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This paper presents a method and experimental results for near-surface wind sensing using reflected Global Navigation Satellite Systems (GNSS) signals received on a spacecraft. The estimation method proposed involves four steps. First, the bistatic radar cross section (BRCS) of the received signal is estimated from the measurements. Second, the BRCS measurements are calibrated to agree with existing theoretical and empirical wind-wave models. Next, a geometric optics-based scattering model is used to estimate the sea surface slopes, based on the reflection geometry and the measured BRCS. Finally, the surface winds are estimated using an empirically derived function relating the surface mean square slopes to near-surface wind speed. The accuracy of the proposed inversion technique is then tested using a set of 25 space-based GNSS reflection measurements over a range of wind speeds. These measurements were all taken in the proximity of ocean buoys which provided in situ ocean wind speed information. The wind estimates from the buoys were then compared with the wind retrievals made from the measurements and found to be accurate to a root-mean-square error of 1.84 m/s. Additionally, the potential error sources in the measurements are analyzed, including a simulation of the effects of wind direction on the BRCS measurements. This first demonstration of space-based GNSS scatterometry using a small set of sample measurements will hopefully provide a benchmark and example for future experiments.