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

Yingbo Hua, Tapan K. Sarkar

Research output: Contribution to journalConference article

1 Scopus citations

Abstract

A review is presented of several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise. The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. The authors show 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)
Pages (from-to)931-935
Number of pages5
JournalConference Record - Asilomar Conference on Circuits, Systems & Computers
Volume2
StatePublished - Dec 1 1991
Event24th Asilomar Conference on Signals, Systems and Computers Part 2 (of 2) - Pacific Grove, CA, USA
Duration: Nov 5 1990Nov 7 1990

ASJC Scopus subject areas

  • Engineering(all)

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