Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling

Fossum, Trygve Olav; Travelletti, Cédric; Eidsvik, Jo; Ginsbourger, David; Rajan, Kanna (2021). Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling. The annals of applied statistics, 15(2), pp. 597-618. Institute of Mathematical Statistics 10.1214/21-AOAS1451

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Improving and optimizing oceanographic sampling is a crucial task for marine science and maritime resource management. Faced with limited resources in understanding processes in the water column, the combination of statistics and autonomous systems provides new opportunities for experimental design. In this work we develop efficient spatial sampling methods for characterizing regions, defined by simultaneous exceedances above prescribed thresholds of several responses, with an application focus on mapping coastal ocean phenomena based on temperature and salinity measurements. Specifically, we define a design criterion based on uncertainty in the excursions of vector-valued Gaussian random fields and derive tractable expressions for the expected integrated Bernoulli variance reduction in such a framework. We demonstrate how this criterion can be used to prioritize sampling efforts at locations that are ambiguous, making exploration more effective. We use simulations to study and compare properties of the considered approaches, followed by results from field deployments with an autonomous underwater vehicle as part of a study mapping the boundary of a river plume. The results demonstrate the potential of combining statistical methods and robotic platforms to effectively inform and execute data-driven environmental sampling.

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