Recursive Least Squares with Matrix Forgetting

This paper considers an extension of recursive least squares (RLS), where the cost function is modified to include a matrix forgetting factor. Minimization of the modified cost function provides a framework for combined variable-rate and variable-direction (RLS-VRDF) forgetting. This extension of RLS simultaneously addresses two key issues in standard RLS, namely, the need for variable-rate forgetting due to changing plant parameters as well as the need for variable-direction covariance updating due to the loss of persistency. The performance of RSL-VRDF is illustrated by an example with abrupt parameter changes and loss of persistency.