A new look at the statistical identification of nonstationary systems

Abstract

The paper presents a new, two-stage approach to identification of linear time-varying stochastic systems, based on the concepts of preestimation and postfiltering. The proposed preestimated parameter trajectories are unbiased but have large variability. Hence, to obtain reliable estimates of system parameters, the preestimated trajectories must be further filtered (postfiltered). It is shown how one can design and optimize such postfilters using the basis function framework. The proposed solution to adaptive tuning of postfilter settings is based on parallel estimation and cross-validatory analysis. When compared with the classical solutions to the problem of parameter tracking, the new approach offers, without compromising good tracking performance, significant computational savings, higher numerical robustness and greater flexibility.