Optimal smoothing in the identification of linear time-varying systems

Several recursive methods are available for the estimation of linear time-varying process models from sampled input/output records. During convergence from poor initial estimates, they give no clear picture of the time variation. A remedy is to base the estimate at every point in time on the whole record, by use of optimal smoothing techniques originally developed for state estimation. Optimal smoothing algorithms are reviewed and their computational requirements and stability in an identification context are examined. The most attractive are tested on synthetic records and on hydrological records. It is concluded that they are feasible and effective. Examples are given of features revealed by optimal smoothing, but not by the usual identification techniques.