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ARMAX models constitute an excellent compromise between performance and complexity and can model in an effective way the presence of disturbances acting on the process state. These models, however, do not take into account the observation errors on the output of the process to be identified and this can be particularly important in applications like filtering and fault diagnosis. This paper concerns extended ARMAX models that consider also the presence of additive white noise on the output observation and describes an approach for their identification that takes advantage of both the errors–in–variables framework and the instrumental variable properties. The paper reports also the results of Monte Carlo simulations that underline the effectiveness of the proposed approach.

A common approach in modeling signals in many engineering applications consists in adopting autoregressive (AR) models, consisting in filters with transfer functions having a unitary numerator, driven by white noise. Despite their wide application, these models do not take into account the possible presence of errors on the observations and cannot prove accurate when these errors are significant. AR plus noise models constitute an extension of AR models that consider also the presence of an observation noise. This paper describes a new algorithm for the identification of AR plus noise models that is characterized by a very good compromise between accuracy and efficiency. This algorithm, taking advantage of both low and high-order Yule–Walker equations, also guarantees the positive definiteness of the autocorrelation matrix of the estimated process and allows to estimate the equation error and observation noise variances. It is also shown how the proposed procedure can be used for estimating the order of the AR model. The new algorithm is compared with some traditional algorithms by means of Monte Carlo simulations. Copyright © 2007 John Wiley & Sons, Ltd.

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cramer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations.

This paper considers the problem of estimating the parameters of an autoregressive (AR) process in presence of additive white noise and proposes a new identification method, based on theoretical results originally developed in errors-in-variables contexts. This approach allows to estimate the AR parameters, the driving noise variance and the variance of the additive noise in a congruent way in that these estimates assure the positive definiteness of the autocorrelation matrix. The performance of the proposed algorithm is compared with that of bias-compensated least-squares methods by means fo Monte Carlo simulations. The results show the effectivenesss of the new method also in presence of high amounts of noise.

This paper proposes a two-step identification procedure for the direction-of-arrival estimation problem in the presence of nonuniform white noise. The first step consists in estimating the unknown sensor noise variances by exploiting the properties of the Frisch scheme. Once that the noise covariance matrix has been identified, the angles of arrival are computed by using the classical ESPRIT algorithm. The effectiveness of the whole procedure is tested by means of Monte Carlo simulations.

The paper proposes a new approach for identifying linear dynamic errors-in-variables (EIV) models, whose input and output are affected by additive white noise. The method is based on a nonlinear system of equations consisting of part of the compensated normal equations and of a set of high order Yule-Walker equations. This system allows mapping the EIV identification problem into a quadratic eigenvalue problem that, in turn, can be mapped into a linear generalized eigenvalue problem. The system parameters are thus estimated without requiring the use of iterative identification algorithms. The effectiveness of the method has been tested by means of Monte Carlo simulations and compared with those of other EIV identification methods.

ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation error family but are endowed with many practical advantages concerning both their estimation and their predictive use. On the other hand the (implicit) assumption of noise-free inputs and of outputs affected by an additive colored noise whose spectrum is defined only by the model poles can be considered as non realistic when all measures are affected by additive errors. This paper considers the family of ARX + noise models that describe ARX processes whose measures are affected by additive white noise. The identification of these models is then mapped into the problem of identifying errors-in-variables models in the context of the Frisch scheme and a specific identification algorithm is described. A Monte Carlo simulation confirms the good results that can be obtained with the whole procedure.