This paper deals with spatio-temporal conditional prediction of sea state parameters given nearby observations of the same parameters or given the observations of other sea state parameters at the same geographic point. An algorithm referred as Non Parametric Viterbi (NPV) and based on Hidden Markov Chain theory is proposed. It is shown that this algorithm can be used, for instance, to predict missing values in sea state data networks such as bouy networks or to predict a sea state process given part of the multivariate observed vector. The reduction of the dimension of the representation state space in which the process is described is also of practical use since this allows jointly to reduce the size of the learning data set and to maintain the algorithmic complexity at a tractable level.
We address the non parametric modeling of cycle-stationary multivariate Markovian processes using a continuous state space and discrete time Hidden Markov lVIodel (HlVIM) for which all necessary densities functions are approximated using samples. Let us first describe two potential applications of the proposed Viterbi algorithm. Pittalis[9] and Puca [10] study a neural network approach to reconstruct missing data in spatial bouys networks. Well known drawbacks of Neural Networks models for time series prediction if the large amount of data and the often high computation time required to learn the model. NPV algorithm is an alternative for missing data reconstruction. And it is shown bellow that good prediction can be obtained with quite small learning samples for significant wave height processes. The principle of their algorithm is to simulate a large number of realistic sea state histories and to estimate the profitability of the line given polar diagram of the boat and the simulated sea state parameters.
