Robust real-time algorithms for identification of linear multivariable time-varying systems

The paper presents a discussion on the problem of the robust real-time identification of linear multivariable time-varying dynamic systems working in a noisy environment. Two methodologically different approaches to the design of such algorithms are presented. The first is based on the one-step estimation, optimal in the sense of the minimal conditional mean-square error, combined with convenient approximations of the underlying error covariance matrix. The second is based on the general formulation of robustified stochastic approximation algorithms, characterized by a suitable non-linear transformation of normalized residuals. Particular algorithms are derived on the basis of step-by-step optimization with respect to the weighting matrix of the algorithm. Monte Carlo simulation results illustrate the discussion, and show the efficiency of the proposed robust algorithms in the presence of large disturbance realizations, the so-called outliers.