Phase ARMA Models Research Articles

Order-recursive blind identification of linear models using mixed cumulants

The problem of determining the AR order and parameters of a nonminimum phase ARMA model from observations of the system output is considered. The model is driven by a sequence of random variables which is assumed unobservable. A novel identification algorithm based on the second- and third-order cumulants of the output sequences is introduced. It performs order-recursively by minimising a well defined cost function. Strong convergence and consistency of the algorithm are proved and the weight of the cost function is balanced between the second-order and the third-order cumulants of output sequences. The influence of the weight on the estimation accuracy is also evaluated. Theoretical analyses and numerical simulations show that the proposed algorithm is satisfactory for both order and parameter identification of an AR model which is subordinate to a nonminimum phase ARMA model.

Adaptive identification of nonminimum phase ARMA models using higher order cumulants alone

An adaptive identification algorithm for causal nonminimum phase ARMA models in additive colored Gaussian noise is proposed. The algorithm utilizes higher order cumulants of the observed signal alone. It estimates the AR and MA parameters successively in each iteration without computing the residual time series. The steepest descent method is used for parameter updating.

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher order cepstra slices, the Fourier phases of two intermediate sequences (h/sub min/(n) and h/sub max/(n)) can be computed, where h/sub min/(n) is composed of the minimum phase parts of the AR and MA models, and h/sub max/(n) of the corresponding maximum phase parts. Under the condition that there are no zero-pole cancellations in the ARMA model, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are by product of the parameter estimation procedure. Through simulations it is shown that, unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h/sub min/(n) and h/sub max/(n), the phase errors due to finite length data are studied and their statistics are derived. >

Maximum likelihood estimation of the parameters of nonminimum phase and noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This paper presents a new method known as the back-filtering-based maximum likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>