Variable step-size non-negative normalised least-mean-square-type algorithm

This paper proposes a fast and precise adaptive filtering algorithm for online estimation under a non-negativity constraint. A novel variable step-size (VSS) non-negative normalised least-mean-square (NLMS)-type algorithm based on the mean-square deviation (MSD) analysis with a non-negativity constraint is derived. The NLMS-type algorithm under the non-negativity constraint is derived by using the gradient descent of the given cost function and the fixed-point iteration method. Furthermore, the VSS derived by minimising the MSD yields improvement of the filter performance in the aspects of the convergence rate and the steady-state estimation error. Simulation results show that the proposed algorithm outperforms existing algorithms.