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Real time ship motion estimation is of interest to naval ship operators for, vertical aircraft landing, as well as to the offshore industry for installing rigs and transferring equipment in rough seas. In the present study the estimation of the heave and pitch motion of a ship is considered, using Kalman filtering techniques. A significant part of the study is devoted to constructing appropriate models for the sea and the ship. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, non-minimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and non-minimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A numerical application is considered for a DD-963 destroyer.