A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Joslyn, Cliff A.; Charles, Lauren E.; DePerno, Christopher S.; Gould, Nicholas; Nowak, Kathleen E.; Praggastis, Brenda L.; Purvine, Emilie A. H.; Robinson, Michael; Strules, Jennifer; Whitney, Paul D.

doi:10.3390/s20123418

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Journal Article · Wed Jun 17 00:00:00 EDT 2020 · Sensors

DOI:https://doi.org/10.3390/s20123418· OSTI ID:1639336

^[1]; ^[2]; ^[3]; Gould, Nicholas ^[3]; Nowak, Kathleen E. ^[2]; Praggastis, Brenda L. ^[1]; ^[1]; ^[4]; Strules, Jennifer ^[3]; Whitney, Paul D. ^[2]

Pacific Northwest National Lab. (PNNL), Seattle, WA (United States)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
North Carolina State Univ., Raleigh, NC (United States)
American Univ., Washington, DC (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1639336

Report Number(s):: PNNL-SA--147453

Journal Information:: Sensors, Journal Name: Sensors Journal Issue: 12 Vol. 20; ISSN 1424-8220

Publisher:: MDPI AGCopyright Statement

Country of Publication:: United States

Language:: English

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Benchmarking Particle Filter Algorithms for Efficient Velodyne-Based Vehicle Localization Blanco-Claraco, Jose Luis; Mañas-Alvarez, Francisco; Torres-Moreno, Jose Luis Sensors, Vol. 19, Issue 14 https://doi.org/10.3390/s19143155	journal	July 2019
Pedestrian Positioning Using a Double-Stacked Particle Filter in Indoor Wireless Networks Sung, Kwangjae; Lee, Hyung Kyu; Kim, Hwangnam Sensors, Vol. 19, Issue 18 https://doi.org/10.3390/s19183907	journal	September 2019
An Extensible Positioning System for Locating Mobile Robots in Unfamiliar Environments Xu, Xiaosu; Liu, Xinghua; Zhao, Beichen Sensors, Vol. 19, Issue 18 https://doi.org/10.3390/s19184025	journal	September 2019
A Meta-Review of Indoor Positioning Systems Mendoza-Silva, Germán Martín; Torres-Sospedra, Joaquín; Huerta, Joaquín Sensors, Vol. 19, Issue 20 https://doi.org/10.3390/s19204507	journal	October 2019
Multi-Target Localization and Tracking Using TDOA and AOA Measurements Based on Gibbs-GLMB Filtering Tian, Zhengwang; Liu, Weifeng; Ru, Xinfeng Sensors, Vol. 19, Issue 24 https://doi.org/10.3390/s19245437	journal	December 2019
An Approach to Segment and Track-Based Pedestrian Detection from Four-Layer Laser Scanner Data Zhang, Mingfang; Fu, Rui; Cheng, Wendong Sensors, Vol. 19, Issue 24 https://doi.org/10.3390/s19245450	journal	December 2019
Improving Positioning Accuracy via Map Matching Algorithm for Visual–Inertial Odometer Meng, Juan; Ren, Mingrong; Wang, Pu Sensors, Vol. 20, Issue 2 https://doi.org/10.3390/s20020552	journal	January 2020
Batch Processing through Particle Swarm Optimization for Target Motion Analysis with Bottom Bounce Underwater Acoustic Signals Oh, Raegeun; Song, Taek Lyul; Choi, Jee Woong Sensors, Vol. 20, Issue 4 https://doi.org/10.3390/s20041234	journal	February 2020
MapReduce Particle Filtering with Exact Resampling and Deterministic Runtime Thiyagalingam, Jeyarajan; Kekempanos, Lykourgos; Maskell, Simon arXiv https://doi.org/10.48550/arxiv.1705.01660	text	January 2017
A tool to automatically analyze electromagnetic tracking data from high dose rate brachytherapy of breast cancer patients Götz, Th. I.; Lahmer, G.; Strnad, V. Universität Regensburg https://doi.org/10.5283/epub.36544	text	January 2017
Inference and control of the nosocomial transmission of methicillin-resistant Staphylococcus aureus Pei, Sen; Morone, Flaviano; Liljeros, Fredrik eLife, Vol. 7 https://doi.org/10.7554/elife.40977	journal	December 2018
A sequential Monte Carlo algorithm for inference of subclonal structure in cancer Ogundijo, Oyetunji Enoch; Zhu, Kaiyi; Wang, Xiaodong Columbia University https://doi.org/10.7916/d8-cj4c-q275	text	January 2019

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