The real-time algorithm of higher order spectral analysis is proposed in order to investigate the non-linear and non-stationary ship motions. The algorithm is based on the time-varying vector auto-regressive (TVVAR) modeling and can be considered as an extension of the instantaneous cross spectral analysis. The TVVAR model is fitted to the data using the Kalman filter algorithm and the instantaneous higher order spectra can be evaluated by using the TVVAR coefficients. In order to examine the validity of the proposed algorithm, numerical simulations of the real-time estimation of higher order spectra was carried out based on the full scale ship motion data. The accuracy of the proposed algorithm was investigated by comparing with the stationary analysis based on the FFT. Furthermore, the algorithm was extended to the trispectral analysis and a result was shown to demonstrate the usefulness of the proposed algorithm.

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