Abstract:The research progress in improving the accuracy of the underwater inertial/gravity integrated navigation based on the principle of the new generation of the GNSS-R constellations altimetry is introduced by following closely the latest hotspot of the international GNSS-R satellite altimetry recovery and underwater integrated navigation, and in order to meet the urgent requirements for the science and national defense. Firstly, some research progresses are introduced, such as the GNSS-R altimetry precision, the GNSS-R along-track spatial resolution, the GNSS-R trajectories spatial resolution, the marine gravity field recovery based on satellite altimetry, and the underwater gravity matching navigation. Secondly, for the GNSS-R satellite altimetry, we’ve proposed a series of specular point positioning methods including the geoid static-state elevation correction, the ocean tidal time-varying elevation correction, the normal projection correction, the GNSS-R nadir antenna receiving SNR model, and the available specular point filtering method to improve the spatial resolution and accuracy of the sea surface altimetry. For the underwater gravity matching navigation, we’ve proposed some methods including the new principal component weighted average normalization method, the geodesic-based method, the hierarchical neighborhood threshold method, the priori recursive iterative least squares mismatch correction method, etc., in order to improve the accuracy, matching efficiency, and reliability of underwater gravity matching navigation. Thirdly, the new two-order fixed-point time-delay extraction method will be proposed, aiming to improve the measurement accuracy of the sea surface height by GNSS-R satellite. The new reflection signal decomposition method will be proposed in order to improve the along-track spatial resolution of the GNSS-R satellite altimetry. The new calibration method of surface roughness error will be proposed for the sake of improving the trajectories spatial resolution of the GNSS-R satellite altimetry. The new regularized robust algorithm will be proposed for improving the recovery accuracy and spatial resolution of the marine gravity field. The new hybrid method of the geometric registration associated with the direct probability criterion will be proposed through combining advantages between the fast convergence rate of geometric registration and the high accuracy of direct probability criterion by the fusion of the multi-source information consisting of the simulated satellite-borne GNSS-R altimetry data, the measured bank/air-based GNSS-R height data and so on, aiming to improve the accuracy and speed of the underwater inertial/gravity integrated navigation.