Optimization of Complex Function Expansions for Gauss-Krüger Projections

Abstract

Compared with complex and lengthy Gauss-Krüger projection series expansions and real number expressions, we improve the complex function representation of Gauss-Krüger projections and rewrite them into the “multiple Angle form”, “exponential form”, and “double Angle form”. The coefficients were expanded in the power series based on the first eccentricity e and the third flattening n, respectively, and the truncation difference was analyzed when expanded to different orders to obtain the simplified practical formulas for each form on the premise of meeting the accuracy requirements of geodesy. Through numerical analysis, the computational efficiency of the forward and inverse solutions of the Gauss-Krüger projection is analyzed, which shows the superiority of the “double Angle form”. Through the above measures, the expressions for forward and inverse solutions of the Gauss-Krüger projection are obtained, meeting the accuracy requirements with a higher computational efficiency and a more concise form.