A new approach for ARMA pole estimation using higher-order crossings

The paper describes a new method for estimating the poles of an ARMA model using higher-order crossings. The method involves transforming counts of crossing events into estimates of ARMA poles via the autocorrelation domain. An important advantage of the method is that the crossing counts are the only features that need to be stored from the original data. The poles of an ARM A model of a control loop correspond to the roots of the characteristic equation and are thus useful for evaluating control performance.

[1]  O. Kaynak,et al.  A Robust Identification Technique for Time-Varying ARMA Processes Based on Variable Structure Systems Theory , 2002 .

[2]  Tore Hägglund,et al.  Detection and Diagnosis of Oscillation in Control Loops , 1997 .

[3]  Yi Liao.  Order recursive algorithm for ARMA identification , 1989, IEEE 1989 International Conference on Systems Engineering.

[4]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[5]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[6]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[7]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[8]  K. Farahmand.  On the Average Number of Real Roots of a Random Algebraic Equation , 1986 .

[9]  Leonardo C. Kammer,et al.  Optimal controller properties from closed-loop experiments , 1998, Autom..

[10]  Ed. McKenzie.  10. Time Series Analysis by Higher Order Crossings , 1996 .

[11]  Benjamin Kedem,et al.  Authors' Reply to Comments on 'Zero-crossing rates of functions of Gaussian processes' , 1991, IEEE Trans. Inf. Theory.

[12]  B. Kedem.  Estimation of the Parameters in Stationary Autoregressive Processes after Hard Limiting , 1980 .

[13]  Michael R. Frey,et al.  Time series analysis by higher order crossings , 1994 .

[14]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[15]  Ying-Chang Liang,et al.  A hybrid approach to time series analysis and spectral estimation , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[16]  S. Rice.  Mathematical analysis of random noise , 1944 .

[17]  A. A. Beex,et al.  A recursive procedure for ARMA modeling , 1985, IEEE Trans. Acoust. Speech Signal Process..

[18]  M. Morf,et al.  Recursive ladder algorithms for ARMA modeling , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[19]  T. Miao,et al.  Automatic detection of excessively oscillatory feedback control loops , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[20]  Ken Sharman,et al.  Performance evaluation of the modified Yule-Walker estimator , 1985, IEEE Trans. Acoust. Speech Signal Process..

[21]  B. Kedem,et al.  Spectral analysis and discrimination by zero-crossings , 1986, Proceedings of the IEEE.

[22]  T. Harris.  Assessment of Control Loop Performance , 1989 .

[23]  J. Schoukens,et al.  Parametric identification of transfer functions in the frequency domain-a survey , 1994, IEEE Trans. Autom. Control..

[24]  Marco C. Campi,et al.  The problem of pole-zero cancellation in transfer function identification and application to adaptive stabilization , 1996, Autom..

[25]  Peter Strobach,et al.  Recursive covariance ladder algorithms for ARMA system identification , 1988, IEEE Trans. Acoust. Speech Signal Process..

[26]  T. Harris,et al.  Performance assessment measures for univariate feedback control , 1992 .

[27]  J. A. McFadden.  The axis-crossing intervals of random functions , 1956, IRE Trans. Inf. Theory.

[28]  Torsten Söderström,et al.  An efficient linear method for ARMA spectral estimation , 1994, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.