The sea waves cause the effect of a rotational motion (i.e., pitch, roll and heading angle) of ships. The ship rotational motions result in beam pointing error of the phased array radar aboard the ship. The antenna stabilization aimed to achieve a beam pointing accuracy over a long dwell time is an important problem for the shipborne phased array radars. Due to the dynamic and stochastic nature of the sea environment, the shipborne phased array radar must be able to compensate for the ship's motion adaptively. In this paper, the linear discrete Kalman filter is proposed as a predictor for the shipborne phased array radar, which can compensate for the beam pointing error and track the air and sea surface targets. The pitch, roll and heading angles and the its velocities data are measured on-line from a gyroscope of the sea vehicle and used from the ship motion mathematical models for their prediction. It is proved, that the pitch, roll, and heading motion models may be considered as independent. All these models are presented as the same second order linear differential equations with different parameters. Besides, equivalent linear discrete state space models for the angles' changes are constructed in the paper. The estimation accuracy of the Kalman filter (predictor) depends on the values of different parameters, such as the parameters of the ship's motion mathematical model, measurement error covariance matrices, etc. The sea environments are very dynamic, hence, there is a need for an adaptive system for the controlling and compensating devices, operating regardless of the ship's motion. Continuous monitoring of the environment and adapting filter ensure parameters with less computational burden needed for a real time application. The paper describes a technique for identification of such parameters by the measured correlation functions of the pitch, roll, and heading angles. Finally, it is proved by the computer simulations that the proposed compensations technique is a real time applicable algorithm for a shipborne phased array radar. The computer simulation was performed with the following parameters: the measurement frequency for the gyroscopes was 100 Hz, the prediction times of the Kalman filter were 0.01 s and 0.1 s. The following two cases were considered. In the first case, only the predicted angles were measured with gyroscopes. In the second case, the angles and the rates of their change were measured. The simulations demonstrated that the presented prediction algorithm ensured higher accuracy (less root mean square errors of the predicted angles) than the initial accuracy of the gyroscopes measurements.