Surface refractive index field estimation from multiple radars

Retrieval of surface layer refractivity via the method of Fabry et al. (1997) is considered. A mathematical framework is constructed, and signal processing algorithms are derived that facilitate refractivity retrieval from the returns from multiple radars viewing a common geographical area. In particular, an approximate discrete model is derived to relate the measured phases to the surface layer refractivity fields, and a modified least squares estimation algorithm is then proposed for the resulting, often ill-conditioned, inversion problem. Because the measurement technique is subject to modulo 2 pi uncertainties which impact retrievals, a novel algorithm which jointly estimates the unwrapped phases and refractive index (RI) field is also provided. Numerical results indicate the effectiveness of the derived algorithms in both the single- and multiple-radar cases, as well as clearly establishing that having multiple views of the same geographical area from separate radars provides for significant improvement of the RI field estimates.