A directional forgetting factor for single-parameter variations

Use of the recursive least-squares algorithm to track parameters that may undergo slow or sudden changes requires refinements to prevent excessive gain decay and the loss of the ability to re-identify parameters. A technique in wide-spread use developed by Fortescue, Kershenbaum and Ydstie (1981) involves variable weighting of past data based on the squared output error through a scalar forgetting factor that divides the covariance matrix. This can slow convergence when only a single parameter is changed because the forgetting factor affects all covariance elements equally. A modification is proposed that replaces the scalar forgetting factor by a diagonal forgetting matrix that contains directional information. This directional information is provided by the relative magnitude of the sum of errors squared for one-parameter estimates over a finite time window. Simulations with single parameter changes showed improved convergence; while multiple parameter variations showed, at worst, comparable performance to the unmodified algorithm