Change Detection in Nonlinear Systems and Applications in Shape Analysis

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。一些例子包括在目标跟踪或定位应用中检测运动模型的变化；或在计算机视觉/生物医学图像分析应用中检测异常形状变化。在上述所有情况中，状态都不是直接观察到的。观测值是一个受噪声干扰的非线性状态函数。对于这种非线性/非高斯跟踪问题，粒子滤波器的有效性已经众所周知。通常，变化的系统模型是未知的，即变化或异常没有特征。例如，变化可能是渐进的，对于一个恒定速度的目标慢慢加速到更高的速度，或者是突然的。该方法基于基于粒子滤波的“慢”和“突然”算法。，未知参数，变化检测。将为实际应用开发和测试健壮的设计策略。智力优势：大多数现有的方法可以分为基于自适应滤波思想或基于轨迹丢失检测。自适应滤波方法要么成本高，要么实现起来不可靠。基于轨迹丢失的方法几乎可以立即检测到突然的变化。然而，缓慢的变化会导致单位时间内的少量跟踪损失，通常需要很长时间才能被检测到，或者有时会被遗漏。我们提出了一种新的方法，利用缓慢变化被部分跟踪的事实，并使用这种“跟踪的变化部分”进行粒子滤波器检测。更广泛的影响：开发的算法将影响大量需要目标跟踪的定位、导航或防御应用；需要异常行为检测的基于视频的监控应用；生物医学信号/图像序列分析应用，其中检测到的异常可以作为疾病的指标，以及计量经济学，金融，机器人和视觉中的许多其他应用。教育活动将包括介绍自适应滤波和蒙特卡罗方法的研究生课程；修改现有本科班级；并在高年级设计项目中实现和比较不同形状提取技术的各种应用。

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.