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.
