Stable solutions of linear dynamic models
Agnar Höskuldsson · Journal of Chemometrics · 2000
Here we present a new approach to analyse dynamic models. It is based on the H-principle of mathematical modelling. The key issue is to identify the covariance matrices involved and solve the set of equations by steps, where at each step we optimize the selection of the covariance. The advantage of the procedure is that updating of model estimates in linear least squares, biased estimation and Kalman filtering can be achieved in a stable and secure manner. It implies that e.g. Kalman filtering can be carried out for hundreds or thousands of variables. The solution obtained at each time step provides the optimal balance between the prediction and the estimation aspect of the model. The developed procedures have several advantages over traditional methods: we do not have initial conditions that are difficult to estimate; it is easy to find influential variables; and it is easy to carry out sensitivity tests and others. Copyright © 2000 John Wiley & Sons, Ltd.