Invariance of the distributions of normalized Gram matrices

Stephen D. Howard, Songsri Sirianunpiboon, Douglas Cochran

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

4 Citations (Scopus)

Abstract

Normalized Gram matrices formed from multiple vectors of sensor data, and functions of the eigenvalues of such matrices in particular, have a long history in connection with multiple-channel detection. The determinant and various other functions of the eigenvalues of these matrices arise as detection statistics in a variety of multichannel problems, and knowledge of their distributions under the H0 assumption that the sensor channels are independent and contain only white gaussian noise is consequently important for determining false-alarm probabilities for multi-channel detectors. Invariance of the H0 distribution of the eigenvalues to one data channel is significant in some applications. This paper derives the H0 distribution of a normalized Gram matrix and, as corollaries, obtains the distribution of the determinant as well as invariance results for the matrix that carry over to its spectrum. The essential symmetry property of white gaussian noise on which these results depend is also noted.

Original languageEnglish (US)
Title of host publicationIEEE Workshop on Statistical Signal Processing Proceedings
PublisherIEEE Computer Society
Pages352-355
Number of pages4
ISBN (Print)9781479949755
DOIs
StatePublished - 2014
Event2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 - Gold Coast, QLD, Australia
Duration: Jun 29 2014Jul 2 2014

Other

Other2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
CountryAustralia
CityGold Coast, QLD
Period6/29/147/2/14

Fingerprint

Gram Matrix
Invariance
Gaussian White Noise
Eigenvalue
Determinant
Sensor
False Alarm
Sensors
Corollary
Detector
Statistics
Symmetry
Detectors

Keywords

  • Coherence
  • Gram matrix
  • Multiple-channel detection
  • Stiefel manifold

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

Cite this

Howard, S. D., Sirianunpiboon, S., & Cochran, D. (2014). Invariance of the distributions of normalized Gram matrices. In IEEE Workshop on Statistical Signal Processing Proceedings (pp. 352-355). [6884648] IEEE Computer Society. https://doi.org/10.1109/SSP.2014.6884648

Invariance of the distributions of normalized Gram matrices. / Howard, Stephen D.; Sirianunpiboon, Songsri; Cochran, Douglas.

IEEE Workshop on Statistical Signal Processing Proceedings. IEEE Computer Society, 2014. p. 352-355 6884648.

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

Howard, SD, Sirianunpiboon, S & Cochran, D 2014, Invariance of the distributions of normalized Gram matrices. in IEEE Workshop on Statistical Signal Processing Proceedings., 6884648, IEEE Computer Society, pp. 352-355, 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014, Gold Coast, QLD, Australia, 6/29/14. https://doi.org/10.1109/SSP.2014.6884648
Howard SD, Sirianunpiboon S, Cochran D. Invariance of the distributions of normalized Gram matrices. In IEEE Workshop on Statistical Signal Processing Proceedings. IEEE Computer Society. 2014. p. 352-355. 6884648 https://doi.org/10.1109/SSP.2014.6884648
Howard, Stephen D. ; Sirianunpiboon, Songsri ; Cochran, Douglas. / Invariance of the distributions of normalized Gram matrices. IEEE Workshop on Statistical Signal Processing Proceedings. IEEE Computer Society, 2014. pp. 352-355
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