Real-Valued Solutions to an Inverse Fresnel Problem in GNSS-R

摘要

Global Navigation Satellite System Reflectometry can be used to derive information about the composition or the properties of ground surfaces, by analyzing GPS signals reflected by the ground. The received power of the signal is proportional to the modulus of the perpendicular and parallel polarization Fresnel coefficients. These coefficients depend on the incidence angle θ, and on the ground's dielectric constant ε, which provides information on the composition and properties of the ground. Thus, one has to solve the inverse problem, consisting of finding the value of ε from the known value of θ and the measured values of the Fresnel reflection coefficients. In general, ε is a complex number; in some cases (e.g., for non-dispersive soils), the imaginary part of ε can be neglected, and a real value of ε is sought. We discuss the mathematical solvability of a particular type of inverse Fresnel problem for real unknown ε.