Mathematical models’ analysis of rectangular coordinates’calculation in the expanded zones of Gauss Kruger conformal projection

Abstract

This article contains analysis of mathematical models built depending on longitude difference degree, that are used for calculating planimetric rectangular coordinates in accordance with geodesic coordinates in the longitudinally expanded zones of Gauss Kruger conformal projection. Coefficients of these expansions are measured by successive differentiation or by recurrence formula. Disadvantages of performed coordinate mathematical transformations using schemes recommended by Federal Agency on Technical Regulating and Metrology and Euro-Asian Council for Standardization, Metrology and Certification GOST 32543-2013 for calculations in18 grade meridian zones with millimetric degree of accuracy are pointed out. Two optimal schemes with high convergence rate are suggested for calculating meridian arc length. Ineffectiveness of using formal power series for large grid zones is proved. Practical necessity of efficient schemes’ creation for calculating coordinates in accordance with any ellipsoid’s characteristics.

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