MATHEMATICAL-ALGORITHMIC ADAPTIVE FOUNDATION FOR SOLVING THE PROBLEM OF DETERMINING OF THE PARAMETERS OF AN INACCESSIBLE OBJECT

Abstract

The present study deal with the development of the combined geometrical model for the most general location of an investigated component of the reconstructed object with respect to the location of the geodetic equipment and, in a complex, mathematical foundations for the processing of experimental data obtained in the determination of the parameters of an inaccessible point of an object. The common issues are revealed and essential steps towards their resolutions are identified. The essence of the problem is in the unavoidable contradiction between a need of obtaining the exact value of the determined parameter and an error involved in any measurement. The objective of the present work is to develop a combined geometrical model and mathematical foundations for the processing of experimental data of the determination of the parameters of an inaccessible point of an object corresponding to this model. The objective is achieved in three steps: 1. Development of a combined geometrical model for the most general relative location of the location of the geodetic equipment and the investigated object. 2. Development of a structure of mathematical foundations for the processing of experimental data obtained in the determination of parameters of an inaccessible point using the developed three-dimensional geometrical model with crossed directional rays. 3. Development of the content of each structural block of the developed mathematical foundations. Efficiency of the developed combined geometrical model is in verified in the course of the solution of the problem of determination of coordinates of two inaccessible points C and C', located on a perpendicular to horizontal plane П₁. The mathematical foundations structurally consist of seven blocks.

The content of each structural block corresponds to the developed optimizing analytical model of determination of domain (area) of values of the parameters of an inaccessible point of an object.

Keywords: an object, point, extremum, directional ray, collimating ray, coordinates of a point, geometrical model, analytical model.