A novel approach for robust state estimation of marine vessels in rough water is proposed in this paper to enable tight collaboration between Unmanned Aerial Vehicles (UAVs) and a marine vessel, such as cooperative landing or object manipulation, regardless of weather conditions. Our study of marine vessel (in our case Unmanned Surface Vehicle (USV)) dynamics influenced by strong wave motion has resulted in a novel nonlinear mathematical USV model with 6 degrees of freedom (DOFs), which is required for precise USV state estimation and motion prediction. The proposed state estimation approach fuses data from multiple sensors onboard the UAV and the USV to enable redundancy and robustness under varying weather conditions of real-world applications. The proposed approach provides estimated states of the USV with 6 DOFs and predicts its future states to enable tight control of both vehicles on a receding control horizon. The proposed approach was extensively tested in the realistic Gazebo simulator and successfully experimentally validated in many real-world experiments representing different application scenarios, including agile landing on an oscillating and moving USV. A comparative study indicates that the proposed approach significantly surpassed the current state-of-the-art.