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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.

The inversion of data to be represented by sums or continuous distributions of exponentials is done by different algorithms and compared. The published CONTIN program presents a chosen solution with an appropriate amount of detail. An in-house program EXDISTR allows operative choice of various constraints in order to show the consequences in quality of fit of allowing various features such as extra maxima or minima. Another in-house program based on the system theory approach, IDENT, treats the data as the output samples of a linear, time-invariant, autonomous dynamic system.

The paper deals with a new identification approach, based on a prediction error method, for multivariable errors-in-variables models (EIV). Starting from the ARMAX decomposition of MIMO EIV processes and congruence conditions between noisy sequences and the constraints of EIV representations, the simultaneous estimate of the model parameters and of the noise covariance matrices is obtained. Numerical simulations are included to illustrate the effectiveness of the proposed algorithm.

This paper presents an identification method for errors-in-variables systems with input-output measurements affected by white and mutually correlated noises. The procedure, based on a frequency-domain approach, allows to uniquely determine both the characteristics of the noises affecting the data and the transfer function of the process under investigation. A numerical example is reported in order to illustrate the suggested technique and to verify its numerical implementation.

The work presents some results concerning robust fault detection for dynamic processes using a disturbance decoupling technique. The first step of the approach consists of exploiting input-output descriptions of the monitored system. In particular, the disturbance term of a model can be used to take into account unknown inputs affecting the system. The next step of the scheme leads to definition of a set of parity relations that can be used as robust residual signals since they are insensitive to the disturbance term. The proposed fault detection procedure has been tested on an industrial process simulator. Sensor and actuator faults have been simulated on a gas turbine model.

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.

A common approach in modeling signals in many engineering applications consists in adopting autoregressive (AR) models, consisting in filters with transfer functions having a unitary numerator, driven by white noise. Despite their wide application, these models do not take into account the possible presence of errors on the observations and cannot prove accurate when these errors are significant. AR plus noise models constitute an extension of AR models that consider also the presence of an observation noise. This paper describes a new algorithm for the identification of AR plus noise models that is characterized by a very good compromise between accuracy and efficiency. This algorithm, taking advantage of both low and high-order Yule–Walker equations, also guarantees the positive definiteness of the autocorrelation matrix of the estimated process and allows to estimate the equation error and observation noise variances. It is also shown how the proposed procedure can be used for estimating the order of the AR model. The new algorithm is compared with some traditional algorithms by means of Monte Carlo simulations. Copyright © 2007 John Wiley & Sons, Ltd.

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.

In the framework of speech enhancement, several parametric approaches based on an a priori model for a speech signal have been proposed. When using an autoregressive (AR) model, three issues must be addressed. (1) How to deal with AR parameter estimation? Indeed, due to additive noise, the standard least squares criterion leads to biased estimates of AR parameters. (2) Can an estimation of the variance of the additive noise for each speech frame be obtained? A voice activity detector is often used for its estimation. (3) Which estimation rules and techniques (filtering, smoothing, etc.) can be considered to retrieve the speech signal? Our contribution in this paper is threefold. First, we propose to view the identification of the noisy AR process as an errors-in-variables problem. This blind method has the advantage of providing accurate estimations of both the AR parameters and the variance of the additive noise. Second, we propose an alternative algorithm to standard Kalman smoothing, based on a constrained minimum variance estimation procedure with a lower computational cost. Third, the combination of these two steps is investigated. It provides better results than some existing speech enhancement approaches in terms of signal-to-noise-ratio (SNR), segmental SNR, and informal subjective tests.

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 introduces an extended environment for Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal (minimal variance) estimation of noise-corrupted input and output sequences. This environment includes as subcases both errors-in-variables filtering (optimal estimate of inputs and outputs from noisy observations) and traditional Kalman filtering (optimal stimate of state and output in presence of state and output noise). A Monte Carlo simulation shows that the performance of this extended filtering technique leads to the expected minimal variance estimates.

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.

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.

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.

Questa breve raccolta di esercizi costituisce una rielaborazione di parte del materiale didattico che è stato utilizzato durante questi ultimi anni nell'insegnamento di Controllli Automatici per i corsi di Laurea in Ingegneria Gestionale e Meccanica dell'Università di Bologna.

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 been tested by means of Monte Carlo simulations and compared with that of compensated and total least squares ones.

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 describes the application of identification techniques in the design and optimization of a vertical navigation (VNAV) autopilot for a light sport aviation (LSA) high performance aircraft(Flight Design CT 2K). The whole design has been based, to reduce global costs, weight and complexity, on the control of the stabilator trim instead than, as is more common, on the direct control of the stabilator by means of a dedicated servo actuator. This solution, despite the abovementioned advantages, is characterized by some critical aspects due to the introduction of additional delays in the control chain and also to potential safety problems thatmust be carefully considered. The first design step has seen the construction of an accurate model concerning the aircraft response to the stabilator trim. This model has been obtained by means of identification techniques applied to data sequences collected in specific flights and has been validated by means of simulations performed on data sets concerning different flights. The model has then been used to design and optimize a PID controller whose performance has been tested first in simulation contexts and subsequently, after its implementation into the autopilot, in flight conditions. This design approach has allowed, on the one hand, a sensible reduction of inflight tests and of trial and error procedures and, on the other hand, to obtain a good final autopilot behavior confirmed by all inflight validation tests.

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. On the other hand the (implicit) assumption of noise-free inputs and of outputs affected by an additive colored noise whose spectrum is defined only by the model poles can be considered as non realistic when all measures are affected by additive errors. This paper considers the family of ARX + noise models that describe ARX processes whose measures are affected by additive white noise. The identification of these models is then mapped into the problem of identifying errors-in-variables models in the context of the Frisch scheme and a specific identification algorithm is described. A Monte Carlo simulation confirms the good results that can be obtained with the whole procedure.

Classical model-based fault detection schemes for linear multivariable systems require the definition of suitable residual functions. This paper shows the possibility of identifying residual generators even when the system model is unknown, by following a black-box approach. The result is obtained by using canonical input-output polynomial forms which lead to characterise in a straightforward fashion the basis of the subspace described by all possible residual generators. The performance of the proposed identification method is tested by means of Monte Carlo simulations.

Parametric approaches based on a priori models of the speech are often used in the framework of speech enhancement using a single microphone. When the speech is modeled by means of a stationary autoregressive (AR) process, a frame-by-frame approach is usually considered. However, it requires the unbiased estimations of the autoregressive parameters and of the noise variances for the subsequent implementation of a filter (Kalman, H-infinity, etc.). The purpose of this paper is twofold. Firstly, we propose to view the AR parameter estimation as an errors-in-variables issue. Secondly, we implement an optimal smoothing procedure based on a constrained minimum variance estimation of the signal. Then, we test the procedure based on both steps in the field of speech enhancement.

The problem considered in this paper is the design of a low cost MEMS based attitude estimation unit to be used in ultralight, experimental and sport pilot aircrafts as auxiliary safety tool in VFR flight conditions. The proposed approach relies on a new data fusion scheme based on a dual Kalman filter design and on acceleration-based switch criteria. Attitude information is extracted from the states of the filters under the restriction of non aerobatic uses that allows the introduction of a priori limits in roll and pitch angles.

A new method for identifying linear dynamic errors-in-variables (EIV) models, whose input and output are affected by additive white noise, is proposed. This approach takes advantage of the properties of both the dynamic Frisch scheme and Yule-Walker equations and allows to identify the system parameters and the noise variances in a congruent way since the estimates assure the positive definiteness of the autocorrelation matrix of the EIV process. The effectiveness of the method has been tested by means of Monte Carlo simulations and compared with those of other EIV identification methods. The proposed procedure is characterized by a good compromise between estimation accuracy and computational efficiency.

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.

In many practical situations the process data are affected by noise on both inputs and outputs. In these contexts, errors–in–variables (EIV) models can be the best choice for identification purposes and several approaches based on these representation are present in the literature. This work refers to one of these methods, the so–called dynamic Frisch scheme. In particular, two different Frisch scheme–based algorithms are analyzed and compared by means of Monte Carlo simulations.

This paper introduces a novel approach, noise signature, in fault detection and isolation, based on the use of errors–in–variables(EIV) models. Differently from more common stochastic environments, in these models all variables (inputs and outputs) are assumed as affected by additive and uncorrelated noise. The identification procedures developed for EIV models allow to estimate the covariance matrix of the noise that constitutes, in absence of faults, a signature for the system. In fact the variations in the estimated noise variances in presence of faults lead to effective ways to detect and isolate faults on both sensors and actuators.

In addition to measurement noise, echoes and reverberations may disturb speech recorded by a microphone. To describe the spatial transformation between the sources and the microphones, FIR filters are considered when modelling the system. Therefore, speech is contaminated by both convolutive and additive noises. In this paper, we propose to retrieve the speech signal from the noisy observations by using two microphones. This speech enhancement method operates in two steps. Firstly, the blind estimations of the FIRs are based on the non negative definiteness property of the autocorrelation matrix of the reverberated versions of speech. The estimation of the original speech is then viewed as an errors-in-variables interpolation issue. It should be noted that this method first deals with a white background noise and has the advantage of not using a voice activity detector (VAD), which is usually required to estimate the noise variances.

The Errors-in-Variables (EIV) stochastic environment constitutes a superset of most common stochastic environments considered, for instance, in Kalman filtering or in equation-error identification here the process input is assumed as noise-free. Errors-in-variables models assume, on the contrary, the presence of unknown additive noise also on the inputs; the associated filtering procedures concern thus the optimal (minimal variance) estimation not only of the system state and output but also of the input. Optimal EIV filtering has been formulated and solved only recently making reference to SISO models; this paper extends the efficient algorithm proposed recently by the authors, based on the Cholesky factorization, to the more general multivariable case.

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.