A novel modified fractional order LMS algorithm

This article contributes a novel modified fractional order LMS (MFOLMS) algorithm with a variable gradient order scale. With the aid of fractional order calculus, a modified fractional order gradient descent (FOGD) method is first proposed. Hence, a MFOLMS algorithm is developed, which significantly improves the estimation accuracy of the existing approaches while slightly sacrifices the convergence speed. A MFOLMS algorithm with variable gradient order is further developed as an alternative approach, which has higher initial convergence speed and lower steady estimation error than the one with fixed gradient order. Finally, simulation results from two numerical examples are provided to demonstrate the performances and advantages of our approaches.