Robust parameter tracking through regional forgetting

The recursive least squares (RLS) algorithm with exponential forgetting (λRLS) is perhaps the best known and most widely used algorithm for tracking the time varying parameters of a linear regression model. The implicit assumption in using the λRLS algorithm is that the information is uniformly distributed over the time horizon. Frequently this assumption does not hold and serious difficulties can be encountered when using many model structures. These include convergence of the parameters to local system or noise characteristics and output bursting, i.e. a large error when the operating point changes. In this paper several simple alternatives to the standard λRLS algorithm are proposed. The proposed algorithms extend the idea of a sliding window by quantising the whole input space. These algorithms considerably reduce the risk of forgetting useful information and eliminate the possibility of output bursting by relating the adaptation capabilities of the algorithm to the amount of input stimulation. Simulation results confirm the efficacy of our approach