Wavelet Based Identification of Second Order Linear System

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Authors:

• Sudipta Majumdar
• Harish Parthasarathy

Keywords:

• Least squares method
• linear system
• system identification
• wavelet transform.

References:

[1] M. I. Doroslovacki and H. Fan, "Wavelet based linear system modeling
and adaptive filtering", IEEE Trans. on Signal Processing, vol. 44, no.5,
pp. 1156-1167, May 5, 1996 .
[2] Carlos E. Christoffersen and Michael B. Steer, "State variable based transient
circuit simulation using wavelets", IEEE Microwave and Guided
Wave Letters, vol. 11, no. 4, pp. 161-173, April 2001.
[3] Li He-Sheng, Mao Jian-Qin and Zhao Ming-Sheng "Impulse response
identification based on varying scale orthogonal wavelet packet transform",
Acta Automatica Sinica vol. 31 no.4, July 2005.
[4] Ivan Taufer and Oldrich Drabek, "Identification of nonlinear systems
based on mathematical physical analysis and least square method", Acta
Montanistica Slovaca Rocnik, cislo vol.4, pp. 188-190, 2003.
[5] Daubechies I., Ten lectures on wavelets, Society for Industrial and
Applied Mathematics, Philadelpha Pennsylvania, 1992.
[6] Michael W. Frazier, An introduction to wavelets through linear algebra,
Springer-Verlag, New York, 1999.
[7] Mallat S. G., "A Theory for multiresolution decomposition: the wavelet
representation", IEEE Trans. on Pattern Analysis and Machine Intelligence,
vol. 2, no.7, pp. 674-693 1989.
[8] Mark J. Shensa, "The discrete wavelet transform: wedding the a Torus
and Mallat algorithm", IEEE Transactions on Signal Processing vol.40,
no. 10, pp.2464-2482, October 1992.
[9] Kambig Nayebi, Thomas P. Barnwell III and Mark J. T. Smith, "Time
domain filter bank design: a new design theory", IEEE Transaction on
Signal Processing, vol. 40, no. 6, pp. 1412-1429, June 1992.
[10] Edward J. Ewen and Donald D., "Weiner identification of weakly
nonlinear systems using input and output measurements", IEEE Trans.
on Circuits and Systems, vol. CAS - 27, no. 12, pp. 1255-1261,
December 1980.
[11] Woldzimierz Greblicki, "Nonparametric identification of Weiner systems
by orthogonal series", IEEE Trans. on Automatic Control, vol. 39, no.
10, pp. 2077-2086, October 1994.
[12] Hengliang Wang, Sheng La, Kihwan Ju, K. H. Chon," A new approach
to closed-loop linear systems identification via a vector autoregressive
model", Annals of Biomedical Engineering, vol. 30, pp. 1204-1214,
2002.
[13] Gang Jin, Michael K. Sain and Billie Spencer, Jr, "Frequency domain
system identification for controlled civil engineering structures", IEEE
Trans on Control Systems Technology, vol. 13, no.6, pp. 1055-1062,
November 2005.
[14] Minh Q Phan, Richard W Longman, "System identification from
multiple-trial data corrupted by non-repeating periodic disturbances",
Int. J. Appl. Math. Comput. Sci., vol. 13, no. 2, pp. 185-192, 2003.