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Papers by Umberto Soverini
This paper describes a new approach for identifying FIR mode ls from a finite number of measureme... more This paper describes a new approach for identifying FIR mode ls from a finite number of measurements, in the presence of additive and uncorrelated white noise. In particular, two different frequency domain algorithms are proposed. The first algorit hm is based on some theoretical results concerning the dynamic Frisch scheme. The second algorithm maps the FIR identification problem into a quadratic eigenvalue problem. Both methods resemble in many aspects some other identification algorithms, originally developed in the time domain. The fe atures of the proposed methods are compared with each other and with those of some time domain algorithms by means of Monte Carlo simulations.
Several estimation methods have been proposed for identify ing errors–in–variables systems, where... more Several estimation methods have been proposed for identify ing errors–in–variables systems, where both input and output measurements are corrupted by no ise. One of the more interesting approaches is the Frisch scheme. The method can be applied us ing either time or frequency domain representations. This paper investigates the general math e tical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differen ces between the time and frequency domain formulations.
IFAC-PapersOnLine
This paper describes a new approach for the blind identification of a two-channel FIR system from... more This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.
IFAC-PapersOnLine
Several estimation methods have been proposed for identifying errors-in-variables systems, where ... more 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.
IFAC-PapersOnLine
This paper describes a new approach for identifying the parameters of two-dimensional complex sin... more This paper describes a new approach for identifying the parameters of two-dimensional complex sinusoids from a finite number of measurements, in presence of additive and uncorrelated two-dimensional white noise. The proposed approach is based on using frequency domain data. As a major feature, it enables the estimation to be frequency selective. The new method extends to the two-dimensional (2D) case some recent results obtained with reference to the frequency ESPRIT algorithm. The properties of the proposed method are analyzed by means of Monte Carlo simulations and its features are compared with those of a classical time domain estimation algorithm. The practical advantages of the method are highlighted. In fact the novel approach can operate just on a specified sub-area of the 2D spectrum. This area-selective feature allows a drastic reduction of the computational complexity, which is usually very high when standard time domain methods are used.
Automatica
This report deals with the identification of errors-in-variables (EIV) models corrupted by additi... more This report deals with the identification of errors-in-variables (EIV) models corrupted by additive and uncorrelated white Gaussian noises when the noise-free input is an arbitrary signal, not required to be periodic. In particular, a frequency domain maximum likelihood (ML) estimator is proposed and analyzed in some detail. As some other EIV estimators, this method assumes that the ratio of the noise variances is known. The estimation problem is formulated in the frequency domain. It is shown that the parameter estimates are consistent. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived. The possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed, analyzed and illustrated.
2015 European Control Conference (ECC), 2015
The paper proposes a new frequency domain method for identifying linear dynamic errors-in-variabl... more The paper proposes a new frequency domain method for identifying linear dynamic errors-in-variables (EIV) models. The noise-free input is an arbitrary signal, not necessarily periodic and the input and output noises are additive and uncorrelated white processes. The method combines, in a frequency domain context, the characteristics of the Frisch scheme and the properties of the Yule-Walker equations. The features of the method are illustrated by means of numerical examples.
The paper proposes a new approach for identifying linear dynamic errors-in-variables (EIV) models... more 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.
Systems & Control Letters, 1992
ABSTRACT
Automatica, 2001
The problem of identifying linear static relations from noisy data is investigated under the assu... more The problem of identifying linear static relations from noisy data is investigated under the assumptions of the Frisch scheme. The work presents an attempt to simplify the search for solutions of the related rank reducibility problem. The proposed approach is based on a relaxation of the original problem by means of algebraic manipulations of the non-linear equations which characterize the
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014
ABSTRACT An important problem in sensor array processing is the estimation of the number of trans... more ABSTRACT An important problem in sensor array processing is the estimation of the number of transmitted signals. Most of the proposed solutions rely on the assumption of uniform additive white noise on the measured signals. In this paper, an approach for estimating the number of sources in the presence of nonuniform white noise is proposed. The method is based on the computation of the maximal corank of the covariance matrix of the noisy data in the Frisch scheme context. The effectiveness of the method is tested by means of Monte Carlo simulations.
Signal Processing, 2005
Blind identification is a very significant problem in many contexts where only the output of tran... more 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 also confirm the good performance of these procedures in severe SNR conditions. r
European Journal of Control, 2010
ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation ... more 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 since their optimal predictors are always stable. Similar considerations can be repeated for ARARX models where the equation error is described by an AR process instead of a white noise. The ARX and ARARX schemes can be enhanced by introducing the assumption of the presence of additive white noise on the input and output observations. These schemes, that will be denoted as ''ARX þ noise'' and ''ARARX þ noise'', can be seen as errors-in-variables models where both measurement errors and process disturbances are taken into account. This paper analyzes the problem of identifying ARX þ noise and ARARX þ noise models. The proposed identification algorithms are derived on the basis of the procedures developed for the solution of the dynamic Frisch scheme. The paper reports also Monte Carlo simulations that confirm the effectiveness of the proposed procedures.
System Structure and Control 1992, 1992
Proceedings of the 44th IEEE Conference on Decision and Control, 2005
This paper deals with the problem of identifying autoregressive models in presence of additive me... more This paper deals with the problem of identifying autoregressive models in presence of additive measurement noise. A new approach, based on some theoretical results concerning the so-called dynamic Frisch scheme, is proposed. This method takes advantage of both low and high order Yule-Walker equations and allows to identify the AR parameters and the driving and output noise variances in a congruent way since the estimates assure the positive definiteness of the autocorrelation matrix of the AR process. Simulation results are reported to show the effectiveness of the proposed procedure and compare its performance with those of other identification methods.
2008 3rd International Symposium on Communications, Control and Signal Processing, 2008
This paper proposes an efficient algorithm for identifying FIR models when also the input is assu... more This paper proposes an efficient algorithm for identifying FIR models when also the input is assumed as affected by additive noise. This procedure is more accurate than instrumental variables approaches and, differently from total least squares, does not require the a priori knowledge of the ratio between the input and output noise variances. The accuracy of the whole procedure has
Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology, 1989
This paper describes a new approach for identifying FIR mode ls from a finite number of measureme... more This paper describes a new approach for identifying FIR mode ls from a finite number of measurements, in the presence of additive and uncorrelated white noise. In particular, two different frequency domain algorithms are proposed. The first algorit hm is based on some theoretical results concerning the dynamic Frisch scheme. The second algorithm maps the FIR identification problem into a quadratic eigenvalue problem. Both methods resemble in many aspects some other identification algorithms, originally developed in the time domain. The fe atures of the proposed methods are compared with each other and with those of some time domain algorithms by means of Monte Carlo simulations.
Several estimation methods have been proposed for identify ing errors–in–variables systems, where... more Several estimation methods have been proposed for identify ing errors–in–variables systems, where both input and output measurements are corrupted by no ise. One of the more interesting approaches is the Frisch scheme. The method can be applied us ing either time or frequency domain representations. This paper investigates the general math e tical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differen ces between the time and frequency domain formulations.
IFAC-PapersOnLine
This paper describes a new approach for the blind identification of a two-channel FIR system from... more This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.
IFAC-PapersOnLine
Several estimation methods have been proposed for identifying errors-in-variables systems, where ... more 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.
IFAC-PapersOnLine
This paper describes a new approach for identifying the parameters of two-dimensional complex sin... more This paper describes a new approach for identifying the parameters of two-dimensional complex sinusoids from a finite number of measurements, in presence of additive and uncorrelated two-dimensional white noise. The proposed approach is based on using frequency domain data. As a major feature, it enables the estimation to be frequency selective. The new method extends to the two-dimensional (2D) case some recent results obtained with reference to the frequency ESPRIT algorithm. The properties of the proposed method are analyzed by means of Monte Carlo simulations and its features are compared with those of a classical time domain estimation algorithm. The practical advantages of the method are highlighted. In fact the novel approach can operate just on a specified sub-area of the 2D spectrum. This area-selective feature allows a drastic reduction of the computational complexity, which is usually very high when standard time domain methods are used.
Automatica
This report deals with the identification of errors-in-variables (EIV) models corrupted by additi... more This report deals with the identification of errors-in-variables (EIV) models corrupted by additive and uncorrelated white Gaussian noises when the noise-free input is an arbitrary signal, not required to be periodic. In particular, a frequency domain maximum likelihood (ML) estimator is proposed and analyzed in some detail. As some other EIV estimators, this method assumes that the ratio of the noise variances is known. The estimation problem is formulated in the frequency domain. It is shown that the parameter estimates are consistent. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived. The possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed, analyzed and illustrated.
2015 European Control Conference (ECC), 2015
The paper proposes a new frequency domain method for identifying linear dynamic errors-in-variabl... more The paper proposes a new frequency domain method for identifying linear dynamic errors-in-variables (EIV) models. The noise-free input is an arbitrary signal, not necessarily periodic and the input and output noises are additive and uncorrelated white processes. The method combines, in a frequency domain context, the characteristics of the Frisch scheme and the properties of the Yule-Walker equations. The features of the method are illustrated by means of numerical examples.
The paper proposes a new approach for identifying linear dynamic errors-in-variables (EIV) models... more 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.
Systems & Control Letters, 1992
ABSTRACT
Automatica, 2001
The problem of identifying linear static relations from noisy data is investigated under the assu... more The problem of identifying linear static relations from noisy data is investigated under the assumptions of the Frisch scheme. The work presents an attempt to simplify the search for solutions of the related rank reducibility problem. The proposed approach is based on a relaxation of the original problem by means of algebraic manipulations of the non-linear equations which characterize the
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014
ABSTRACT An important problem in sensor array processing is the estimation of the number of trans... more ABSTRACT An important problem in sensor array processing is the estimation of the number of transmitted signals. Most of the proposed solutions rely on the assumption of uniform additive white noise on the measured signals. In this paper, an approach for estimating the number of sources in the presence of nonuniform white noise is proposed. The method is based on the computation of the maximal corank of the covariance matrix of the noisy data in the Frisch scheme context. The effectiveness of the method is tested by means of Monte Carlo simulations.
Signal Processing, 2005
Blind identification is a very significant problem in many contexts where only the output of tran... more 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 also confirm the good performance of these procedures in severe SNR conditions. r
European Journal of Control, 2010
ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation ... more 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 since their optimal predictors are always stable. Similar considerations can be repeated for ARARX models where the equation error is described by an AR process instead of a white noise. The ARX and ARARX schemes can be enhanced by introducing the assumption of the presence of additive white noise on the input and output observations. These schemes, that will be denoted as ''ARX þ noise'' and ''ARARX þ noise'', can be seen as errors-in-variables models where both measurement errors and process disturbances are taken into account. This paper analyzes the problem of identifying ARX þ noise and ARARX þ noise models. The proposed identification algorithms are derived on the basis of the procedures developed for the solution of the dynamic Frisch scheme. The paper reports also Monte Carlo simulations that confirm the effectiveness of the proposed procedures.
System Structure and Control 1992, 1992
Proceedings of the 44th IEEE Conference on Decision and Control, 2005
This paper deals with the problem of identifying autoregressive models in presence of additive me... more This paper deals with the problem of identifying autoregressive models in presence of additive measurement noise. A new approach, based on some theoretical results concerning the so-called dynamic Frisch scheme, is proposed. This method takes advantage of both low and high order Yule-Walker equations and allows to identify the AR parameters and the driving and output noise variances in a congruent way since the estimates assure the positive definiteness of the autocorrelation matrix of the AR process. Simulation results are reported to show the effectiveness of the proposed procedure and compare its performance with those of other identification methods.
2008 3rd International Symposium on Communications, Control and Signal Processing, 2008
This paper proposes an efficient algorithm for identifying FIR models when also the input is assu... more This paper proposes an efficient algorithm for identifying FIR models when also the input is assumed as affected by additive noise. This procedure is more accurate than instrumental variables approaches and, differently from total least squares, does not require the a priori knowledge of the ratio between the input and output noise variances. The accuracy of the whole procedure has
Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology, 1989