标题： 基于切换微分方程的非线性动力学在线鉴别 显示英文标题

标题： Online Discrimination of Nonlinear Dynamics with Switching Differential Equations

摘要： 如何识别观察到的人是行走还是跑步？ 我们考虑一个动态环境，其中观察结果（例如人的姿势）是由不同的动态过程（行走或跑步）引起的，这些过程一次只起作用，并且可能在任何时候从一个过渡到另一个。 对于这种设置，之前已经提出了切换动态模型，主要是针对离散时间中的线性和非线性动力学。 受大脑计算基本原理（动态、内部模型）的启发，我们提出了一种用于切换非线性微分方程的模型。 该模型中的切换过程由一个Hopfield网络实现，并我们使用参数化动态运动基元来表示任意的周期性运动。 该模型通过切换变量加权的基元进行线性插值来生成观察到的动力学，并且其构造使得可以应用标准的滤波算法。 在两个实验中，包括合成平面运动和人体运动捕捉数据集，我们展示了使用无迹卡尔曼滤波器进行推理可以成功地在线区分多个动态过程。 显示英文摘要

摘要： How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online.