Abstract
In the aftermath of radiation or chemical accidents, responders must rapidly map out regions of contamination as quickly and accurately as possible. One important and relevant statistical method for this kind of disaster response is spatial kriging, which makes predictions based on incomplete knowledge of spatially referenced observations. Given an Unmanned Aerial System (UAS) equipped with radiation sensors, we develop a spatial statistics-based approach to optimally map out a contamination field over a geographic region. In this article, we evaluate three approaches to UAS mapping: a Variance Driven Sampling (VDS) approach that minimizes kriging variance, a more computationally intensive Hybrid Entropy Search (HES), and a baseline Levy Flight search. Considering limited UAS range, we also implement a restricted version of these approaches that only considers nearby points. We find that HES is optimal for small numbers of sampled points with the restricted versions of HES and VDS becoming optimal for larger samples. Ultimately, the best method is dependent on the number of samples to be taken, with each method providing clear benefits over a random search in terms of both mean squared error and path length. We demonstrate the advantages of our methodology using actual radiation field test data from the Idaho National Lab.
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Materials Availability
The data is provided as Appendix B. Code for reproducing results is available upon request from the corresponding author.
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The authors would like to thank the reviewers and editor for several useful comments that greatly improved this work.
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Daniel Echeveste provided all coding and conducted all simulations in this manuscript. He originated the idea of entropy based sampling.
Andrew Lee provided subject matter expertise on UAS systems and ensured the algorithms provided were applicable for UAS systems.
Nicholas Clark provided statistical analysis and oversight for the project and served as Daniel Echeveste’s advisor for this work. He proposed the initial idea of using spatial statistics to inform flight paths.
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Appendices
Appendix A: Log Scale MSE Plots
This appendix includes graphs of MSE on a \(\log \) scale, which makes difference in performance more clear.
Plot of mean MSE on a \(\log \) scale at n sampled points for VDS, HES, and RS after 1000 simulations
Plot of mean MSE on a \(\log \) scale at n sampled points for RVDS, RHES, and RRS, with a distance restrictions of 3m, after 1000 simulations
Plot of mean MSE on a \(\log \) scale at n sampled points for RVDS, RHES, and RRS, with a distance restrictions of 7m, after 1000 simulations
Plot of mean MSE on a \(\log \) scale at n sampled points for VDS and RVDS with three different distance restrictions after 1000 simulations
Plot of mean MSE on a \(\log \) scale at n sampled points for HES and RHES with three different distance restrictions after 1000 simulations
Appendix B: Radiation Field Data
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Echeveste, D., Lee, A. & Clark, N. Using Spatial Uncertainty to Dynamically Determine UAS Flight Paths. J Intell Robot Syst 101, 76 (2021). https://doi.org/10.1007/s10846-021-01331-3
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DOI: https://doi.org/10.1007/s10846-021-01331-3