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Center for Nonlinear Studies |
Analysts must understand the behaviors and intent of targets from persistent, but sporadic observations. This is a signal processing problem, in which data sources could be traditional sensors or other analytics. The available data sources have different capabilities and back end data processing chains — making their resulting data streams inconsistent. This frustrates their use by automated inference algorithms because a consistent mathematical theory of fusion has not been developed.
It is therefore imperative that we develop a unified mathematical theory of data fusion that permits assembly of local sensor coverage regions into a global picture. Such a theory must also inspire effective, practical algorithms that exploit whatever sensor resources are available, and suggest ways to redeploy sensors for more effective collection.
The mathematical theory of sheaves appears to meet these needs, and has recently become useful in signal processing, providing new insight into such traditional topics as sampling theory, filter design, and detection processing. However, sheaves based on partially ordered sets are poised to make inroads into more complex problems involving target identification, track disambiguation, sensor handoff, and false alarm suppression.
Since sheaves are not commonplace in signal processing, the talk will explain why they are uniquely valuable and effective. The discussion will center around critical illustrative examples that are particularly challenging for traditional methods, but are treated effectively by sheaves.
Host: Frank Alexander 5-4518