Numerically stable algorithm for identification of linear dynamical systems by extended instrumental variables

Abstract

Instrumental variables are widely used to identify linear dynamical systems. The advantages of instrumental variables include low computational complexity, as well as the possibility of identification for different models of color noise. Often the method of instrumental variables leads to ill-conditioned problems, which significantly limits the application of this method. The paper proposes a solution to the problem of extended instrumental variables based on augmented normal equations. Test examples showed a high accuracy of the proposed approach.