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

该项目旨在开发从高维、非欧几里得数据中被噪声和异常值破坏的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的挑战。例如，大多数分布式算法，如“共识”，通过局部平均低维欧几里得数据来获得全局平均值。然而，在大多数应用中，数据是高维的，并且受到噪声和异常值的困扰。此外，目标不一定是对度量进行平均，而是对从度量推断出的模型达成一致。由于这些模型的估计通常涉及流形上的优化，因此解决这些问题的几乎所有算法都是集中的，并且需要无线传感器节点中无法获得的资源。该项目在基于流形的新颖鲁棒共识算法的分布式感知中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参数相关的数据。第二个目标是开发基于鲁棒统计和机器学习的分布式传感算法，这些算法对噪声和异常值具有鲁棒性。第三个目标是将这些流形上的鲁棒一致性算法应用于无线传感器网络中的分布式定位问题。流形上健壮的分布式估计技术的发展可以影响许多应用领域，如监视、安全、远程沉浸、空间探索、环境监测和辅助家庭生活。这些应用需要在混合、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交叉领域受过培训的专业人员。该团队的多学科专业知识将促进这些学科交叉的培训。

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.