The variations of the sky brightness are defined mainly by the volatility of the aerosol part of the atmosphere, which possesses strong scattering ability. Theoretical study of the radiation transfer problems is impossible without knowing it's optical parameters. In this paper the problem of reconstructing the aerosol scattering matrix by using observations of polarized radiation in the solar almucantar, i.e., in various directions that make the same angle with the zenith as the line of sight to the Sun, is considered. Several iterative algorithms for estimation of the scattering indicatrix are constructed in -. In these algorithms the indicatrix is successively refining by mathematical modeling based on the information of the angle distribution of the radiation intensity on the underlying surface and under the assumption that the contribution of the single-scattered radiation is rather large. In this work the predictor-corrector modification of the method is suggested, it allows to find more precise approximation of the scattering indicatrix and of two other scattering matrix elements responsible for the polarization of the radiation. In order to numerically substantiate the convergence of these methods, an algorithm of Jacobi matrices calculation for the iteration operators of the methods was developed, and calculations were carried out for various parameters of the atmosphere. Also a study of the influence of measurement errors on the reconstruction of the scattering matrix was carried out. Test calculations showed the stability of algorithms to errors in the initial data.