A recursive algorithm based on non-linear functions of the error

In this work, we propose an adaptive filter based on a non linear function, namely Recursive Non Linear (RNL) algorithm, which is inspired in the Recursive Lest Square (RLS) algorithm. We derive equations based on a nonlinear function in order to obtain criterions that guarantee convergence. We also make a study about the covariance of the weight vector on steady state and determine equations that measure the misadjustment and the convergence time of the adaptive process of the RNL algorithm. Simulations of this algorithm are performed to validate the theory and we study the convergence behavior of the RNL algorithm. The results showed that the RNL had faster convergence for the smaller misadjustment when compared to RLS algorithm.