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This paper deals with the identification of errors–in–variables models where the additive input and output noises are mutually correlated white processes. The proposed solution is based on the extension of the dynamic Frisch scheme introduced in (Beghelli et al., 1990). First, a geometric characterization of the whole set of admissible solutions in the noise space is described. Then, a criterion that allows to select the solution of the identification problem inside the locus is proposed. This criterion relies on the properties of a set of high–order Yule–Walker equations. The effectiveness of this identification approach is tested by means of Monte Carlo simulations.

This paper deals with the identification of multi–input multi–output errors–in–variables (EIV) models in the Frisch scheme context. The extension of the Frisch scheme to MIMO models introduces some problems not present in the SISO case. The approach proposed in this paper relies on the association of EIV models to directions in the noise space and on the statistical properties of the residual of the EIV model. In particular, a selection criterion based on the comparison of the theoretical statistical properties of the residual with those computed from the data is introduced. The performance of the proposed identification algorithm is evaluated by means of numerical simulations.

The extension of the Frisch scheme from the original algebraic case to the dynamic one leads to the use of errors–in–variables models where the measurements of the input and output are affected by additive white and independent noises. This problem admits a single solution when the assumptions of the scheme are exactly fulfilled but its application to real processes requires the introduction of specific model selection criteria. This paper analyzes the additional problems encountered in the extension of Frisch identification to the multivariable case and introduces a geometric approach for its solution.

This paper describes an identification procedure for minimally parametrized multivariable models in the Errors–in–Variables (EIV) context of the Frisch scheme that considers additive white observation noise on the process inputs and outputs. This procedure relies on the geometric approach described in (Guidorzi and Diversi, 2009) that associates EIV models to directions in the noise space. The proposed procedure has been tested by means of a Monte Carlo simulation that confirms its effectiveness.

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.

In this paper the problem of identifying a fuzzy model from noisy data is addressed. The piecewise-affine fuzzy model structure is used as non-linear prototype for a multi–input, single–output unknown system. The consequents of the fuzzy model are identified from noisy data which are collected from experiments on the real system. The identification procedure is formulated within the Frisch scheme, well established for linear systems, which is extended so that it applies to piecewise-affine, constrained models.

The fuzzy model identification problem from noisy data is addressed. The piecewise linear fuzzy model structure is used as a nonlinear prototype for a multi-input, single-output unknown system. The consequent of the fuzzy model is identified using noisy data, e.g. collected from experiments on a real system. The identification procedure is formulated within the Frisch scheme, well established for linear systems, which has been modified and improved to be applied in fuzzy systems field.

This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension of the Frisch scheme to the identification of dynamical systems is considered for both SISO and MIMO cases and the problem of its application to real processes is investigated. For this purpose suitable identification criteria and model parametrizations are described. Finally two classical identification problems are mapped into the Frisch scheme, the blind identification of FIR channels and the identification of AR + noise models. This allows some theoretical and practical extensions.