Modeling stochastic systems in Riemannian manifolds

该项目旨在开发新的统计信号处理和控制工程算法和工具，以便能够在陆地和空间远程跟踪物体。越来越多的应用需要研究黎曼流形中的随机过程，即受几何约束演化的过程。该项目旨在提供这些过程的数值模拟方法，从这些过程的数据和渐近性能分析中进行在线和离线系统识别的方法;以及服从几何形状的过程状态估计算法。这些成果将推动并有益于运输、卫生和视频安全等领域的时空数据分析。

This project aims to develop new statistical signal processing and control engineering algorithms and tools that will enable tracking of objects remotely on land and in space. A growing number of applications require the study of random processes in Riemannian manifolds, that is processes that evolve subject to a geometric constraint. This project aims to provide methods for the numerical simulation of such processes, methods of online and offline system identification from data on such processes and asymptotic performance analysis; and algorithms for process state estimation that obeys the geometry. The outcomes will advance and benefit spatio-temporal data analysis in areas such as transport, health and video-security.