摘要翻译：
Volterra级数是建模各种非线性动态系统的有力工具。然而，由于其非参数性质，随着存储长度和序列阶数的增加，序列中的参数数目迅速增加，由此产生的模型估计的不确定性也随之增加。本文提出了一种辨识方法，通过正交基函数展开间接估计Volterra核，并将正则化直接应用于展开系数，以减小最终模型估计中的方差，并在以前不可行的级数阶上提供有用模型的访问。高维核展开用一种允许平滑和衰减强加于整个超曲面的方法进行正则化。数值算例证明了利用正则基函数方法改进的Volterra级数估计可达4阶。
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英文标题：
《Volterra Kernel Identification using Regularized Orthonormal Basis
  Functions》
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作者：
Jeremy G. Stoddard and James S. Welsh
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  The Volterra series is a powerful tool in modelling a broad range of nonlinear dynamic systems. However, due to its nonparametric nature, the number of parameters in the series increases rapidly with memory length and series order, with the uncertainty in resulting model estimates increasing accordingly. In this paper, we propose an identification method where the Volterra kernels are estimated indirectly through orthonormal basis function expansions, with regularization applied directly to the expansion coefficients to reduce variance in the final model estimate and provide access to useful models at previously unfeasible series orders. The higher dimensional kernel expansions are regularized using a method that allows smoothness and decay to be imposed on the entire hyper-surface. Numerical examples demonstrate improved Volterra series estimation up to the 4th order using the regularized basis function method.
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PDF链接：
https://arxiv.org/pdf/1804.07429