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Blind identification is a significant problem in many communication systems. A new approach to blind estimation and input deconvolution is developed in this paper. By using the structural shift properties of the generalized Sylvester matrix of the system, an estimate of the covariance matrix of the unknown source is obtained and a suitable identification criterion for the estimation of the channel coefficients is introduced. A reconstruction of the input sequence is then obtained by means of a standard LS equalizer.

Identification procedures, while based on abstract (mathematical) concepts and procedures, must be applied to processes belonging to the real world. This faces teachers with the challenge of transmitting to their students adequate theories and of guiding their practice in identifying processes not belonging to any considered class of models. This requires, from an educational point of view, the use of suitable environments endowed with a proper mix of theoretical tools and of practical application opportunities. This paper describes an experience in delivering an identification course through the Internet and the results that have been obtained so far.

The Frisch scheme for identification of mathematical models from data corrupted by additive noise contains many unsolved aspects. One of the principal problems, of particular interest for factor analysis and structural regression methodologies, concerns rank reducibility of a covariance matrix simply by changing its diagonal entries. With reference to this topic, the paper shows that the mathematical models compatible with the data are the solutions of a set of polynomial equations which satisfy some well-defined constraints. The approach is based on the rank reducibility criteria suggested in a well-known paper by Ledermann, generalized to take into account the definiteness conditions on the noise-free covariance matrix. The results obtained give a deeper insight on the theoretical properties of the Frisch scheme and can represent a starting point for the design of numerical algorithms to solve the problem.

This paper deals with the identifiability of scalar dynamic errors-in-variables models characterized by rational spectra. The hypothesis of causality for the underlying dynamic system is taken into account. By making use of stochastic realization theory and of the structural properties of state-space representations, it is shown that, under mild assumptions, the model is uniquely identified.

This paper investigates some of the many algebraic properties of the solution of the Frisch identification scheme applied to dynamic systems. These properties are related to the design of a robust selection criterion leading to a single model also when the assumptions of the scheme are not fulfilled.

In this paper consideration is given to the problem of determining an optimal estimate of the output of a linear dynamic SISO system from the knowledge of the input-output data corrupted by additive noise. The solution of this problem can be divided into two steps: first. the model of the system and of the noise affecting the data is identified. then a Kalman filter is designed on the basis of this model. Since the result of the identification scheme may be a whole family of models. a comparison between these different systems is analyzed with refcrence to the behavior of the associated Kalman filters. Some silmulation results are finally discussed.

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.

ARMAX models are widely used in identification and are a standard tool in control engineering for both system description and control design. These models, however, can be non realistic in many practical contexts because of the presence of measurement errors that play an important role in applications like fault diagnosis and optimal filtering. ARMAX models can be enhanced by introducing also additive error terms on the input and output observations. This scheme, that can be denoted as “ARMAX + noise”, belongs to the errors–in–variables family and allows taking into account the presence of both process disturbances and measurement noise. This paper proposes a three-step procedure for identifying “ARMAX + noise” processes. The first step of the identification algorithm in based on an iterative search procedure while the second and third ones rely on simple least–squares formulas. The paper reports also the results of some Monte Carlo simulations that underline the effectiveness of the proposed approach.

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.

The identification of dynamic processes can be performed by means of different classes of models relying on different stochastic environments to describe the misfit between the model and process observations. This paper introduces a new class of models by considering additive error terms on the observations of the input and output of ARARX models and proposes a three–step identification procedure for their identification. ARARX + noise models extend the traditional ARARX or ARMAX ones and can be seen as errors–in–variables models where both measurement errors and process disturbances are taken into account. The results of Monte Carlo simulations show the good performance of the proposed identification procedure.

The errors–in–variables framework concerns static or dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors–in–variables models. One of the more promising approaches is the so–called Frisch scheme. This paper decribes three different estimation criteria within the Frisch context and compares their estimation accuracy on the basis of the asymptotic covariance matrices of the estimates. Some numerical examples support well the theoretical results.

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.

Blind identification is a very significant problem in many contexts where only the output of transmission channels can be observed. The solutions that can be found in the literature are limited to the case of equal amounts of additive noise on the observations; this paper proposes new identification procedures that can be applied to the case of two FIR channels affected by unknown and unbalanced amounts of additive noise. The identified models are then used for the minimal variance deconvolution of the unknown input signal. Several Monte Carlo simulations confirm the good performance of these procedures also in severe SNR conditions.