Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number

A. Sano, H. Tsuji, Hiromitsu Ohmori

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

Abstract

The singular value decomposition (SVD) is an excellent tool to attain reliable and stable least squares type of parameter estimate in ill-conditioned cases, by discarding small singular values adequately. However, large singular values and small singular values do not always separate neatly. In the present paper, we introduce multiple regularization parameters to modify the Moore-Penrose type of pseudo-inverse matrix, to stabilize the ill-posed least squares problems. The optimal values of the regularization parameters can be determined so as to minimize an estimated mean squares error (EMSE) criterion calculated by using only accessible signal data. Thus, the proposed scheme can give a threshold condition whether the singular value should be adopted or discarded. The relationship with the optimal truncation of the singular values are also investigated analytically. Proposed method and its properties are discussed through the applications to the optimal extrapolation of band-limited signals and the detection of the number of sinusoid in white noise.

Original languageEnglish
Title of host publicationIFAC Symposia Series - Proceedings of a Triennial World Congress
EditorsU. Jaaksoo, V.I. Utkin
PublisherPubl by Pergamon Press Inc
Pages123-128
Number of pages6
Volume2
Publication statusPublished - 1991
EventProceedings of the 11th Triennial World Congress of the International Federation of Automatic Control - Tallinn, USSR
Duration: 1990 Aug 131990 Aug 17

Other

OtherProceedings of the 11th Triennial World Congress of the International Federation of Automatic Control
CityTallinn, USSR
Period90/8/1390/8/17

Fingerprint

Singular value decomposition
White noise
Extrapolation
Mean square error

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Sano, A., Tsuji, H., & Ohmori, H. (1991). Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number. In U. Jaaksoo, & V. I. Utkin (Eds.), IFAC Symposia Series - Proceedings of a Triennial World Congress (Vol. 2, pp. 123-128). Publ by Pergamon Press Inc.

Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number. / Sano, A.; Tsuji, H.; Ohmori, Hiromitsu.

IFAC Symposia Series - Proceedings of a Triennial World Congress. ed. / U. Jaaksoo; V.I. Utkin. Vol. 2 Publ by Pergamon Press Inc, 1991. p. 123-128.

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

Sano, A, Tsuji, H & Ohmori, H 1991, Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number. in U Jaaksoo & VI Utkin (eds), IFAC Symposia Series - Proceedings of a Triennial World Congress. vol. 2, Publ by Pergamon Press Inc, pp. 123-128, Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, 90/8/13.
Sano A, Tsuji H, Ohmori H. Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number. In Jaaksoo U, Utkin VI, editors, IFAC Symposia Series - Proceedings of a Triennial World Congress. Vol. 2. Publ by Pergamon Press Inc. 1991. p. 123-128
Sano, A. ; Tsuji, H. ; Ohmori, Hiromitsu. / Optimized singular value decomposition with applications to signal extrapolation and detection of sinusoid number. IFAC Symposia Series - Proceedings of a Triennial World Congress. editor / U. Jaaksoo ; V.I. Utkin. Vol. 2 Publ by Pergamon Press Inc, 1991. pp. 123-128
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