Licentiate thesis 2002-005

Identification of Dynamic Errors-in-Variables Models

Kaushik Mahata

May 2002

The problem of identifying dynamic errors-in-variables models is of fundamental interest in many areas like process control, array signal processing, astronomical data reduction. In recent years, this field has received increased attention of the research community. In this thesis, some time domain and frequency domain approaches for identifying the errors-in-variables model is studied. The first chapter gives an overview of various methods for identifying dynamic errors-in-variables systems. Several approaches are classified and a qualitative comparison of different existing methods is also presented. The second chapter deals with instrumental variables based approaches. The least squares and the total least squares methods of solving the Yule-Walker equation is of central interest here. The methods are compared from the view point of asymptotic performance, numerical robustness and computation. The method presented in the third chapter uses prefiltered data. The input-output data is passed through a pair of user defined prefilters and the output data from the prefilters is subjected to a least-squares like algorithm. Compared to the IV approach, the proposed method shows a significant improvement in the small-sample properties of the MA parameter estimates, without any increase in the computational load. In the fourth chapter, we show that the two-dimensional process composed of the input-output data admits a finite order ARMA representation. Then we propose a parametric identification algorithm and another non-parametric identification method based on the ARMA representation.

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