Analysis of robust recursive least squares: Convergence and tracking

•This study proposes a robust method for recursive least squares.•Convergence and performance are analyzed in both the stationary and non-stationary environments.•Maximum correntropy criterion (MCC) is designed for loss function optimization problem.•A half-quadratic method is used to successively convert complex correntropy based objective to a simple quadratic for establishing convergence and performance.•A robust adaptive filter is designed when the desired signal is contaminated with non-Gaussian noises. Outliers and impulsive noise are inevitable factors in recursive least squares (RLS). Developing robust RLS is vital in practical applications such as system identification in which outliers in the desired signals may severely divert the solutions. Almost all suggested robust RLS schemes have been designed for the impulsive noise and Gaussian environments. Recently, employing the Maximum Correntropy Criterion (MCC), the RGMCC (Recursive General MCC) algorithm has been given which yields more exact results for system identification problem in non-Gaussian environments. Here, we develop a new Robust RLS (R2LS) scheme based on the MCC. In contrast to RGMCC, the structure of our model, although being complex, makes it possible to conduct convergence and performance analysis in both the stationary and non-stationary environments. Especially, the model is capable to reasonably predict and track the signals when the original signal is contaminated by non-Gaussian noise. To establish convergence and performance, we apply a half-quadratic optimization algorithm in the multiplicative form to successively convert our model to a quadratic problem which can be effectively solved by the classical tools. Numerical experiments are done on real and synthetic datasets; they show that the proposed algorithm outperforms the conventional RLS as well as some of its recent extensions.