Identification of Physical Parameters and Instrumental Variables Validation With Two-Stage Least Squares Estimator

Abstract

This paper addresses physical parameters identification of mathematical models that are linear in relation to these physical parameters. We can obtain good results with the least squares technique, provided that a well-tuned data filtering is used, and by using instrumental variable (IV) methods, which deal with the problem of noisy observation matrix. However, IV theory is based on instruments validity. In econometrics, statistical tests evaluating instruments quality have been developed. They make use of the two-stage least squares estimator and the concentration parameter introduced by Basmann. In this paper we show how to extend econometric theory to control engineering. An algorithm evaluating instruments quality is presented and experimentally validated on a two-degrees-of-freedom SCARA robot.