Name
Title | ||
|---|---|---|
Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems |
Abstract | ||
|---|---|---|
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⩾3) occur in array signal processing and model-based object recognition applications |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/78.651206 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
array signal processing,direction-of-arrival estimation,eigenvalues and eigenfunctions,frequency estimation,harmonic analysis,matrix decomposition,object recognition,Jacobi-type method,R-dimensional extension,Unitary ESPRIT,array signal processing,automatic pairing,average eigenstructure,closed-form procedure,cost function minimization,high-resolution frequency estimation technique,model-based object recognition applications,multidimensional harmonic retrieval problems,nonsymmetric matrices,simultaneous Schur decomposition,undamped R-dimensional modes | Linear algebra,Mathematical optimization,Matrix (mathematics),Matrix decomposition,Harmonic,Pairing,Schur decomposition,Eigenvalues and eigenvectors,Mathematics,Multidimensional systems | Journal |
Volume | Issue | ISSN |
46 | 1 | 1053-587X |
Citations | PageRank | References |
89 | 7.55 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Haardt | 1 | 495 | 45.19 |
| Josef A. Nossek | 2 | 726 | 112.24 |