A bias-compensated fractional order normalized least mean square algorithm with noisy inputs

作者：Yin, Weidi; Cheng, Songsong; Wei, Yiheng; Shuai, Jianmei^*; Wang, Yong

来源：Numerical Algorithms, 2019, 82(1): 201-222.

DOI：10.1007/s11075-018-0600-5

• Fractional order
• Noisy inputs
• BC-FONLMS
• Stability
• Convergence speed
• Steady-state error

This paper comes up with a stable bias-compensated fractional order normalized least mean square (BC-FONLMS) algorithm with noisy inputs. This kind of bias-compensated algorithm needs the estimation of input noise variance to avoid the bias caused by noisy inputs. Yet, existing algorithms either cause instability because of the method used to estimate input noise variance, or surmount the instability problems at the price of performance diminishment. This paper introduces fractional order calculus into LMS algorithm to be a new BC-FONLMS algorithm. Then, analyze the stability of the BC-FONLMS algorithm through probing the recursive equations of mean deviation (MD) and mean square deviation (MSD). On the basis of the stability analysis, methods to estimate input noise variance and to adjust step size are suggested to stabilize the algorithm and likewise to enhance the performance such as convergence speed and steady-state error. Numerical simulations are given at last, whose results show that the proposed BC-FONLMS algorithm performs well.

• 出版日期2019-9
• 单位中国科学技术大学