In order to predict future observations of a noise-driven system, we have to find a model that exactly or at least approximately describes the behavior of the system so that the current system state can be recovered from past observations. However, sometimes it is very difficult to model a system accurately, such as real ocean waves. It is therefore particularly interesting to analyze ocean wave properties in the time-domain using autoregressive moving average (ARMA) models. Two ARMA/AR based models and their equivalent state space representations will be used for predicting future ocean wave elevations, where unknown parameters will be determined using linear least squares and auto-covariance least squares algorithms. Compared to existing wave prediction methods, in this paper (i) an ARMA model is used to enhance the prediction performance, (ii) noise covariances in the ARMA/AR model are computed rather than guessed and (iii) we show that, in practice, low pass filtering of historical wave data does not improve the forecasting results.
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