PARAMETER ESTIMATION OF MOVING AVERAGE PROCESSES USING CUMULANTS AND NONLINEAR OPTIMIZATION ALGORITHMS

M. Boulouird, M. M. Hassani, G. Favier

2005

Abstract

In this paper nonlinear optimization algorithms, namely the Gradient descent and the Gauss-Newton algorithms, are proposed for blind identification of MA models. A relationship between third and fourth order cumulants of the noisy system output and the MA parameters is exploited to build a set of nonlinear equations that is solved by means of the two nonlinear optimization algorithms above cited. Simulation results are presented to compare the performance of the proposed algorithms.

References

  1. Abderrahim, K., Ben Abdennour, R., Favier, G., Ksouri, M., and Msahli, F. (2001). New Results on FIR Identification using Cumulants. Journal Européen des Systèmes Automatisés-JESA, Vol. 35, No. 5, pp. 601-622.
  2. Alshebeili, S. A., Venetsanopoulos, A. N., and Cetin, A. E. (1993, April). Cumulant Based Identification Approaches for Nonminimum Phase FIR Systems. IEEE Transactions on Signal Processing, Vol. 41, No. 4, pp. 1576-1588.
  3. Giannakis, G. B., and Mendel, J. M. (1989, March). Identification of Nonminimum Phase Systems Using Higher Order Statistics. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, No. 3, pp. 360-377.
  4. Martin, J. K., and Nandi, A. K. (1996, January). Blind System Identification using Second, Third and Fourth Order Cumulants. Journal of the Franklin Institute : Enginnering and applied mathematics, Pergamon, Vol. 333(B), No. 1, pp. 1-13.
  5. Mendel, J. M. (1991, March). Tutorial on Higher-Order Statistics (Spectra) in Signal Processing and System Theory : Theoretical Results and some Applications. Proceedings of the IEEE, Vol. 79, No. 3, pp. 278-305.
  6. Na, Y. N., Kim, K. S., Song, I., and Kim, T. (1995, December). Identification of Nonminimum Phase FIR Systems Using the Third- and Fourth-Order Cumulants. IEEE Transactions on Signal Processing, Vol. 43, No. 8, pp. 2018-2022.
  7. Nikias, C. L., and Mendel, J. M. (1993, July). Signal Processing With Higher Order Spectra. IEEE Signal Processing Magazine, pp. 10-37.
  8. Srinivas, L., and Hari, K. V. S. (1995, December). FIR System Identification Using Higher Order Cumulants - A Generalized Approach. IEEE Transactions on Signal Processing, Vol. 43, No. 12, pp. 3061-3065.
  9. Stogioglou, A. G., and McLaughlin, S. (1996, July). MA Parameter Estimation and Cumulant Enhancement. IEEE Transactions on Signal Processing, Vol. 44, No. 7, pp. 1704-1718.
  10. Tugnait, J. K. (1990, July). Approaches to FIR System Identification With Noisy Data Using Higher Order Statistics. IEEE Transactions on Signal Processing, Vol. 38, No. 7, pp. 1307-1317.
  11. Tugnait, J. K. (1991, October). New Results on FIR System Identification Using Higher-Order Statistics. IEEE Transactions on Signal Processing, Vol. 39, No. 10, pp. 2216-2221.
  12. Gauss-Newton algorithm - h(2)=0.6667 (True value of h(2)) 10 20 30 40 50 60
Download


Paper Citation


in Harvard Style

Boulouird M., M. Hassani M. and Favier G. (2005). PARAMETER ESTIMATION OF MOVING AVERAGE PROCESSES USING CUMULANTS AND NONLINEAR OPTIMIZATION ALGORITHMS . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 972-8865-31-7, pages 11-15. DOI: 10.5220/0001182900110015


in Bibtex Style

@conference{icinco05,
author={M. Boulouird and M. M. Hassani and G. Favier},
title={PARAMETER ESTIMATION OF MOVING AVERAGE PROCESSES USING CUMULANTS AND NONLINEAR OPTIMIZATION ALGORITHMS},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2005},
pages={11-15},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001182900110015},
isbn={972-8865-31-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - PARAMETER ESTIMATION OF MOVING AVERAGE PROCESSES USING CUMULANTS AND NONLINEAR OPTIMIZATION ALGORITHMS
SN - 972-8865-31-7
AU - Boulouird M.
AU - M. Hassani M.
AU - Favier G.
PY - 2005
SP - 11
EP - 15
DO - 10.5220/0001182900110015