This article gives a review of techniques applied to make sea state estimation on the basis of measured responses on a ship. The general concept of the procedures is similar to that of a classical wave buoy, which exploits a linear assumption between waves and the associated motions. In the frequency domain, this assumption yields the mathematical relation between the measured motion spectra and the directional wave spectrum. The analogy between a buoy and a ship is clear, and the author has worked on this wave buoy analogy for about fifteen years. In the article, available techniques for shipboard sea state estimation are addressed, but with a focus on only the wave buoy analogy. Most of the existing work is based on methods established in the frequency domain but, to counteract disadvantages of the frequency-domain procedures, newer studies are working also on procedures formulated directly in the time domain. Sample results from several studies are included, and the main findings from these are mentioned.
Short-term variability of ship responses is investigated by cross-spectrum analysis. In a steady state condition, it is well known that a certain length of sampled data is required for stable results of the spectral analysis. However, the phase lag between responses, in terms of the phase angle of the cross-spectra, has not been discussed in detail. Using long stationary time series, the transition of amplitudes and relative phase angles of the cross-spectra has
been investigated by iterative analyzes with a few seconds of time shifting. In the results, the short-term variability of the relative phase angle was observed. In effect, the variability may compromise the accuracy of the wave buoy analogy.