Objectives In surveying and cartography, solving geodetic latitude is a common reverse calculation by conformal latitude.
Methods Several different algorithms of reverse solution are studied, including iterative method, series expansion of solving geodetic latitude by difference of conformal latitude and direct algorithm of inverse solution of geodetic latitude with conformal latitude. The calculation formulas of the latter two algorithms are derived by Mathematica. The higher-order coefficient expansion formula are given. At the same time, problems in existing algorithms are analyzed.
Results and Conclusions E xamples results of Lambert conic conformal projection show that the accuracy of the formula derived in this paper can reaches (1×10-7)″-(1×10-8)″. It fully meets the requirements of high precision in surveying and map projection.