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Integration of heterogeneous sensors is a challenging problem across a rangeof applications. Prominent among these are multi-target tracking, where onemust combine observations from different sensor types in a meaningful way totrack multiple targets. Because sensors have differing error models, we seek atheoretically-justified quantification of the agreement among ensembles ofsensors, both overall for a sensor collection, and also at a fine-grained levelspecifying pairwise and multi-way interactions among sensors. We demonstratethat the theory of mathematical sheaves provides a unified answer to this need,supporting both quantitative and qualitative data. The theory providesalgorithms to globalize data across the network of deployed sensors, and todiagnose issues when the data do not globalize cleanly. We demonstrate theutility of sheaf-based tracking models based on experimental data of a wildpopulation of black bears in Asheville, North Carolina. A measurement modelinvolving four sensors deployed among the bears and the team of scientistscharged with tracking their location is deployed. This provides a sheaf-basedintegration model which is small enough to fully interpret, but of sufficientcomplexity to demonstrate the sheaf's ability to recover a holistic picture ofthe locations and behaviors of both individual bears and the bear-humantracking system. A statistical approach was developed for comparison, a dynamiclinear model which was estimated using a Kalman filter. This approach alsorecovered bear and human locations and sensor accuracies. When the observationsare normalized into a common coordinate system, the structure of the dynamiclinear observation model recapitulates the structure of the sheaf model,demonstrating the canonicity of the sheaf-based approach. But when theobservations are not so normalized, the sheaf model still remains valid.

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information