Change Detection in Nonlinear Systems and Applications in Shape Analysis

ECCS-0725849 Vaswani变化检测在大多数跟踪应用中很重要，因为系统模型很少是真正的时不变的。一些示例包括在目标跟踪或定位应用中检测运动模型变化;或者在计算机视觉/生物医学图像分析应用中检测异常形状变化。在上述所有情况下，状态都不是直接观察到的。观测值是状态的噪声和非线性函数。粒子滤波器对于这种非线性/非高斯跟踪问题的有效性已经是众所周知的。通常，改变的系统模型是未知的，即改变或异常没有被表征。例如，对于恒定速度目标缓慢地加速到较高速度，变化可以是逐渐的变化，或者是突然的变化。该方法是基于粒子滤波算法的"慢”和？突然？，未知参数，变化检测。稳健的设计策略将开发和测试现实的应用程序。智力优点：大多数现有的方法可以被归类为基于自适应滤波的想法或基于丢失的跟踪检测。自适应滤波方法要么是昂贵的，要么是不可靠的实现。基于失轨的方法几乎可以立即检测到突变。然而，缓慢的变化，这导致每单位时间的少量丢失，通常需要很长时间才能被检测到，或者有时会被错过。我们提出了一种新的方法，利用这一事实，缓慢的变化得到部分跟踪，并使用这"跟踪的一部分变化”的检测使用粒子滤波器。更广泛的影响：开发的算法将影响大量的定位，导航或国防应用，需要目标跟踪;视频监控应用，需要异常行为检测;生物医学信号/图像序列分析应用，其中检测到的异常可以是疾病的指标，以及计量经济学，金融，机器人和视觉中的许多其他应用。教育举措将包括引入自适应滤波和蒙特卡罗方法的研究生课程;修改现有的本科课程;和高级设计项目，以实现和比较各种应用程序的不同形状提取技术。

ECCS-0725849VaswaniChange detection is important in most tracking applications, since it is rarely true that the system model is truly time-invariant. Some examples include detecting motion model changes in target tracking or positioning applications; or detecting abnormal shape changes in computer vision/biomedical image analysis applications. In all of the above, the state is not directly observed. The observation is a noise-corrupted and nonlinear function of the state. The effectiveness of particle filters for such nonlinear/non-Gaussian tracking problems is already well known. Often, the changed system model is not known, i.e. the change or abnormality is not characterized. For example, the change may be a gradual one, for a constant velocity target slowly accelerating to a higher speed, or a sudden one. The approach is based on particle filter based algorithms for ``slow" and ?sudden?, unknown parameter, change detection. Robust design strategies will be developed and tested for realistic applications.Intellectual Merit: Most existing approaches can be classified as either based on adaptive filtering ideas or based on loss-of-track detection. Adaptive filtering approaches are either expensive or unreliable to implement. Loss-of-track based approaches detect abrupt changes almost immediately. However, slow changes, which result in a small loss of track per unit time, usually take a long time to get detected, or sometimes get missed. We propose a novel approach that utilizes the fact that slow changes get partially tracked, and uses this ``tracked part of the change" for detection using particle filters.Broader Impact: The developed algorithms will impact a large number of positioning, navigation or defense applications that require target tracking; video based surveillance applications that require abnormal behavior detection; biomedical signal/image sequence analysis applications where detected abnormalities can be indicators of disease, as well as many other applications in econometrics, finance, robotics and vision. Educational initiatives will include introduction of a graduate class on Adaptive filtering and Monte Carlo methods; modification of existing undergraduate classes; and senior design projects to implement and compare different shape extraction techniques for various applications.