DDM-Former: Transformer networks for GNSS reflectometry global ocean wind speed estimation

Global navigation satellite system reflectometry (GNSS-R) has shown a capability in recent years to be applied as a novel remote sensing technique to retrieve ocean wind speeds. The combination of GNSS-R observable delayDoppler maps (DDMs) and deep learning algorithms provides the possibility to build an end-to-end pipeline for improving wind speed estimations. Recent studies have proven that data-driven approaches can be applied to generate enhanced estimation products. However, these are usually trained with convolutional neural networks (CNNs), which include inductive bias throughout the models. The inbuilt translation equivariance in CNNs represents an inexactitude for the feature extraction on DDMs. To address this issue, we propose Transformerbased models, named DDM-Former and DDM-Sequence-Former (DDM-Seq-Former), to exploit delay-Doppler correlation within and between DDMs, respectively. The advantages of our methods over conventional retrieval algorithms and other deep learning-based approaches are presented based on the Cyclone GNSS (CYGNSS) version 3.0 dataset. In addition, a comprehensive study on the attention mechanism for our models is demonstrated. The proposed DDM-Former yields the best overall performance with a root mean square error (RMSE) of 1.43 m/s and a bias of -0.02 m/s over the nine months test period. Moreover, with an RMSE of 2.89 m/s and a bias of -1.88 m/s, the proposed DDM-Seq-Former can promisingly improve the estimations in the cases with wind speeds higher than 12 m/s. There are still opportunities for further enhancements in creating more robust models that could perform well in all wind regimes given a non-uniform wind distribution. We will make our code publicly available.