Mathematical Sciences: Curve Estimation in Motion Analysis

该项目涉及到一个过程的扩展， 工作中，非参数平滑和自助 应用于生物力学中的几个真实的工作问题， 机器人 动机和许多未来的应用 来自步态分析，即研究自由速度的人 在水平面上行走。 我们利用一个模型，其主要方面 是标量或矢量函数，其描述 “主体”。 在拟合来自学习样本的数据之后， 应用自举，预测区域的曲线， 计算随后“测试对象”。 预测区域 都需要从数值和理论上进行研究。 其他方面 涉及到通过内核方法的方法，使用 数据来选择基础和模型，以及 预测区域。 我们还将研究多变量问题， 规定的类型，因为他们适用于机器人和数字 控制铣床。

This project is concerned with the expansion of a course of work in which nonparameteric smoothing and the bootstrap are applied to several real work problems in biomechanics and robotics. The motivation and many of the future applications come from gait analysis, ie, the study of free-speed human walking on a level surface. We utilize a model whose main aspect is a scalar or vectorial function that describes motion of a "subject". After fitting data from a learning sample, and applying the bootstrap, prediction regions for the curves of a subsequent "test subject" are computed. The prediction regions are to be studied numerically and theoretically. Other aspects of the project involve approaches through kernel methods, using data to pick bases and models, and conditional versions of the prediction regions. We also will study multivariate problems of the prescribed type as they apply to robots and numerically controlled milling machines.