On SVD for estimating generalized eigenvalues of singular matrix pencil in noise

Yingbo Hua, Tapan Kumar Sarkar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise are reviewed. The singular value decomposition (SVD) is explored as the common structure in three basic algorithms: direct matrix pencil algorithm, Pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in those algorithms are equivalent to the first-order approximation. Also, Pro-ESPRIT and TLS-Pro-ESPRIT are shown to be equivalent, and TLS-ESPRIT and LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first-order approximation. The threshold phenomenon is illustrated by a simulation result based on a damped sinusoidal signal. An improved state space algorithm is found to be the most robust to noise.

Original languageEnglish (US)
Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
PublisherIEEE Computer Society
Pages2780-2783
Number of pages4
Volume5
StatePublished - 1991
Externally publishedYes
Event1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5) - Singapore, Singapore
Duration: Jun 11 1991Jun 14 1991

Other

Other1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5)
CitySingapore, Singapore
Period6/11/916/14/91

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

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    Hua, Y., & Sarkar, T. K. (1991). On SVD for estimating generalized eigenvalues of singular matrix pencil in noise. In Proceedings - IEEE International Symposium on Circuits and Systems (Vol. 5, pp. 2780-2783). IEEE Computer Society.