System identification—A survey

The survey explains the least squares method and several of its variants which may solve the problem of correlated residuals, viz. repeated and generalized least squares, maximum likelihood method, instrumental variable method, tally principle.

Abstract

The field of identification and process-parameter estimation has developed rapidly during the past decade. In this survey paper the state-of-the-art/science is presented in a systematic way. Attention is paid to general properties and to classification of identification problems. Model structures are discussed; their choice hinges on the purpose of the identification and on the available a priori knowledge. For the identification of models that are linear in the parameters, the survey explains the least squares method and several of its variants which may solve the problem of correlated residuals, viz. repeated and generalized least squares, maximum likelihood method, instrumental variable method, tally principle. Recently the non-linear situation, the on-line and the real-time identification have witnessed extensive developments. These are also reported. There are 230 references listed, mostly to recent contributions. In appendices a resume is given of parameter estimation principles and a more detailed exposition of an example of least squares estimation.