Real-time inverse estimation of multi-directional random waves from vessel-motion sensors using Kalman filter

Abstract

The real-time inverse estimation of the ocean wave spectra and elevation from a vessel-motion sensor is highly valuable, although it is still in the early stages of development. The Kalman filter method using motion measurements has advantages over other methods in terms of real-time capability, cost savings, and easy installation. In this paper, the Kalman filter method is developed for the inverse estimation of multi-directional waves in real time. The problematic divergence in the high-frequency region encountered by previous papers using similar approaches is resolved by employing the Wiener filter method. The developed method is also shown to be robust against potential sensor noises. The real-time multidirectional-wave spectrum and elevations can be recovered, including the high-frequency region, using the developed methodology with the numerically generated motion-sensor signals with noise. The developed Kalman filter algorithm is tested and validated for various sea states of uni- and multi-directional waves. The inverse estimation of multi-directional waves is generally less accurate compared to that of unidirectional waves, mainly due to the significant increase of unknowns (component waves) in the Kalman filter processes. Nevertheless, the overall wave spectra, elevation time series, significant wave heights, peak period, main direction, and directional spreading were well recovered.