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Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

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 describes a new approach for identifying ARX models from a finite number of measurements, in presence of additive and uncorrelated white noise. The proposed algorithm is based on some theoretical results concerning the so–called dynamic Frisch Scheme. As a major novelty, the proposed approach deals with frequency domain data. In some aspects, the method resembles the characteristics of other identification algorithms, originally developed in the time domain. The proposed method is compared with other techniques by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain is highlighted by means of a numerical example.

This paper describes a new approach for identifying autoregressive models from a finite number of measurements, in presence of additive and uncorrelated white noise. As a major novelty, the proposed approach deals with frequency domain data. In particular, two different frequency domain algorithms are proposed. The first algorithm is based on some theoretical results concerning the so--called dynamic Frisch Scheme. The second algorithm maps the AR identification problem into a quadratic eigenvalue problem. Both methods resemble in many aspects some other identification algorithms, originally developed in the time domain. The features of the proposed methods are compared each other and with those of other time domain algorithms by means of Monte Carlo 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.

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.

Multivariable output-error identification does not constitute, in any way, a straightforward extension of the scalar case. The aim of this paper is twofold: 1) Introduction of a new minimal parametrization for multivariable output error models leading to an easily implementable prediction error identification procedure; 2) Comparison of PEM and errors-in-variables approaches based on the dynamic Frisch scheme in the identification of MIMO output error processes.

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.

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.