Autoregressive Moving Average System Identification Research Articles

An Overview of Important Practical Aspects of Continuous-Time ARMA System Identification

The problem of estimating the parameters in continuous-time autoregressive moving average (ARMA) processes from discrete-time data is considered. Both direct and indirect methods are studied, and similarities and differences are discussed. A general discussion of the inherent difficulties of the problem is given together with a comprehensive study on how the choice of the sampling interval influences the estimation result. A special focus is given to how the Cramer-Rao lower bound depends on the sampling interval.

Recursive covariance ladder algorithms for ARMA system identification

The recently developed method of pure-order recursive ladder algorithms (PORLA) is extended to facilitate the identification of autoregressive moving-average (ARMA) models. Since the time recursion in this method is limited in the calculation of the input data covariance matrix, roundoff errors cannot propagate in time in higher stages of the pure-order recursively constructed ladder form. Thus, the superior least-squares tracking and fast start-up capability of the proposed algorithms is not corrupted by roundoff error. Furthermore, the algorithms allow the use of higher-order recursive windows on the data (e.g., recursive Hanning), which again significantly improves the tracking as well as the steady-state behavior. A computer program, an instructive example for implementation of the method on a massively parallel processor, and several experimental results which confirm the superior properties of the PORLA method over conventional techniques are shown. >

The iterative NCDE algorithm for ARMA system identification and spectral estimation

The problem of identifying autoregressive moving average (ARMA) models with observational output data is addressed within this report. In the absence of actual input data, the ARMA identification problem is nonlinear in the parameters. The new general ARMA algorithm derived within, entitled NCDE, makes use of the Yule-Walker equations for input estimation and a least squares input-output ARMA algorithm for initial parameter estimation. The NCDE algorithm has been tested and results show that it is both effective and efficient for autoregressive (AR), moving average (MA) and ARMA system identification via the application of an ARMA model.

ARMA system identification via the Cholesky least squares method

A computationally efficient method for the identification of scalar autoregressive moving average (ARMA) models of the form a(z)y = b(z)u+ c(z)\epsilon is introduced; it is called the Cholesky Least Squares (CLS) method. This technique iteratively estimates the coefficients of the polynomials a(z) and b(z) by using the least squares method on data which, at each iteration step, are a filtered version of the original observations \{y_{1},...,y_{N}; u_{1},...,u_{N}\} . The filter employed at each stage is the inverse of the current estimate of c(z) and this estimate is generated by factoring the sample covariance matrix of the residual sequence by using a fast Cholesky factorization algorithm [6], [7]. We describe a natural extension of the CLS method for the identification of multivariable ARMA systems and present computational experiments demonstrating the operation of this extended version of the algorithm. Our method is a variant of the Generalized Least Squares method [1]-[3], and computational experiments comparing a particular version of this method with the CLS algorithm are presented. Finally, some evidence is presented to support the view that the CLS algorithm, like many other identification methods, computes approximations to the true system's impulse response when it is provided with a (possibly incorrect) set of orders for the polynomials a(z), b(z), c(z) .