In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.
[1] A. Al-Smadi and A. Alshamali, "Fitting ARMA Models to Linear non-
Gaussian Processes using Higher Order Statistics", Signal Processing,
Vol. 82, No. 11, pp. 1789-1793, November 2002.
[2] S. A. Alshebeili, A. N. Venetsanopoulos, and A. E. Çetin, "Cumulant
Based Identification Approaches for Nonminimum Phase FIR Systems",
IEEE Transactions on Signal Processing, Vol. 41, No. 4, pp. 1576-1588,
April 1993.
[3] A. Belouchrani and B. Derras, "An Efficient Fourth-Order System Identification
FOSI Algorithm Utilizing the Joint Diagonalization Procedure",
In Proceedings of the 10-th IEEE Workshop on Statistical Signal and
Array Processing, Pennsylvania, USA, pp. 621-625, August 2000.
[4] M. Boulouird, G. Favier, and M. M. Hassani, "Parameter Estimation of
Moving Average Processes using Cumulants and Non-linear Optimization
Algorithms", Proceedings of the 2nd IFAC International Conference
on Informatics in Control, Automation and Robotics-ICINCO-05, Barcelona,
Spain, pp. 11-15, September 14-17, 2005.
[5] M. Boulouird, G. Favier, and M. M. Hassani, "Blind Identification of
MA Models Using Gradient Descent and Newton-Raphson Algorithms",
Proceedings of the First Mediterranean Days of Physics-JMP1-05,
Tetuan, Morocco, November 24-26, 2005.
[6] M. Boulouird, C. E. R. Fernandes, G. Favier, M. M. Hassani, and
J. C. M. Mota, "Identification of Non-minimum Phase Systems using
Nonlinear Optimization Algorithms and a Joint-Diagonalization Based
Method", Proceedings of the IEEE-International conference on Signal-
Image Technology and Internet-based Systems-SITIS-05, Yaounde, Cameroon,
November 27th - December 1st, 2005.
[7] M. Boulouird and M. M. Hassani, "Blind Channel Identification using
Higher-Order Statistics", Submitted to the Journal of Statistical Computation
and Simulation, Taylor and Francis, 2005.
[8] D. Brillinger and M. Rosenblatt, "Computation and interpretation of kth
order spectra", In Spectral Analysis of Time Signals, New York : Wiley,
pp. 907-938, 1967.
[9] P. Comon, "MA Identification Using Fourth Order Cumulants", Signal
Processing, Vol. 26, No. 3, pp. 381-388, March 1992.
[10] J. A. R. Fonollosa and J. Vidal, "System Identification Using a Linear
Combination of Cumulants slices", IEEE Transactions on Signal Processing,
Vol. 41, No. 7, pp. 2405-2411, July 1993.
[11] G.B. Giannakis, "Cumulants : a Powerful Tool in Signal Processing",
Proceedings of the IEEE, Vol. 75, No. 9, pp. 1333-1334, September
1987.
[12] J. M. Mendel, "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, March
1991.
[13] Y. J. Na, K. S. Kim, I. Song, and T. Kim, "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,
December 1995.
[14] C. L. Nikias and J. M. Mendel, "Signal Processing With Higher Order
Spectra", IEEE Signal Processing Magazine, pp. 10-37, July 1993.
[15] C. L. Nikias and A. P. Petropulu, "Higher-Order Spectra Analysis", PTR
Prentice-Hall, Englewood Cliffs, New Jersey, 1993.
[16] C. L. Nikias and M. R. Raghuveer, "Bispectrum estimation : A digital
signal processing framework", Proceedings of the IEEE, pp. 869-891,
July 1987.
[17] A. G. Stogioglou and S. McLaughlin, "MA Parameter Estimation and
Cumulant Enhancement", IEEE Transactions on Signal Processing, Vol.
44, No. 7, pp. 1704-1718, July 1996.
[18] J. K. Tugnait, "Approaches to FIR System Identification With Noisy
Data Using Higher Order Statistics", IEEE Transactions on Signal
Processing, Vol. 38, No. 7, pp. 1307-1317, July 1990.
[19] J. K. Tugnait, "New Results on FIR System Identification Using Higher-
Order Statistics", IEEE ASSP Workshop on Spectrum Estimation, pp.
202-206, October 1990.
[20] J. K. Tugnait, "New Results on FIR System Identification Using Higher-
Order Statistics", IEEE Transactions on Signal Processing, Vol. 39, No.
10, pp. 2216-2221, October 1991.
[1] A. Al-Smadi and A. Alshamali, "Fitting ARMA Models to Linear non-
Gaussian Processes using Higher Order Statistics", Signal Processing,
Vol. 82, No. 11, pp. 1789-1793, November 2002.
[2] S. A. Alshebeili, A. N. Venetsanopoulos, and A. E. Çetin, "Cumulant
Based Identification Approaches for Nonminimum Phase FIR Systems",
IEEE Transactions on Signal Processing, Vol. 41, No. 4, pp. 1576-1588,
April 1993.
[3] A. Belouchrani and B. Derras, "An Efficient Fourth-Order System Identification
FOSI Algorithm Utilizing the Joint Diagonalization Procedure",
In Proceedings of the 10-th IEEE Workshop on Statistical Signal and
Array Processing, Pennsylvania, USA, pp. 621-625, August 2000.
[4] M. Boulouird, G. Favier, and M. M. Hassani, "Parameter Estimation of
Moving Average Processes using Cumulants and Non-linear Optimization
Algorithms", Proceedings of the 2nd IFAC International Conference
on Informatics in Control, Automation and Robotics-ICINCO-05, Barcelona,
Spain, pp. 11-15, September 14-17, 2005.
[5] M. Boulouird, G. Favier, and M. M. Hassani, "Blind Identification of
MA Models Using Gradient Descent and Newton-Raphson Algorithms",
Proceedings of the First Mediterranean Days of Physics-JMP1-05,
Tetuan, Morocco, November 24-26, 2005.
[6] M. Boulouird, C. E. R. Fernandes, G. Favier, M. M. Hassani, and
J. C. M. Mota, "Identification of Non-minimum Phase Systems using
Nonlinear Optimization Algorithms and a Joint-Diagonalization Based
Method", Proceedings of the IEEE-International conference on Signal-
Image Technology and Internet-based Systems-SITIS-05, Yaounde, Cameroon,
November 27th - December 1st, 2005.
[7] M. Boulouird and M. M. Hassani, "Blind Channel Identification using
Higher-Order Statistics", Submitted to the Journal of Statistical Computation
and Simulation, Taylor and Francis, 2005.
[8] D. Brillinger and M. Rosenblatt, "Computation and interpretation of kth
order spectra", In Spectral Analysis of Time Signals, New York : Wiley,
pp. 907-938, 1967.
[9] P. Comon, "MA Identification Using Fourth Order Cumulants", Signal
Processing, Vol. 26, No. 3, pp. 381-388, March 1992.
[10] J. A. R. Fonollosa and J. Vidal, "System Identification Using a Linear
Combination of Cumulants slices", IEEE Transactions on Signal Processing,
Vol. 41, No. 7, pp. 2405-2411, July 1993.
[11] G.B. Giannakis, "Cumulants : a Powerful Tool in Signal Processing",
Proceedings of the IEEE, Vol. 75, No. 9, pp. 1333-1334, September
1987.
[12] J. M. Mendel, "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, March
1991.
[13] Y. J. Na, K. S. Kim, I. Song, and T. Kim, "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,
December 1995.
[14] C. L. Nikias and J. M. Mendel, "Signal Processing With Higher Order
Spectra", IEEE Signal Processing Magazine, pp. 10-37, July 1993.
[15] C. L. Nikias and A. P. Petropulu, "Higher-Order Spectra Analysis", PTR
Prentice-Hall, Englewood Cliffs, New Jersey, 1993.
[16] C. L. Nikias and M. R. Raghuveer, "Bispectrum estimation : A digital
signal processing framework", Proceedings of the IEEE, pp. 869-891,
July 1987.
[17] A. G. Stogioglou and S. McLaughlin, "MA Parameter Estimation and
Cumulant Enhancement", IEEE Transactions on Signal Processing, Vol.
44, No. 7, pp. 1704-1718, July 1996.
[18] J. K. Tugnait, "Approaches to FIR System Identification With Noisy
Data Using Higher Order Statistics", IEEE Transactions on Signal
Processing, Vol. 38, No. 7, pp. 1307-1317, July 1990.
[19] J. K. Tugnait, "New Results on FIR System Identification Using Higher-
Order Statistics", IEEE ASSP Workshop on Spectrum Estimation, pp.
202-206, October 1990.
[20] J. K. Tugnait, "New Results on FIR System Identification Using Higher-
Order Statistics", IEEE Transactions on Signal Processing, Vol. 39, No.
10, pp. 2216-2221, October 1991.
@article{"International Journal of Electrical, Electronic and Communication Sciences:55843", author = "Mohamed Boulouird and Moha M'Rabet Hassani", title = "Blind Identification of MA Models Using Cumulants", abstract = "In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.
", keywords = "Cumulants, Identification, MA models, Parameter estimation", volume = "1", number = "6", pages = "834-5", }
