Use of instrumental variables methods in trajectory measurements’ problems

Abstract

Possibilities of theinstrumental variables method using to improve the matrix properties of algebraic equations system are shown in the article. The problem of trajectory measurements from a network of ground-based, no-demand measuring stations using GLONASS navigation satellites is considered. The need to increase information content of trajectory measurements is especially important for trajectory measurements in the southern hemisphere of the Earth with a small number of measuring stations. The numerical experiment results with the simulation modeling use of trajectory measurements of the navigation satellite movement from two and three request-free measuring stations with geometric constraints are presented. The possibility of the measurements’ information content increasing from such base stations using the instrumental variables method is shown. Comparison of an indicator of the trajectory measurements informativenessis made according to the degree of the matrix conditionality of the algebraic equations system being solved. Based on the numerical experiment results, it isconsidered thepossibility to increase the information content of trajectory measurements from a network of non-query measuring stations with geometric constraints, with the instrumental variables involvement in the method processing. A quantitative estimate of the increase in information content was obtained in the form of a decrease in the condition number of the system matrix being solved by more than one order of magnitude. In the future, the research is predicted on the possibility of the trajectory measurements informativeness increasing for various basic functions used as instrumental variables, and their effect on the geometric constraints reducing an uneven network of measuring stations.