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The identification of Errors-in-variables (EIV) models refers to systems where the available measurements of their inputs and outputs are corrupted by additive noise. A large variety of solutions are available when dealing with this estimation problem, in particular when the corrupting noises are white processes. However, the number of available solutions decreases when the output noise is assumed as a colored process, which is a case of great practical interest. On the other hand, many applications require estimation algorithms to work on-line, tracking a dynamical system behavior for control, signal processing, or diagnosis. In many cases, they even have to take into account computational constraints. In this paper, we propose an estimation method that is able to both lay out an algorithm to solve the identification problem of EIV systems with arbitrarily correlated output noise and also provide an efficient recursive version that does not make use of variable size matrix inversions.

A new approach for estimating multichannel AR (M-AR) models from noisy observations is proposed. It relies on the so-called Frisch scheme, whose rationale consists in finding the solution of the identification problem within a locus of solutions compatible with the second order statistics of the noisy data. Once that the locus of solutions has been defined, it is necessary to introduce a suitable selection criterion in order to identify a single solution. The criterion proposed in the paper is based on the comparison of the theoretical statistical properties of the residual of the noisy M-AR model with those computed from the data. The results obtained by means of Monte Carlo simulations show that the proposed algorithm outperforms some existing methods.

This paper concerns the identification of multivariable errors-in-variables (EIV) models, i.e. models where all inputs and outputs are assumed as affected by additive errors. The identification of MIMO EIV models introduces challenges not present in SISO and MISO cases. The approach proposed in the paper is based on the extension of the dynamic Frisch scheme to the MIMO case. In particular, the described identification procedure relies on the association of EIV models with directions in the noise space and on the properties of a set of high order Yule–Walker equations. A method for estimating the system structure is also described.

This paper deals with the problem of identifying linear errors-in-variables (EIV) models corrupted by white noise on the input and colored noise on the output. This allows to take into account the presence of both measurement errors and process disturbances. The proposed approach is based on a nonlinear system of equations whose unkowns are the system parameters and the input noise variance. The obtained set of equations allows mapping the EIV identification problem into a quadratic eigenvalue problem that, in turn, can be mapped into a linear generalized eigenvalue problem. The performance of the proposed approach is illustrated by means of Monte Carlo simulations and compared with those of existing techniques.

The most common approach in Structural Health Monitoring (SHM) consists in performing accelerometric measures of the response of the monitored structures to natural or artificial stimuli (e.g. wind, urban traffic, seismic events etc.) and in modeling the dynamic behavior of the structure on the basis of these measures. The models can be used, in particular, to extract and compare the main modes i.e. the main resonant frequencies and in comparing these frequencies with those concerning the initial state of integrity of the building. This paper compares the results given by traditional AR and ARMA models with those offered by AR+noise models where an additive observation error is considered and shows that these models can offer some advantages in SHM applications in that describe more accurately the stochastic context of the process. The comparisons have been performed on two different sets of data: the first one has been collected on an industrial building in occasion of an heavy seismic event whereas the second one has been collected on a medieval tower excited by urban traffic.

This paper deals with the identification of an autoregressive (AR) process disturbed by an additive moving-average (MA) noise. Our approach operates as follows: Firstly, the AR parameters are estimated by using the overdetermined high-order Yule–Walker equations. The variance of the AR process driving process can be deduced by means of an orthogonal projection between two types of estimates of AR process correlation vectors. Then, the correlation sequence of the MA noise is estimated. Secondly, the MA parameters are obtained by using inner–outer factorization. To study the relevance of the resulting method, we compare it with existing algorithms, and we analyze the identifiability limits. The identification approach is then combined with Kalman filtering for channel estimation in mobile communication systems.

In this paper, we propose to address the moving average (MA) parameters estimation issue based only on noisy observations and without any knowledge on the variance of the additive stationary white Gaussian measurement noise. For this purpose, the MA process is approximated by a high-order AR process and its parameters are estimated by using an errors-in-variables (EIV) approach, which also makes it possible to derive the variances of both the driving process and the additive white noise. The method is based on the Frisch scheme. One of the main difficulties in this case is to evaluate the minimal AR-process order that must be considered to have a 'good' approximation of the MA process. To this end, we propose a way based on K-means method. Simulation results of the proposed method are presented and compared to existing MA-parameter estimation approaches.

This paper deals with the identification of FIR models corrupted by white input noise and colored output noise. An identification algorithm that exploits the properties of both the dynamic Frisch scheme and the high-order Yule-Walker (HOYW) equations is proposed. It is shown how the HOYW equations allow to define a selection criterion for identifying the input noise variance (and then the FIR coefficients) within the Frisch locus of solutions. The proposed approach does not require any a priori knowledge about the input and output noise variances. The algorithm performance is assessed by means of Monte Carlo simulations.