Recursive Least Squares with Variable-Rate Forgetting Based on the F-Test

A variable-rate forgetting factor for recursive least squares is developed for parameter identification of time-varying systems. The variable-rate forgetting factor uses the F-test to compare short- and long-term variances of the one-step prediction errors of recursive least squares (RLS). If the short-term error variance is statistically larger than the long-term error variance, then it is assumed that the underlying parameters have changed and forgetting is required. The level of forgetting is proportional to how far the ratio of the short-term and long-term error variances deviate from the expected ratio given by the F-distribution. RLS with F-test variable-rate forgetting (RLS/FTVRF) is shown to generalize an existing variable-rate forgetting factor that uses a ratio of the root-mean-square (RMS) performance error and noise standard deviation. The approach is applied to a parameter identification task and is compared to a constant-rate forgetting factor and the RMS performance error and noise standard-deviation-based forgetting factor.