Solving nonlinear estimation problems using splines [Lecture Notes]

Dong Yu; Li Deng

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Solving nonlinear estimation problems using splines [Lecture Notes]

机译：使用样条曲线解决非线性估计问题[讲义]

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We describe the use of splines for solving nonlinear model estimation problems, in which nonlinear functions with unknown shapes and values are involved, by converting the nonlinear estimation problems into linear ones at a higher- dimensional space. This contrasts with the typical use of the splines for function interpolation where the functional values at some input points are given and the values corresponding to other input points are sought for via interpolation. The technique described in this column applies to arbitrary nonlinear estimation problems where one or more one-dimensional nonlinear functions are involved and can be extended to cases where higher-dimensional nonlinear functions are used.

机译：我们描述了样条线用于解决非线性模型估计问题的方法，其中涉及将形状和值未知的非线性函数转换为高维空间中的非线性估计问题。这与样条线在函数插值中的典型用法形成对比，在样条函数中，某些输入点处的功能值已给出，而其他输入点所对应的值则通过插值来寻找。本专栏中介绍的技术适用于涉及一个或多个一维非线性函数的任意非线性估计问题，并且可以扩展到使用高维非线性函数的情况。

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来源
《Signal Processing Magazine, IEEE》 |2009年第4期|p.86-90|共5页
作者
Dong Yu; Li Deng;
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作者单位

Microsoft Speech Res. Group, Redmond, WA, USA;

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原文格式 PDF
正文语种 eng
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关键词
interpolation; nonlinear functions; splines (mathematics); 1D nonlinear function; function interpolation; high-dimensional space; higher-dimensional nonlinear function; nonlinear estimation problem; nonlinear model estimation; splines; unknown shapes;

机译：插值非线性函数样条（数学）一维非线性函数函数插值高维空间高维非线性函数非线性估计问题非线性模型估计样条未知形状;

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Solving nonlinear estimation problems using splines [Lecture Notes]

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