Simultaneous schur decomposition of several nonsymmetric matrices to achieve

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 B-dimensional extension of Unitary ESPRIT to estimate several undamped B-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 B-dimensional modes via a closed-form procedure that neither requires any search nor any other heuristic pairing strategy. Moreover, we describe how B-dimensional harmonic retrieval problems (with R > 3) occur in array signal processing and model-based object recognition applications.