MODIFIED REGULARIZATION IN SYSTEM STATE ESTIMATION AND PARAMETER IDENTIFICATION FOR STATE SPACE MODELS

摘要

Regularization as standard procedure dealing with ill-posed problems has gained acceptance in system identification. State estimation problem for given model with disturbances and noise is considered at first. Simple relation between regulariza-tion coefficient and the rough properties of the perturbations in system is obtained. As a result the simple-to-tune filter can be constructed on the base of derived equations. The introduced approach was then developed to the case of state and parameter joint estimation including system identification and to more complicated case of model structure selection. Using more sophisticated regularization for the overparametrized model the approximate solution with minimal norm on the observation interval can be found for the extended estimation problem. Numerical experiments were held to illustrate the filter's and criterion's properties.