Sequential reconstruction of nonlinear ocean wave fields from floating body motion using the ensemble Kalman filter

We present a sequential data assimilation framework for reconstructing a nonlinear wave field from the motion history of a floating body. An ensemble Kalman filter method is employed, which includes a forecast step and assimilation step in each observation cycle. In the forecast step, the surface wave field is simulated using a higher-order spectral (HOS) method and the body motion is computed though Cummin's equation taking wave excitation force from the HOS result. In the assimilation step, the measurement of body motion is used, through a Kalman filter analysis equation, to correct the modeled state which includes both the wave field and body motion. We also address a critical question on the proper initial guess of the wave field to start the full algorithm, when no wave measurement is available. This developed methodology is validated and tested on synthetic problems of bodies with simple shapes floating on the surface of irregular waves. With accumulation of measured body motions, we show that both the body and wave states converge accurately to the hidden reference states underlying the observation data.