrays that leverages both positive and negative noise eigenvalues. The proposed covariance matrix estimate can be used in conjunction with subspace based algorithms and adaptive beamformers to yield accurate signal direction estimates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
