Journal of the Institute of Electronics Engineers of Korea TC (대한전자공학회논문지TC)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지

A Study on the AR Identification of unknown system using Cumulant

Cumulant를 이용한 미지 시스템의 AR 식별에 관한 연구

  • Lim, Seung-Gag (Department of Information and Telecommunication Engineering, Kongju, National University)
  • 임승각 (국립 공주대학교 정보통신공학부)
  • Published : 2006.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the AR Identification of unknown system using cumulant, which is the 3rd order statistics of output signal in the presence of the noise signal. The algorithms for identification of unknown system we applies to the AR identification method using the cumulant which is possible to the guarantees of global convergence and the representation of amplitude and phase information of system among with the method of parametric modeling. In the process of identification, we considered unknown system to the one of AR system. After the generation of input signal, it was being passed through the system then We use the its output signal that the noise is added. As a result of identification of AR system by changing the signal to noise ratio, we get the fairly good results compared to original system output values and confirmed that the pole was located in the unit circle of z transform.

본 논문은 잡음이 존재하는 미지 시스템 출력 신호의 3차 통계치인 cumulant를 이용한 AR 식별에 관한 것이다. 미지 시스템 식별을 위한 알고리즘에서는 Parametric Modeling 기법중에서 Global Convergence 보장 및 시스템의 진폭과 위상 정보를 모두 표현할 수 있는 Cumulant를 이용한 AR (Auto Regressive) 식별 방법을 적용하였다. 식별 과정에서 미지 시스템을 하나의 AR 시스템으로 간주하였고 입력 신호를 발생하여 이를 통과시킨 후 잡음이 부가된 출력 신호를 얻어 이를 이용하였다. 신호대 잡음비의 변화에따른 AR 시스템의 식별을 수행한 결과 원래의 시스템 출력치와 유사한 양호한 식별 결과를 얻을 수 있었고 극점이 z 변환의 단위원내에 존재함을 확인하였다.

Keywords

References

  1. P.Eykhoff, 'System Identification', North-Holland, Amsterdam, 1974
  2. Lennart Ljunng, 'System Identification: Theory for the user', Prentice Hall, 1987
  3. J.K Tugnait, 'Identification of Linear Stochastic Systems via Second-and Fourth-Order Cumulant Matching', IEEE Trans. on Information Theory, vol. IT-33, no. 3, pp.393-407, 1987 https://doi.org/10.1109/TIT.1987.1057308
  4. R.Pan, C.L.Nikias, 'The Complex Cepstrum of Higher Order Cumulants and Nonminimum Phase system Identification', IEEE Trans. on ASSP., vol. 36, no. 2, pp.186-205, Feb. 1988 https://doi.org/10.1109/29.1513
  5. G.B.Giannakis, J.M.Mendel, 'Identification of nonminimum phase system using higher-order statistics', IEEE. Trans. ASSP, vol. 37, pp.360-377, March 1989 https://doi.org/10.1109/29.21704
  6. J.K Tugnait, 'Approaches to FIR system identification with noisy data using higher-order statistics', IEEE Trans. ASSP, vol. 38, pp. 1307-1317, July 1990 https://doi.org/10.1109/29.57559
  7. J.M.Mendel, 'Tutorial on Higher-Order Statistics in Signal Processing and System Theory', Proc. of the IEEE, vol. 79, no. 3, pp. 277-305, Mar. 1991 https://doi.org/10.1109/5.75086
  8. A.Swami, J.M.Mendel, 'Identifiablility of the AR parameters of an ARMA Process using cumulants', IEEE Trans. on AC., vol. 37, pp.268-273, Feb 1992 https://doi.org/10.1109/9.121633
  9. C.L.Nikias, A.P.Petropuou, 'Higher-Order Spectra Analysis', Prentice Hall, 1993