Разработка методики определения параметров преобразования систем координат на основе метода нелинейного программирования первого порядка при сопровождении строительства зданий и сооружений

Abstract

Objective: to analyze the advantages and disadvantages of existing nonlinear programming methods for solving problems of coordinate system transformation (SC). To consider the need to convert the coordinates of points from local SC to urban. To determine the possibility of using the generalized reduced gradient method to transform the coordinates of points located both at a distance between points of about 150 m and at a distance of about 1.5 km. Methods: the theoretical foundations of this method are revealed. Information is provided on the procedure for performing transformations of coordinate systems. The algorithm of the generalized reduced gradient (OPG) method is given. A study has been conducted on the transformation of coordinate systems of starting points from SK1 to SK2 using the OPG method. The requirement for the value of the mean square error (SQR) of determining the position of the starting points when converting them from one coordinate system to another is justified. Results: a check was performed on the possibility of applying the obtained transformation parameters to recalculate the coordinates of points from the local SC to the city SC. Based on the verification of the obtained transformation parameters, the possibility of using them to recalculate the coordinates of points located at a distance of about 1,5 km was revealed. The need for additional research on the application of the generalized reduced gradient method to solve coordinate system transformation problems has been identified. Practical significance: the necessity of transformation of coordinate systems in the field of construction of buildings and structures is shown. The possibility of applying the generalized reduced gradient method to transform coordinate systems is presented. Using this method will allow you to convert the coordinates of the starting points from the local coordinate system to the coordinate system of the city with geodetic support for the construction of buildings and structures of various categories.