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Standard identification methods give biased parameter estimates when recorded signals are corrupted by noise on both input and output sides. In previous papers it has been shown that the bias is significant in case the system is almost non-identifiable. This situation is investigated here for some general model structures.

Standard identification methods give biased parameter estimates when the recorded signals are corrupted by noise on both input and output sides. When the system is close to be non-identifiable, the bias can be large. The paper discusses the possibilities and potential benefits when using either a reduced model structure or a full errors-in-variables model. The case of using an instrumental variable estimator is also treated.

Prediction error (PE) and maximum likelihood (ML) methods are often treated as synonyms when identifying linear dynamic systems from Gaussian data. It is shown how these methods differ when specifically dealing with errors-in-variables problems. These problems can modeled using multivariable times series with a specific internal structure. In such situations the ML estimates have lower variances than the PE estimates. Explicit expressions for the covariance matrices of the estimates are given and analyzed. For the special case when the unperturbed input is white noise it is shown that the PE estimate is not identifiable, while the ML estimates still have quite small variances. Another special case concerns non-Gaussian data. In that case a pseudo-ML estimate (using the ML criterion as if the data were Gaussian) will no longer be superior to the PE estimate in terms of error variances.

When recorded signals are corrupted by noise on both input and output sides, standard identification methods give biased parameter estimates, due to the presence of input noise. This paper discusses in what situations such a bias is large and, consequently, when errors-in-variables identification methods should preferably be used.

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.

This paper describes a new approach for identifying FIR models 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 algorithm 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 features 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 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.

Recently, maximum likelihood estimators were derived for frequency domain identification of linear time-invariant models with Gaussian input output uncertainty. This note draws attention to an issue that arises in one of the steps in the optimization of the likelihood function.