On improving the accuracy of analytical and numerical methods ofgeodesic and cartometric operations

Purpose of this work is to determine and justify the use of analytical and numerical geodetic and cartometric methods on the reference ellipsoid, as well as their calculation accuracy in the geographic information environment. Methodology. The research compiled a register of geodetic and cartometric methods used in geodetic practice and implemented in modern geographic information systems. Standard tools in GIS often use approximate numerical methods, which affects the accuracy of models of geospatial objects in the GIS environment. Therefore, we have analysed and established for each operation of geodetic and cartometric methods a mathematical model that determines a particular cartometric property with maximum accuracy either by analytical or numerical methods with the number of terms in the binomial series of 6 or more. Results. The author proposed 10 operations of the geodetic method and 3 operations of the cartometric method, for which mathematical models and their accuracy were established and substantiated with their corresponding implementation in the MATLAB v. R2018a. The defined list of geodetic and cartometric operations made it possible to move away from the classification of distance lengths that influenced the further use of certain surfaces (map projection plane, sphere, spheroid, or reference ellipsoid) and mathematical models of operations. The presented mathematical models allow performing the relevant geodetic and cartometric methods with maximum accuracy using modern computer technologies. The mathematical models of geodetic and cartometric methods are investigated, which have practically no limitations for achieving the required accuracy, especially for large and ultra-large distances. The scientific novelty of the research is to define and justify a clear list of mathematical models of numerical and analytical geodetic and cartometric methods instead of cartometric methods on the map and standard methods of instrumental GIS; using the surface of the reference ellipsoid, and not just cartographic projections, spheroid or sphere. The practical significance of the research lies in the use of numerical and analytical geodetic and cartometric methods that significantly increase the accuracy of operations in these works, as well as in the creation/updating of digital topographic maps, navigation and route planning, etc. The research results can be concluded that well-founded mathematical models will ensure an increase in the accuracy of computational operations taking into account the curvature of the Earth in all sectors and areas of the economy, which will affect the quality of accounting and monitoring of relevant objects, integration and geospatial analysis of heterogeneous geospatial data, improve the quality (topological consistency) of geospatial data, etc