On the singular points of the Abelian integral transformation in the GPS/LEO occultation technique

In the inversion terrestrial atmosphere technique the inversion of theAbelian integral is one of the most often used methods for deriving the refractive index profile of the terrestrial atmosphere from GPS/LLEO radio occultation data. There exists the problem of singular point in the Abelian integral. Different methods for solving this problem are discussed and a method of finding an analytic solution of the Abelian integral after a variable transformation is proposed. The accuracies of the various methods are compared by means of simulation calculations.