A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information
Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sens...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/12/3418 |
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| author | Cliff A. Joslyn Lauren Charles Chris DePerno Nicholas Gould Kathleen Nowak Brenda Praggastis Emilie Purvine Michael Robinson Jennifer Strules Paul Whitney |
| author_facet | Cliff A. Joslyn Lauren Charles Chris DePerno Nicholas Gould Kathleen Nowak Brenda Praggastis Emilie Purvine Michael Robinson Jennifer Strules Paul Whitney |
| author_sort | Cliff A. Joslyn |
| collection | DOAJ |
| description | Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid. |
| first_indexed | 2024-03-10T19:06:14Z |
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| id | doaj.art-8bca54c96039483499c26a7f5f6a2ee4 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T19:06:14Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-8bca54c96039483499c26a7f5f6a2ee42023-11-20T04:08:03ZengMDPI AGSensors1424-82202020-06-012012341810.3390/s20123418A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation InformationCliff A. Joslyn0Lauren Charles1Chris DePerno2Nicholas Gould3Kathleen Nowak4Brenda Praggastis5Emilie Purvine6Michael Robinson7Jennifer Strules8Paul Whitney9Pacific Northwest National Laboratory, Seattle, WA 98109, USAPacific Northwest National Laboratory, Richland, WA 99352, USACollege of Natural Resources, Department of Forestry and Environmental Resources, Fisheries, Wildlife, and Conservation Biology, North Carolina State University, Raleigh, NC 27695, USACollege of Natural Resources, Department of Forestry and Environmental Resources, Fisheries, Wildlife, and Conservation Biology, North Carolina State University, Raleigh, NC 27695, USAPacific Northwest National Laboratory, Richland, WA 99352, USAPacific Northwest National Laboratory, Seattle, WA 98109, USAPacific Northwest National Laboratory, Seattle, WA 98109, USADepartment of Mathematics and Statistics, American University, Washington, DC 20016, USACollege of Natural Resources, Department of Forestry and Environmental Resources, Fisheries, Wildlife, and Conservation Biology, North Carolina State University, Raleigh, NC 27695, USAPacific Northwest National Laboratory, Richland, WA 99352, USAIntegration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.https://www.mdpi.com/1424-8220/20/12/3418topological sheavesinformation integrationconsistency radiuswildlife managementstochastic linear modelKalman filter |
| spellingShingle | Cliff A. Joslyn Lauren Charles Chris DePerno Nicholas Gould Kathleen Nowak Brenda Praggastis Emilie Purvine Michael Robinson Jennifer Strules Paul Whitney A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information Sensors topological sheaves information integration consistency radius wildlife management stochastic linear model Kalman filter |
| title | A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information |
| title_full | A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information |
| title_fullStr | A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information |
| title_full_unstemmed | A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information |
| title_short | A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information |
| title_sort | sheaf theoretical approach to uncertainty quantification of heterogeneous geolocation information |
| topic | topological sheaves information integration consistency radius wildlife management stochastic linear model Kalman filter |
| url | https://www.mdpi.com/1424-8220/20/12/3418 |
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