SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

This article is part of the series Advances in Subspace-Based Techniques for Signal Processing and Communications.

Open Access Research Article

Model Order Selection for Short Data: An Exponential Fitting Test (EFT)

Angela Quinlan1*, Jean-Pierre Barbot2, Pascal Larzabal2 and Martin Haardt3

Author Affiliations

1 Department of Electronic and Electrical Engineering, University of Dublin, Trinity College, Ireland

2 SATIE Laboratory, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, Cachan Cedex 94235, France

3 Communications Research Laboratory, Ilmenau University of Technology, P.O. Box 100565, Ilmenau 98684, Germany

For all author emails, please log on.

EURASIP Journal on Advances in Signal Processing 2007, 2007:071953  doi:10.1155/2007/71953

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2007/1/071953


Received:29 September 2005
Revisions received:31 May 2006
Accepted:4 June 2006
Published:4 October 2006

© 2007 Quinlan et al.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

High-resolution methods for estimating signal processing parameters such as bearing angles in array processing or frequencies in spectral analysis may be hampered by the model order if poorly selected. As classical model order selection methods fail when the number of snapshots available is small, this paper proposes a method for noncoherent sources, which continues to work under such conditions, while maintaining low computational complexity. For white Gaussian noise and short data we show that the profile of the ordered noise eigenvalues is seen to approximately fit an exponential law. This fact is used to provide a recursive algorithm which detects a mismatch between the observed eigenvalue profile and the theoretical noise-only eigenvalue profile, as such a mismatch indicates the presence of a source. Moreover this proposed method allows the probability of false alarm to be controlled and predefined, which is a crucial point for systems such as RADARs. Results of simulations are provided in order to show the capabilities of the algorithm.

References

  1. H Akaike, A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716–723 (1974). Publisher Full Text OpenURL

  2. TW Anderson, Asymptotic theory for principal component analysis. Annals of Mathematical Statistics 34, 122–148 (1963). Publisher Full Text OpenURL

  3. WB Bishop, PM Djurić, Model order selection of damped sinusoids in noise by predictive densities. IEEE Transactions on Signal Processing 44(3), 611–619 (1996). Publisher Full Text OpenURL

  4. B Champagne, Adaptive eigendecomposition of data covariance matrices based on first-order perturbations. IEEE Transactions on Signal Processing 42(10), 2758–2770 (1994). Publisher Full Text OpenURL

  5. W Chen, KM Wong, J Reilly, Detection of the number of signals: a predicted eigen-threshold approach. IEEE Transactions on Signal Processing 39(5), 1088–1098 (1991). Publisher Full Text OpenURL

  6. A Di, Multiple source location - a matrix decomposition approach. IEEE Transactions on Acoustics, Speech, and Signal Processing 33(5), 1086–1091 (1985). Publisher Full Text OpenURL

  7. PM Djurić, Model selection based on asymptotic Bayes theory. Proceedings of the 7th IEEE SP Workshop on Statistical Signal and Array Processing, June 1994, Quebec City, Quebec, Canada, 7–10

  8. J Grouffaud, P Larzabal, H Clergeot, Some properties of ordered eigenvalues of a Wishart matrix: application in detection test and model order selection. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '96), May 1996, Atlanta, Ga, USA 5, 2463–2466

  9. AT James, Test of equality of latent roots of the covariance matrix. Journal of Multivariate Analysis, 205–218 (1969)

  10. NL Johnson, S Kotz, Distributions in Statistics: Continuous Multivariate Distributions (John Wiley & Sons, New York, NY, USA, 1972) chapter 38-39 OpenURL

  11. M Kaveh, H Wang, H Hung, On the theoretical performance of a class of estimators of the number of narrow-band sources. IEEE Transactions on Acoustics, Speech, and Signal Processing 35(9), 1350–1352 (1987). Publisher Full Text OpenURL

  12. PR Krishnaiah, FJ Schurmann, On the evaluation of some distribution that arise in simultaneous tests of the equality of the latents roots of the covariance matrix. Journal of Multivariate Analysis 4, 265–282 (1974). Publisher Full Text OpenURL

  13. AP Liavas, PA Regalia, On the behavior of information theoretic criteria for model order selection. IEEE Transactions on Signal Processing 49(8), 1689–1695 (2001). Publisher Full Text OpenURL

  14. A Quinlan, J-P Barbot, P Larzabal, Automatic determination of the number of targets present when using the time reversal operator. The Journal of the Acoustical Society of America 119(4), 2220–2225 (2006). PubMed Abstract | Publisher Full Text OpenURL

  15. J Rissanen, Modeling by shortest data description length. Automatica 14(5), 465–471 (1978). Publisher Full Text OpenURL

  16. LL Scharf, DW Tufts, Rank reduction for modeling stationary signals. IEEE Transactions on Acoustics, Speech, and Signal Processing 35(3), 350–355 (1987). Publisher Full Text OpenURL

  17. P Stoica, Y Selén, Model-order selection: a review of information criterion rules. IEEE Signal Processing Magazine 21(4), 36–47 (2004). Publisher Full Text OpenURL

  18. M Tanter, J-L Thomas, M Fink, Time reversal and the inverse filter. The Journal of the Acoustical Society of America 108(1), 223–234 (2000). PubMed Abstract | Publisher Full Text OpenURL

  19. S Valaee, P Kabal, An information theoretic approach to source enumeration in array signal processing. IEEE Transactions on Signal Processing 52(5), 1171–1178 (2004). Publisher Full Text OpenURL

  20. HL Van Trees, Optimum Array Processing, Detection, Estimation and Modulation Theory (John Wiley & Sons, New York, NY, USA, 2002) 4

  21. M Wax, T Kailath, Detection of signals by information theoretic criteria. IEEE Transactions on Acoustics, Speech, and Signal Processing 33(2), 387–392 (1985). Publisher Full Text OpenURL

  22. M Wax, I Ziskind, Detection of the number of coherent signals by the MDL principle. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(8), 1190–1196 (1989). Publisher Full Text OpenURL

  23. KM Wong, Q-T Zhang, J Reilly, P Yip, On information theoretic criteria for determining the number of signals in high resolution array processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 38(11), 1959–1971 (1990). Publisher Full Text OpenURL

  24. Q Wu, D Fuhrmann, A parametric method for determining the number of signals in narrow-band direction finding. IEEE Transactions on Signal Processing 39(8), 1848–1857 (1991). Publisher Full Text OpenURL

  25. H-T Wu, J-F Yang, F-K Chen, Source number estimators using transformed Gerschgorin radii. IEEE Transactions on Signal Processing 43(6), 1325–1333 (1995). Publisher Full Text OpenURL

  26. YQ Yin, PR Krishnaiah, On some nonparametric methods for detection of the number of signals. IEEE Transactions on Acoustics, Speech, and Signal Processing 35(11), 1533–1538 (1987). Publisher Full Text OpenURL

  27. I Ziskind, M Wax, Maximum likelihood localization of multiple sources by alternating projection. IEEE Transactions on Acoustics, Speech, and Signal Processing 36(10), 1553–1560 (1988). Publisher Full Text OpenURL