Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems
Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems
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DOI：
10.1109/78.651206
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
M. Haardt;J. Nossek
中科院分区：
文献类型：
--
作者：
M. Haardt;J. Nossek
本文提出了一种新的Jacobi型方法，通过最小化适当的代价函数来计算多个实值非对称矩阵的同时Schur分解（SSD）。因此，SSD揭示了这些非对称矩阵的“平均特征结构”。这使得酉ESPRIT的R维扩展能够估计几个无阻尼R维模式或频率沿着它们在多维谐波恢复问题中的正确配对。酉ESPRIT是一种ESPRIT类型的高分辨率频率估计技术，其始终以实值计算来制定。对于每个R维，从实值矩阵的真实的特征值获得相应的频率估计。SSD联合估计所有R矩阵的特征值，从而通过一个封闭形式的过程，既不需要任何搜索，也不需要任何其他启发式配对策略，实现自动配对的估计R维模式。此外，我们描述了如何R维谐波恢复问题（R/spl ges/3）发生在阵列信号处理和基于模型的对象识别应用。
This paper presents a new Jacobi-type method to calculate a simultaneous Schur decomposition (SSD) of several real-valued, nonsymmetric matrices by minimizing an appropriate cost function. Thereby, the SSD reveals the "average eigenstructure" of these nonsymmetric matrices. This enables an R-dimensional extension of Unitary ESPRIT to estimate several undamped R-dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems. Unitary ESPRIT is an ESPRIT-type high-resolution frequency estimation technique that is formulated in terms of real-valued computations throughout. For each of the R dimensions, the corresponding frequency estimates are obtained from the real eigenvalues of a real-valued matrix. The SSD jointly estimates the eigenvalues of all R matrices and, thereby, achieves automatic pairing of the estimated R-dimensional modes via a closed-form procedure that neither requires any search nor any other heuristic pairing strategy. Moreover, we describe how R-dimensional harmonic retrieval problems (with R/spl ges/3) occur in array signal processing and model-based object recognition applications.