RECURSIVE LEAST SQUARES ESTIMATION USING MULTIDIMENSIONAL FORGETTING

摘要

In case of non-sufficient excitation of a system, Recursive Least Squares (RLS) algorithms with exponential forgetting suffer from a so-called wind-up. Even adaptive forgetting factors do not prevent this effect reliably. Here a RLS algorithm with multidimensional forgetting is presented. The idea is based on an interpretation of the eigenvalues and eigenvectors of the covariance matrix. They provide cognition of cumulated past information along so-called information directions. The currently measured data can be projected onto the different information directions. The information is not distributed uniformly in parameter space, i.e. there are directions with more and with less informational content. A conventional forgetting factor will affect the level of information in every direction in the same manner. Thus the non-uniform distribution of information cannot be taken into account by such a forgetting factor. A multidimensional forgetting by using a forgetting matrix instead of a scalar factor, opens the possibility to manipulate each eigenvalue by itself. Thus you can modify each level of information and the step size of the algorithm in each direction independently due to the distribution of information. So a wind-up can be avoided securely without losing the algorithm's adaptivity.