A New Criterion in EIV Identification and Filtering Applications

IFAC Proceedings Volumes

Soverini

et al. 2008

Self Cite

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-invariables models. One of the more promising approaches is the so-called Frisch scheme. This report 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 final numerical examples support the theoretical results and analyze the behaviour of the methods in case of finite number of data.

“…It was developed to identify dynamic EIV systems in [3] and was further elaborated in [2,4,5,6]. Consider the relation…”

Section: Three Variants Of the Frisch Schemementioning

confidence: 99%

“…• The second alternative is to compute residuals and compare their statistical properties with what can be predicted from the model, proposed in [4].…”

Section: Three Variants Of the Frisch Schemementioning

confidence: 99%

“…For the Frisch-SR, we choose the extended vector as ϕ(t) = −y(t − n a − 1). In Frisch-CM, the lag m equals 5 and the weighting matrix Γ is taken as in [4] and [12]:…”

Section: Numerical Comparison Of the Asymptotic Covariance Matrices Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of three Frisch methods for errors-in-variables identification

Mei

IFAC Proceedings Volumes

Soverini

et al. 2008

Self Cite

“…It has its roots in [3], where a regression problem was treated. It has been proposed for identifying dynamic systems in [1] and was further elaborated in [2]. So far, theoretical analysis has been limited to consistency.…”

Section: Introductionmentioning

confidence: 99%

Accuracy Analysis of the Frisch Scheme for Identifying Errors-in-Variables Systems

IEEE Trans. Automat. Contr.

2007

Several estimation methods have been proposed for identifying errors-invariables systems, where both input and output measurements are corrupted by noise. One of the promising approaches is the so called Frisch scheme. This paper provides an accuracy analysis of the Frisch scheme applied to system identification. The estimates of the system parameters and the noise variances are shown to be asymptotically Gaussian distributed. An explicit expression for the covariance matrix of the asymptotic distribution is given as well. Numerical simulations support the theoretical results. A comparison with the Cramer-Rao lower bound is also given in examples, and it is shown that the Frisch scheme gives a performance close to the Cramer-Rao bound for large signal-to-noise ratios.

Approximative weighting for a covariance-matching approach for identifying errors-in-variables systems

Mossberg

Int. J. Adapt. Control Signal Process.

2010

A covariance-matching approach for identifying errors-in-variables systems has previously been proposed and analyzed. It has been demonstrated that the gain in accuracy can be substantial if an optimal weighting is used. The computation of the optimal weighting requires knowledge of true parameters of signals and systems. This paper describes how the optimal weighting can be computed approximately from the available noisy data and thereby offers a way to identify errors-in-variables systems with high accuracy. Numerical examples indicate that using this approximately optimal weighting gives an accuracy that is close to the accuracy obtained by using the optimal weighting.