Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performan...Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performance and computational complexity analyses are carried out also.Furthermore,compared with existing SAF algorithms,the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets.Numerical results show that the SAF-Adagrad and SAFRMSProp algorithms have better convergence performance than some existing SAF algorithms(i.e.,SAF-SGD,SAF-ARC-MMSGD,and SAF-LHC-MNAG).The analysis results of various measured real datasets also verify this conclusion.Overall,the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.展开更多
Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic...Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.展开更多
基金supported by the National Natural Science Foundation of China(61871420)the Natural Science Foundation of Sichuan Province,China(23NSFSC2916)the introduction of talent,Southwest MinZu University,China,funding research projects start(RQD2021064).
文摘Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performance and computational complexity analyses are carried out also.Furthermore,compared with existing SAF algorithms,the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets.Numerical results show that the SAF-Adagrad and SAFRMSProp algorithms have better convergence performance than some existing SAF algorithms(i.e.,SAF-SGD,SAF-ARC-MMSGD,and SAF-LHC-MNAG).The analysis results of various measured real datasets also verify this conclusion.Overall,the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.
基金Supported by the National Natural Science Foundation of China(60933008,61272300 and 11226327)the Science&Technology Program of Shanghai Maritime University(20120099)
文摘Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.
