Dynamic state estimation of floating offshore wind turbines (FOWTs) in complex marine environments is a core challenge for digital twin systems. This study proposes a joint estimation framework that integrates windowed dynamic mode decomposition (W-DMD) and an adaptive strong tracking Kalman filter (ASTKF). W-DMD extracts dominant modes under stochastic excitations through a sliding-window strategy and constructs an interpretable reduced-order state-space model. ASTKF is then employed to enhance estimation robustness against environmental uncertainties and noise. The framework is validated through numerical simulations under turbulent wind and wave conditions, demonstrating high estimation accuracy and strong robustness against sudden environmental disturbances. The results indicate that the proposed method provides a computationally efficient and interpretable tool for FOWT digital twins, laying the foundation for predictive maintenance and optimal control.