Collaborative Research: CSR-EHCS(EHS), TM: Distributed Sensing via Robust Consensus on Manifolds

该项目旨在开发从被噪声和离群值破坏的高维、非欧几里德数据中进行分布式传感的理论和算法。这种分布式传感框架的开发面临着几个关键挑战。例如，大多数分布式算法(如“Consensus”)通过对低维欧几里得数据进行局部平均来获得全局平均值。然而，在大多数应用中，数据是高维的，并且受到噪声和离群值的困扰。此外，目标不一定是对测量结果进行平均，而是就从测量结果中推断出的模型达成共识。由于这类模型的估计往往涉及流形上的优化，因此几乎所有解决这些问题的算法都是集中式的，并且需要无线传感器节点无法获得的资源。该项目在基于流形上的新的稳健共识算法的分布式传感方面提供了重大的范式转变。第一个目标是开发基于几何控制、图论和机器学习的分布式传感算法，用于处理与黎曼流形中的参数相关的数据。第二个目标是开发基于稳健统计和机器学习的分布式传感算法，这些算法对噪声和离群值都是稳健的。第三个目标是将这些流形上的稳健共识算法应用于无线传感器网络中的几个分布式定位问题。在流形上发展稳健的分布式估计技术可以影响到许多应用领域，如监视、安全、远程沉浸、空间探索、环境监测和辅助家庭生活。这样的应用需要在混合、嵌入式和网络系统、机器人、传感器网络、控制理论、计算机视觉和机器学习等领域接受过培训的专业人员。该团队的多学科专业知识将促进在这些学科的交叉点进行培训。

This project aims to develop theory and algorithms for distributed sensing from high-dimensional, non-Euclidean data corrupted with noise and outliers. The development of such a distributed sensing framework faces several critical challenges. For instance, most distributed algorithms such as "consensus" proceed by locally averaging low-dimensional Euclidean data to obtain a global average. In most applications, however, data are high-dimensional, and plagued with noise and outliers. Moreover, the goal is not necessarily to average the measurements, but to reach a consensus on a model inferred from the measurements. Since the estimation of such models often involves optimization on manifolds, nearly all algorithms for solving these problems are centralized, and require resources not available in wireless sensor nodes. This project offers a significant paradigm shift in distributed sensing based on novel robust consensus algorithms on manifolds. The first goal is to develop distributed sensing algorithms based on geometric control, graph theory, and machine learning, for processing data related by parameters lying in Riemannian manifolds. The second goal is to develop distributed sensing algorithms based on robust statistics and machine learning, that are robust to noise, and outliers. The third goal is to apply these robust consensus algorithms on manifolds to several distributed localization problems in wireless sensor networks. The development of robust distributed estimation techniques on manifolds can impact many application areas, such as surveillance, security, tele-immersion, space exploration, environmental monitoring, and assisted home living. Such applications require professionals trained at the intersection of hybrid, embedded, and networked systems, robotics, sensor networks, control theory, computer vision and machine learning. The multidisciplinary expertise of the team will foster training at the intersection of these disciplines.