June 2021 Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling
Trygve Olav Fossum, Cédric Travelletti, Jo Eidsvik, David Ginsbourger, Kanna Rajan
Author Affiliations +
Ann. Appl. Stat. 15(2): 597-618 (June 2021). DOI: 10.1214/21-AOAS1451


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.

Funding Statement

TOF acknowledges support from the Centre for Autonomous Marine Operations and Systems (AMOS), Center of Excellence, project number 223254, Nansen Legacy Program, project number 276730 and the Applied Underwater Robotics Labortatory (AURLab). CT and DG acknowledge support from the Swiss National Science Foundation, project number 178858. JE and KR acknowledge support from Norwegian research council (RCN), project number 305445. DG would like to acknowledge support of Idiap Research Institute, his primary affiliation in an early version of this manuscript.


We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. The authors would also like to thank Niklas Linde of the University of Lausanne for providing constructive feedback about this work and members of the NTNU AURLab for help with AUV deployments.


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Trygve Olav Fossum. Cédric Travelletti. Jo Eidsvik. David Ginsbourger. Kanna Rajan. "Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling." Ann. Appl. Stat. 15 (2) 597 - 618, June 2021. https://doi.org/10.1214/21-AOAS1451


Received: 1 October 2019; Revised: 1 January 2021; Published: June 2021
First available in Project Euclid: 12 July 2021

MathSciNet: MR4298973
zbMATH: 1478.62354
Digital Object Identifier: 10.1214/21-AOAS1451

Keywords: adaptive information gathering , autonomous robots , Excursion sets , Experimental design , Gaussian processes , ocean sampling

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 2 • June 2021
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