Using uncertain prior knowledge to improve identified nonlinear dynamic models

This paper addresses the parameter-estimation problem for linear-in-the-parameter nonlinear models for the case in which uncertain prior knowledge is available in the form of noisy steady-state data. An uncertainty-weighted least-squares (UWLS) algorithm is developed which takes into account not only the dynamical and the steady-state data but also a measure of relative uncertainty of both data sets. Also, it is shown that a previously developed bi-objective optimization estimator is a special case of UWLS. A consequence of this is that UWLS can take advantage of tools developed in the context of multiobjective optimization to automatically determine an adequate relative uncertainty measure for dynamical and steady-state data sets. The developed algorithm and related ideas are investigated and illustrated by means of examples that use simulated and measured data.