Sea-surface reconstruction for surface marine vehicles: A matrix completion approach

This paper addresses the problem of reconstructing the height of the sea-surface proximal to marine vessels, based upon a finite set of point-wise in space height samples from onboard light detection and ranging (LiDAR) sensors. This is a necessary precursor to developing the autopilot systems for next generation unmanned surface vehicles (USVs) that can efficiently navigate through rough seas, based upon limited sensory information of the surrounding sea-surface. The technical challenges are twofold. Firstly, the sea-surface dynamics are highly complex, posing a significant challenge to the use of model-based estimation techniques. Secondly, the measurements of the sea-surface are spatially irregular, sparse, and time-varying owing to the effects of dynamic wave-shadowing. As a significant first step, we show how the challenge of sea-surface reconstruction can be posed as a matrix completion problem whose solution is model-free and is merely reliant on a low-rank property stemming from the bandwidth-limited nature of ocean wave spectra. Validation tests are conducted on ocean surfaces generated from Elfouhaily spectra, with synthetic sensor data generated from geometric intersection of LiDAR beams with each surface. The results demonstrate remarkably good recovery of the large matrices that store sea-surface height data, using fewer than 3% of their sampled entries. In addition, results are presented that demonstrate the robustness of the matrix completion technique to random sample loss.