From points to waves: Fast ocean wave spatial–temporal fields estimation using ensemble transform Kalman filter with optical measurement

Accurate spatial–temporal wave measurement is vital for ocean engineering applications. Although stereo vision shows great potential in this field, performing dense reconstruction requires processing vast amounts of pixel data, which reduces the efficiency of stereo image matching and subsequent point cloud processing. Recently, the paradigm of fusing sparse 3D points with predictions has emerged as a promising solution that balances accuracy and efficiency, yet requires an optimization framework capable of handling both state estimation and robust outlier filtering. Therefore, this study proposes a Kalman filter (KF)-based method for ocean wave field estimation, aiming to improve efficiency through recursion and to remove outliers and interpolation errors in measurements. The method leverages linear gravity wave dispersion relations for prediction, with sparse 3D points interpolated to a uniform grid as measurements. To address limitations of high-dimensional data processing, the study implements the Ensemble Transform Kalman Filter (ETKF), incorporating fuzzy logic to handle potential outliers. By maintaining an ensemble of states and employing ensemble transformation techniques to avoid computationally expensive matrix inversions, ETKF significantly improves recursive processing efficiency. Both CPU and GPU implementations were evaluated on published and field-collected datasets, demonstrating superior performance in efficiency, accuracy, and robustness compared to existing methods under the same paradigm.