Collaborative Research: ATD: Algorithmic Aspects of Geometry for Using LIDAR and Wireless Sensor Networks for Combating Chemical Terror Attacks

该项目考虑使用各种传感器来监测具有未知几何形状的空间域上的未知信号场，该空间域可能具有海拔变化。该项目的主要目标是开发数学算法，可以整合来自大量分布式设备的传感器读数，并重建信号场和地形。具体而言，该项目涉及的传感器包括光探测和测距技术（LIDAR）和网络无线传感器，以实现其互补功能。激光雷达使用恒定数量的强大传感器，每个传感器从远处拍摄图像。另一方面，分布式无线传感器使用大量廉价的传感器（可能搭载在蜂窝电话上），每个传感器在其位置处获取密度阅读。本计画的方法是利用保形与双曲几何、离散曲率流、拓扑学与数值分析来发展新的演算法来产生精确的密度图。从网络的角度来看，该项目解决了LIDAR图像融合，网络定位，传感器部署以及LIDAR和传感器数据集成的问题。 该项目的动机是潜在的破坏性化学恐怖袭击。敌人使用的生物和化学制剂可能在短时间内扩散到一个大区域。该项目的重点是开发算法工具和技术，以便在发生这种攻击时及时收集关于化学或生物扩散的准确和有用的信息。通过利用激光雷达数据和传感器网络数据的几何特性，该项目提供了关于如何组织这样一个大规模网络的基本问题的关键观察;如何管理传感器数据;以及如何使用网络对环境和用户采取行动。

The project considers using a variety of sensors to monitor an unknown signal field over a spatial domain with unknown geometry, which may bear elevational variations. The main objective of this project is to develop mathematical algorithms that can integrate sensor readings from a large number of distributed devices and reconstruct both the signal field and the terrain. Specifically, the sensors involved in the project include the Light Detection And Ranging technology (LIDAR) and networked wireless sensors, for their complementary capabilities. LIDAR uses a constant number of powerful sensors, each takes an image from a distance. On the other hand, distributed wireless sensors use a large number of inexpensive sensors (possibly piggybacking on cellular phones), each takes a density reading at its position. The approach in this project is to use conformal and hyperbolic geometry, discrete curvature flows, topology and numerical analysis to develop novel algorithms to generate accurate density map. From the networking perspective, this project addresses the problems of LIDAR image fusion, network localization, sensor deployment, and integration of LIDAR and sensor data. The project is motivated by the potentially devastating chemical terror attacks. Biological and chemical agents, used by adversaries, could potentially spread to a large region in a short time. This project focuses on development of algorithmic tools and techniques for gathering timely, accurate and useful information about the chemical or biological spread in case of such an attack. By exploiting the geometric properties of LIDAR data and sensor network data, the project provides critical observations on fundamental questions of how to organize such a large scale network; how to manage sensor data; and how to use the network for acting on the environment and the users.