Elaboration of a Quasi-Geoid Height Model for the Construction of Linear Structures

One of the main characteristics of linear structures determined during geodetic works is the normal height. The importance and necessity of using satellite geodesic technologies in the construction of linear structures is shown, which will allow for the rapid transition to normal heights when constructing models of quasi-geoid heights. A theoretical justification is given for creating a model of height anomalies of a linear structure based on the use of a network of geodetic reference points, for which geodetic heights are obtained from satellite definitions and normal heights from geometric leveling. The technique of creating a model of height anomalies of a quasi-geoid of a linear structure is given, which includes: introduction of initial data; creation of a regular coordinate grid, selection of a grid step; approximation of the heights of a quasi-geoid; determination of the main statistical characteristics of approximation; calculation of the average square error of determining heights using control points; analysis of the accuracy of approximation and recommendations for choosing an approximation method for use in production. Experimental studies have been carried out to create a model of the heights of a quasigeoid using various approximation methods in Surfer software: cubic splines, the method of polynomial approximation of the second degree and the modified Shepard method. It is shown that the method of polynomial approximation of the 2nd degree is recommended for use in production to create models of the heights of a quasi-geoid of linear structures. The average quadratic errors of creating models by the proposed method do not exceed 5 mm.