On the Determination of the Specular Reflection Point in GNSS Reflectometry

The use of GNSS (Global Navigation Satellite System) for remote sensing and environmental monitoring has been an important research topic in recent years due to the omnipresence and performance of GNSS signals. In particular, the use of GNSS reflectometry (GNSS-R) in probing sea surface height, wind velocity, salinity, soil moisture, roughness, and snow depth has been realized in several space mission. The TRITON mission from Taiwan is one GNSS-R mission under planning. A key step in onboard GNSS-R signal processing is the determination of the specular reflection point. With the information of the specular reflection point, the GNSS-R processing unit can estimate the propagation delay between the direct line-of-sight signal and the reflected signal so that the correlation processing within the GNSS-R processing unit can be appropriately adjusted. In prior work, the specular reflection point on the spherical Earth is computed by solving a quartic polynomial equation. To deal with ellipsoidal Earth model, an iterative algorithm is often used. To our knowledge, an explicit characterization of the specular reflection point on the ellipsoidal Earth has not been developed. In this paper, an analytic approach is developed to determine the specular reflection point on the ellipsoidal Earth. By exploiting the Snells law and minimal distance property, a sextic polynomial equation is obtained that characterizes the specular reflection point. This leads to an analytic approach in solving the specular reflection point that is not subject to initial condition uncertainty and iteration complexity. To account for the error in the determination of the specular reflection point, two metrics are proposed to depict the dilution of precision with respect to errors of the positions of the transmitter and receiver. Moreover, error ellipse on the surface can be established for the assessment of the accuracy in the determination of the specular reflection point. The results can be used on-board a spaceborne mission with bounded computational load and assured quality.