A robust recursive least squares algorithm

It is shown that, for both the LMS (least mean square) and the RLS (recursive least squares) algorithms, the normalized bias introduced due to perturbation may not remain bounded, implying possible divergence. An algorithm is developed for which the normalized bias due to such perturbation in the data remains bounded. Robustness analysis and mean squared error analysis are also presented for this algorithm. There is a small price to be paid for incorporating robustness, namely a small degradation in the MSE (mean squared error) performance. Simulation shows that, when operating on good data, the MSE for the robust RLS (RRLS) is greater than that for the RLS algorithm. Nevertheless, as the data perturbation increases, the RRLS performs better.<>