一类基于分数阶梯度信息的变阶次扩散LMS算法  

A class of diffusion LMS algorithm with variable fractional order gradient

作　　者：杨洋[1] 莫立坡 左敏[2] 于永光 Yang YANG;Lipo MO;Min ZUO;Yongguang YU(School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China;School of Computer and Artificial Intelligence,Beijing Technology and Business University,Beijing 100048,China;School of Mathematics and Statistics,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京工商大学数学与统计学院,北京100048 [2]北京工商大学计算机与人工智能学院,北京100048 [3]北京交通大学数学与统计学院,北京100044

出　　处：《中国科学：信息科学》2024年第8期1907-1923,共17页Scientia Sinica(Informationis)

基　　金：北京市属高等学校高水平科研创新团队建设支持计划项目(批准号:BPHR20220104);国家自然科学基金(批准号:61973329)资助项目。

摘　　要：针对分布式网络中的参数估计问题,本文提出了一类基于分数阶梯度信息的扩散LMS算法,主要利用分数阶梯度的变阶次机制来提升算法的各项性能.首先,针对已有的集中式分数阶梯度LMS算法,将其推广到分布式网络中的参数估计问题上来.进而,讨论了所提算法的收敛速度和收敛精度.其次,考虑到分数阶阶次对于算法性能的影响,设计了一个变分数阶阶次的策略来充分发挥分数阶的优点以提升算法的收敛特性.进一步,证明了切换拓扑结构下所提算法的收敛性.最后,通过数值仿真结果,从收敛速度、收敛精度、鲁棒性等角度验证了所提算法的有效性和优越性.For the parameter estimation issues in distributed networks,this paper mainly proposes a class of diffusion least mean squares(LMS)algorithm.A variable mechanism of fractional gradient orders is introduced to enhance the performance of the proposed algorithm.First,we extend the centralized fractional gradient LMS algorithms to the parameter estimation problems in distributed networks and study the convergence speed and accuracy of the proposed algorithm.Second,considering the effect of fractional orders on algorithm performance,a strategy with variable fractional orders is introduced to enhance the convergence performance of the proposed algorithm by giving full play to the advantage of fractional orders.Besides,we also prove the convergence of the proposed algorithm under switched topologies.Finally,some numerical simulation results are provided to validate the effectiveness and superiority of the proposed algorithm from the aspects of convergence speed,accuracy,and robustness.

关 键 词：分布式估计 扩散式LMS算法 适应性滤波 切换拓扑 分数阶微积分 

分 类 号：O157.5[理学—数学]