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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.

Abstract. An estimate of the on-site wave spectrum can be obtained from measured ship responses by use of Bayesian modelling, which means that the wave spectrum is found as the optimum solution from a probabilistic viewpoint. The paper describes the introduction of two hyperparameters into Bayesian modelling so that the prior information included in the modelling is based on two constraints: the wave spectrum must be smooth directional-wise as well as frequency-wise. Traditionally, only one hyperparameter has been used to control the amount of smoothing applied in both the frequency and directional ranges. From numerical simulations of stochastic response measurements, it is shown that the optimal hyperparameters, determined by use of ABIC (a Bayesian Information Criterion), correspond to the best estimate of the wave spectrum, which is not always the case when only one hyperparameter is included in the Bayesian modelling. The paper includes also an analysis of full-scale motion measurements where wave spectra estimated by the Bayesian modelling are compared with results from ocean surface measurements by satellite and from a wave radar. The agreement is found to be reasonable.

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This paper presents a novel method for estimating the sea state parameters based on the heave, roll and pitch response of a vessel in dynamic positioning (DP), i.e., without forward speed. The algorithm finds the wave spectrum estimate from the response measurements by directly solving a set of linear equations, and as a result it is computationally efficient. The main vessel parameters are required as input. Apart from this the method is signal-based, with no assumptions on the wave spectrum shape. Performance of the proposed algorithm is demonstrated on full-scale experimental DP data of a vessel in three different sea states at head, bow, beam, quartering and following sea waves, respectively.

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