Mapping Waves with an Uncrewed Surface Vessel via Gaussian Process Regression

Mobile robots are well suited for environmental surveys because they can travel to any area of interest and react to observations without the need for pre-existing infrastructure or significant setup time. However, vehicle motion constraints limit where and when measurements occur. This is challenging for a single vehicle observing a time-varying phenomenon, such as coastal waves, but the ability to generate a spatiotemporal map would have immediate scientific and engineering applications. In this paper, an uncrewed surface vessel (USV) was used to measure waves on the coast of Lake Ontario, Canada. Data were collected from a low-cost inertial measurement system onboard the USV and processed in an offline Gaussian process regression (GPR) workflow to create a spatiotemporal wave model. Frequency analysis of raw sensor data was used to best select and design kernel functions, and to initialize hyperparameters. The relative speed of the waves limited the ability to make complete wave reconstructions, but GPR captured the dominant periodic components of the waves despite irregularities in the signals. After optimization, the hyperparameters indicate a dominant signal with a wave period of 0.87
$\mathbf{s}$
, which concurs with ground truth estimates.