An efficient non-negative least mean squares algorithm based on q-gradient for system identification

Abstract

The system identification under non-negative constraints problem is a common and important one in the real-life problems. A non-negative least mean squares algorithm was proposed to address such problems. However, it suffers from slow and unbalanced convergence. Motivated by the introduction of non-Newtonian gradient in least mean squares algorithm can accelerate the convergence. In this paper, an efficient non-negative least mean squares algorithm based on q-gradient is developed. At first, the q-gradient of the mean square error cost function is derived from the definition of Jackson's derivative. Then, the modified algorithm is developed by replacing the conventional gradient with the q-gradient on a fixed-point iteration scheme using Karush-Kuhn-Tucker condition. Simulations for stationary and non-stationary system identification are conducted to illustrate the effectiveness of the developed algorithm for constrain the system parameters to be non-negative and accelerate the convergence speed. Besides, it can balance the convergence rate for widely distributed parameters, especially for the convergence of small parameters. For practical application, the accuracy of system identification when the order of the adaptive filter is larger than the order of the system is also verified by the simulation.