A New State-Regularized QRRLS Algorithm With a Variable Forgetting Factor

This brief proposes a new state-regularized (SR) and QR-decomposition-based (QRD) recursive least squares (RLS) adaptive filtering algorithm with a variable forgetting factor (VFF). It employs the estimated coefficients as prior information to minimize the exponentially weighted observation error, which leads to reduced variance over a conventional RLS algorithm and reduced bias over an L
₂
-regularized RLS algorithm. To improve the tracking performance, a new measure of convergence status is introduced in controlling the forgetting factor. Consequently, the resultant SR-VFF-RLS algorithm stabilizes the update and adaptively selects the number of measurements by means of the VFF. Improved tracking performance, steady-state mean-square error, and robustness to power-varying inputs over conventional RLS algorithms can be achieved. Furthermore, the proposed algorithm can be implemented using QRD, which leads to a lower roundoff error and more efficient hardware realization than the direct implementation. The effectiveness of the proposed algorithm is demonstrated by computer simulations.