A Crossformer-Based Method for Sea Surface Height Prediction Using Delay–Doppler Map Feature Points

Global navigation satellite system-reflectometry (GNSS-R) provides an effective remote sensing technique for accurate retrieval of sea surface height (SSH) measurements. However, accuracy is severely affected by environmental disturbances such as wind-induced sea clutter and wave interference, degrading delay–Doppler map (DDM)-derived measurements. In this study, we propose an advanced trajectory-based deep learning model, Crossformer, explicitly designed to capture temporal dependencies inherent in GNSS-R sequential data. The method leverages five distinct DDM features: peak power point (PPP), maximum slope point (MSP), center pixel intensity (CPI), average power point (APP), and kurtosis (KUR). A dimension-segmentwise (DSW) embedding technique combined with a two-stage attention (TSA) mechanism effectively models both temporal and cross-dimensional correlations. Evaluation using CYGNSS data validated against Jason-3 Level 2 measurements demonstrates the superior performance of our approach, yielding a root mean square error (RMSE) of 0.93 m, mean absolute error (MAE) of 0.65 m, and a coefficient of determination ( $R^{2}$ ) of 0.9901. Comparative analyses with baseline methods confirm significant improvements in robustness and predictive accuracy, particularly across varying sea states. This research underscores the potential of advanced temporal modeling techniques in GNSS-R altimetry applications.