On Random Sampling and Fourier Transform Estimation in Sea Waves Prediction

Improving the safety of a wide range of launch and recovery operations is of great international maritime interest. Deterministic sea wave prediction (DSWP) is a relatively new branch of science that can offer such opportunities by predicting the actual shape of the sea surface and its evolution for short time in the future. Fourier transform technique is the main building block in DSWP, which requires measurements of the sea surface. Nonetheless, uniformly sampled measurements of the sea surface cannot be practically achieved for various reasons. Conventional X-band radars are the most realistic candidate to provide a low-cost convenient source of two-dimensional wave profile information for DSWP purposes. Ship movement and mechanically rotating scanning antennas are among sources of irregularity in sea surface sampling. This in turn introduces errors when traditional Fourier transform based wave prediction methods are used. In this paper we show that by modelling the radar sampling instants as random variables and using the estimator of Tarczynski and Allay to process the samples, a reliable solution for DSWP can be constituted.