Comparison of some instrumental variable methods-Consistency and accuracy aspects

  • Authors:

  • T. Söderström;P. Stoica

  • Affiliations:

  • Department of Automatic Control and Systems Analysis, Institute of Technology, Uppsala University, P.O. Box 534, S-751 21 Uppsala, Sweden;Facultatea de Automatica, Institutul Politehnic Bucuresti, Splaiul Independentei 313, Sector 7, R-77206 Bucharest, Romania

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1981

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Abstract

A general analysis of various instrumental variable methods is given. The investigation includes methods for open loop operation as well as methods designed for closed loop operation. The instrumental variables are formed as different combinations of inputs, delayed inputs, delayed outputs, filtered inputs and external setpoint variations. Necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed. The paper also includes some simple counter-examples to general consistency for some common instrumental variable methods. Also asymptotic accuracy properties are reviewed. It is e.g. studied how the use of filters will influence the covariance matrix of the parameter estimates.