# Latest Advances in the Global Navigation Satellite System--Reflectometry (GNSS-R) Field
\left(\overrightarrow{\rho}\right)\Big{|}^{2}\frac{\mathrm{q}^{4}\!\left( \overrightarrow{\rho}\right)}{\mathrm{q}^{4}\!\left(\overrightarrow{\rho} \right)}\wp\!\left(-\frac{\mathrm{q}_{\perp}\!\left(\overrightarrow{\rho} \right)}{\mathrm{q}_{\perp}\!\left(\overrightarrow{\rho}\right)}\right)\), where \(\mathcal{R}\) is the Fresnel reflection coefficient, \(\wp\) is the probability density function of the surface slopes, and \(\mathrm{q}_{\mathrm{z}}\) and \(\mathrm{q}_{\perp}\) are the tangential and perpendicular components of the bisector vector or scattering vector \(\overrightarrow{\mathrm{q}}\). Comparatively, Equation (2) describes the reflected GNSS signal that would be received from a surface dominated by coherent scattering. \[\mathrm{P_{coh}}\!\left(\tau,\mathrm{f_{d}}\right)=\mathrm{T_{i}^{2}}\frac{ \mathrm{P_{tx}}\mathrm{G_{tx}}\mathrm{G_{rx}}\!\left(\overrightarrow{\rho} _{\mathrm{sp}}\right)\!\lambda^{2}\Lambda^{2}\!\left(\tau-\tau_{\mathrm{s}} \!\left(\overrightarrow{\rho}_{\mathrm{sp}}\right)\right)}{\left(4\pi\right) ^{3}\!\left(\mathrm{R_{rx}}\!\left(\overrightarrow{\rho}_{\mathrm{sp}} \right)+\mathrm{R_{rx}}\!\left(\overrightarrow{\rho}_{\mathrm{sp}}\right) \right)^{2}}\times\left|\mathrm{S}\!\left(\mathrm{f_{d}}\!\left(\overrightarrow {\rho}_{\mathrm{sp}}\right)-\mathrm{f}\right)\right|^{2}\!\left|\!\left| \widetilde{\mathcal{R}}\!\left(\overrightarrow{\rho}_{\mathrm{sp}}\right) \right|^{2} \tag{2}\]  
where:  
* \(\overrightarrow{\rho}_{\mathrm{sp}}\) corresponds to the surface specular point;
* \(\widetilde{\mathcal{R}}\!\left(\overrightarrow{\rho}_{\mathrm{sp}}\right)\) is the averaged reflection coefficient at \(\overrightarrow{\rho}_{\mathrm{sp}}\). This is computed from evaluating the scattering surface average reflection coefficient \(\widetilde{\mathcal{R}}\!\left(\overrightarrow{\rho}\right)\) at the specular direction by performing \(\widetilde{\mathcal{R}}\!\left(\overrightarrow{\rho}_{\mathrm{sp}}\right)= \widetilde{\mathcal{R}}\!\left(\overrightarrow{\rho}\right)\!\delta\!\left( \overrightarrow{\rho}-\overrightarrow{\rho}_{\mathrm{sp}}\right)\). To illustrate the different types of scattering we provide in Figure 5 the different types of scattering and the corresponding DDMs that are characteristic of different types of surfaces. The following sections review the different aspects of the GNSS-R field. Section 2 reviews the technology advancements in the field, providing first a review of the evolution since it was first proposed in 1988. Section 3 covers the advancements specific to ocean applications. Section 4 covers the advancements specific to land applications. Section 5  
Figure 5: Two examples of delay–Doppler maps (DDM) of two different surfaces. Earth image credit: NASA Goddard Space Flight Center image by [PERSON] (land surface, shallow water, clouds). is dedicated to describing the applications on the Earth's cryosphere; Section 6 provides insight into novel applications derived from GNSS-R, but which are not specifically part of the ocean, land, or cryosphere. Section 7 provides a discussion on where the GNSS-R field seems to be heading in the near future. Finally, conclusions are presented in Section 8.