Experimental Modeling of Two-Dimensional Systems with ARMA Structure
Subject Areas : electrical and computer engineering
M.
sadabadi
1
M.
shafiee
2
M.
karrari
3
Abstract :
In this paper, experimental modeling of two-dimensional discrete systems with ARMA structure is considered. Therefore two-dimensional model order selection and parameter estimation problems are proposed. This method shows that the information of AR and MA orders are implicitly contained in two different correlation matrices and the AR and MA orders of the 2-D ARMA model can be independently determined before parameter estimation. The two-dimensional model is assumed to be causal, stable, linear, and spatial shift-invariant with quarter plane (QP) support. Numerical Simulations are presented to show the good performance and effectiveness of the proposed method in two-dimensional discrete system with ARMA structure.
[1]H. Kaufman, J. W. Woods, S. Dravida, and M. Tekalp, "Estimation and identification of two-dimensional images," IEEE Trans. Automatic Control, vol. 8, no. 7, pp. 745-756, Jul. 1983.
[2]A. C. Tan, "Image enhancement with 2-D block LMS adaptive IIR filters," in Proc. IEEE 39th Midwest Symposium on Circuits and Systems, vol. 3, pp. 1389-1392, USA, Ames, Aug. 1997.
[3]M. B. Zarrop and P. E. Wellstead, "Two-dimensional and EM technique for cross directional estimation and control," in IEE Proc. Control Theory Application, vol. 149, no. 5, pp. 457-462, Sep. 2002.
[4]D. M. Gacon, Control and Estimation for Web-Forming Processes, Ph.D Dissertation, University of Manchester Institute of Science and Technology (UMIST), Electrical Engineering and Electronics Department, Sep. 1997.
[5]P. E. Wellstead and M. H. Waller, "Control and signal processing for two dimensional systems in web forming industries," in Proc. UKACC Int. Conf. on Control 96, no. 427, pp. 1272-1277, Sep. 1996.
[6]Z. Geng, R. Carroll, and J. Xie, "Two-dimensional model and algorithm for a class of iterative learning control systems," Int. J. of Control, vol. 52, no. 4, pp. 833-862, Oct. 1990.
[7]D. H. Owens, N. Amann, E. Rogers, and M. French, "Analysis of linear iterative learning control schemes: a 2-D repetitive systems approach," Multidimensional Systems and Signal Processing, vol. 11, no. 1-2, pp. 125-177, Apr. 2000.
[8]T. Al-Towaim, A. D. Barton, P. L. Lewin, E. Rogers, and D. H. Owens, "Iterative learning control: 2D control systems from theory to application," Int. J. of Control (Special Issue: Multidimensional Control Systems: Theory with a View to Applications), vol. 77, no. 9, pp. 877-893, Jun. 2004.
[9]X. D. Li, T. W. S. Chow, and J. K. L. Ho, "2-D system theory based iterative learning control for linear continuous systems with time delays," IEEE Trans. Circuits and Systems-I: Regular Papers, vol. 52, no. 7, pp. 1421-1430, Jul. 2005.
[10]D. Ucinski and J. Korbicz, "Parameter identification of two- dimensional distributed systems," Int. J. of System Science, vol. 21, no. 12, pp. 2441-2456, Dec. 1990.
[11]L. Ljung, System Identification: Theory for the User, Prentice - Hall, Inc., Englewood Cliffs, NJ, 2nd Edition, 1999.
[12]H. Li, W. Sun, P. Stoica, and J. Li, "Two-dimensional system identification using amplitude estimation," IEEE Signal Processing Letters, vol. 9, no. 2, pp. 61-63, Feb. 2002.
[13]J. A. Cadzow and K. Ogino, "Two-dimensional spectral estimation," IEEE Trans. Acoust., Speech, Signal Processing , vol. 29, no. 3, pp. 396-401, Jun. 1981.
[14]X. D. Zhang and J. Cheng, "High resolution two-dimensional ARMA spectral estimation," IEEE Trans. Signal Processing, vol. 39, no. 3, pp. 765-770, Mar. 1991.
[15]W. B. Mikhael and Y. Haoping, "A linear approach for two- dimensional frequency domain, least square, signal, and system modeling," IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 2, no. 12, pp. 786-795, Dec. 1994.
[16]Q. Zhang, J. R. Roman, D. W. Davis, and W. B. Mikhael, "A generalized two-dimensional frequency domain least square algorithm for ARMA system modeling," in Proc. of the 40th Midwest Symp. on Circuits and Systems, vol. 2, pp. 965-968, Aug. 1997.
[17]A. Kizilkaya and A. H. Kayran, "Estimation of 2-D ARMA model parameters by using equivalent AR approach," J. of the Franklin Institute, vol. 342, no. 1, pp. 39-67, Jan. 2005.
[18]A. Kizilkaya, C. M. Yetis, A. H. Kayran, and S. Seker, "Estimation of the 2-D ARMA model parameters based on the equivalent MA approach," in Proc. of the IASTED In. Conf. on Circuits, Signals, and Systems, CSS’06, vol. 16, pp. 263-268, San Francisco, California, US, Nov. 2006.
[19]M. S. Sadabadi, M. Shafiee, and M. Karrari, "System identification of two-dimensional continuous-time systems using wavelets as modulating functions," ISA Trans.-Elsevier, vol. 47, no. 3, pp. 256-266, Jul. 2008.
[20]Q. Zhang, W. B. Mikhael, J. R. Roman, and D. W. Davis, "Two new model order selection approaches for ARMA system modeling using the two-dimensional frequency domain least square algorithm," in Proc. IEEE ISCAS, vol. 5, pp. 297-300, Jun. 1998.
[21]B. Aksasse and L. Radouane, "Two-dimensional autoregressive (2 - D AR) model order estimation," IEEE Trans. Signal Processing, vol. 47, no. 7, pp. 2072-2077. Jul. 1999.
[22]B. Aksasse, L. Badidi, and L. Radouane, "A rank test based approach to order estimation- part I: 2-D AR models application," IEEE Trans. Signal Processing, vol. 47, no. 7, pp. 2069-2072, Jul. 1999.
[23]S. Rital, A. Meziane, M. Rziza, and D. Aboutajdine, "Two-dimensional non-gaussian autoregressive model order determination," IEEE Trans. Signal Processing, vol. 9, no. 12, pp.426-428, Dec. 2002.
[24]G. Liang, M. Wilkes, and J. A. Cadzow, "ARMA model order estimation based on the eigenvalues of the covariance matrix," IEEE Trans. Signal Processing, vol. 41, no. 10, pp. 3003-3009, Oct. 1993.
[25]A. Al-Smadi and A. Al-Zaben, "ARMA model order determination using edge detection: a new perspective," Circuits Systems Signal Processing, vol. 24, no. 6, pp. 723-732, Dec. 2005.
[26]X. D. Zhang and Y - S Zhang, "Determination of the MA order of an ARMA process using sample correlations," IEEE Trans. Signal Processing, vol. 41, no. 6, pp. 2277-2280, Jun. 1993.
[27]C. B. Xiao, X. D. Zhang, and Y. D. Li, "A new method for AR order determination of an ARMA process," IEEE Trans. Signal Processing, vol. 44, no. 11, pp. 2900-2903, Nov. 1996.
[28]M. S. Sadabadi, M. Shafiee, and M. Karrari, "AR order determination of a 2-D ARMA model," in Proc. of the European Control Conf., ECC’07, pp. 3877-3882, Greece, Jul. 2007.
[29]P. Kiernan, "Two-dimensional AR spectral estimation using a two dimensional minimum free energy method," IEEE Trans. Signal Processing, vol. 43, no. 12, pp. 3075-3081, December 1995.
[30]A. Rosenfeld, Image Modeling, New York: Academic, 1981.
[31]D. Gimeno, L. Torres, and J. R. Casas, "A new approach to texture coding using stochastic vector quantization," in Proc. IEEE ICIP, Austin, TX, vol. 2, pp. 119-123, Nov. 1994.
[32]E. J. Delp, R. L. Kashyap, and O. R. Michell, "Image data compression using autoregressive time series models," Pattern Recognit., vol. 11, no. 5-6, pp. 313-323, 1979.
[33]W. R. Wu and A. Kundu, "Image estimation using fast modified reduced update kalman filter," IEEE Trans. Signal Processing, vol. 40, no. 4, pp. 915-926, Apr. 1992.
[34]S. Ranganath and A. K. Jain, "Two-dimensional linear prediction models-part I: spectral factorization and realization," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 1, pp. 280-299, Feb