Landing an aircraft on a ship deck in high sea states can be challenging due to the risk for adverse interactions between the moving ship deck and aircraft components. When deck motion is significant, aircraft must sometimes wait for an extended duration until a calm period is detected to land safely. This paper presents a deck motion estimation (DME) algorithm that can decrease landing times. The DME algorithm runs in real-time allowing for fully autonomous ship deck landings without a human operator in the loop. The proposed solution uses generalized predictive control to predict future ship deck states based on prior observations. A landing is commanded when ship deck states are predicted to be within quiescent bounds for a pre-determined prediction horizon in which a safe landing could be completed. Monte-Carlo simulations utilizing ship state data show that the deck motion estimation can accurately predict quiescent landing periods. Further, flight test experiments have demonstrated the feasibility of implementing the system for an unmanned aircraft.