CONVERGENCE ANALYSIS OF THE RLS IDENTIFICATION ALGORITHM WITH EXPONENTIAL FORGETTING IN STATIONARY ARX-STRUCTURES

摘要

The recursive least-squares (RLS) identification algorithm is often extended with exponential fOrgetting as a tool for parameter estimation in time-varying stochastic systems. The statistical properties of the parameter estimates obtained from such an extended RLS-algorithm depend in a non-linear way on the time-varying characteristics and on the forgetting factor. In this paper, the RLS-estimator with exponential forgetting is applied to time-invariant Gaussian autoregressions with second-order stationary external inputs, i.e. to Gaussian ARX-processes. Approximate expressions for the asymptotic bias and covariance of the parameter estimates when the forgetting factor tends to one and time to infinity are given, showing that the bias is non-zero and that the covariance function decays exponentially with a rate that is given by the forgetting factor. The orders of magnitude of the errors in the asymptotic expressions are also derived. Copyright