任意个数的多项式NARMAX的下界误差 自然区间扩张

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摘要翻译：
多项式NARMAX（具有外源输入的非线性自回归滑动平均模型）是一种表征物理系统动力学的模型。这个多项式包含了过去过程的输入和输出的信息，也就是说，它是一个递归模型。在数字计算机中，这会产生舍入误差的传播。我们的过程是基于估计下界误差的最大值，考虑任意数目的伪轨道由不同的自然区间扩张产生，并计算后验Lyapunov指数。我们成功地将我们的技术应用于两个系统的辨识模型：正弦映射和Duffing-Ueda振子
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英文标题：
《The Lower Bound Error for polynomial NARMAX using an Arbitrary Number of
  Natural Interval Extensions》
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作者：
Priscila F. S. Guedes, M. L. C. Peixoto, A. M. Barbosa, S. A. M.
  Martins, E. G. Nepomuceno
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最新提交年份：
2017
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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 polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is a model that represents the dynamics of physical systems. This polynomial contains information from the past of the inputs and outputs of the process, that is, it is a recursive model. In digital computers this generates the propagation of the rounding error. Our procedure is based on the estimation of the maximum value of the lower bound error considering an arbitrary number of pseudo-orbits produced from different natural interval extensions, and a posterior Lyapunov exponent calculation. We applied successfully our technique for two identified models of the systems: sine map and Duffing-Ueda oscillator
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PDF链接：
https://arxiv.org/pdf/1711.07594

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关键词：ARMAX ARMA RMA ARM 多项式 Error 辨识 数字 polynomial Ueda