MATHEMATICAL MODEL AND METHOD OF OPTIMAL PLACEMENT OF OPTICAL-ELECTRONIC SYSTEMS FOR TRAJECTORY MEASUREMENTS OF AIR OBJECTS AT TEST

Abstract

To study the dynamic properties of the new generation of airplanes, helicopters, un- manned aerial vehicles, rocket and artillery weapons and ammunition at test sites (polygons) use mobile laser optical-electronic stations of the trajectory of measurement (LOETMS). Each LOETMS provides the detection of test air objects in the visible and infrared spectral ranges, their high-precision tracking, measurement and delivery of the parameters of the coordinates of the movement of air objects in real time. In order to eliminate systematic and suppress random errors of trajectory measurements, LOETMSs are integrated into a unified polygon information- measuring system (UPIMS). Since the cost of each LOETMS is high enough, when constructing the UPIMS, the problem arises of choosing the minimum number of LOETMSs and their location along the test tracks of the polygon so that the dispersion of estimates of the parameters of the coordinates of the movement of air objects is minimal or at least less than or equal to a given threshold. The report provides a mathematical formulation and solution of the two-criterion problem of optimal placement of LOETMS on the territory of the polygon. The main attention is paid to the mathematical formulation and the method of solving the problem of metrological certification of the UPIMS for a fixed number and location of LOETMSs along the test tracks of the polygon. It is shown that the solution of the UPIMS metrological certification problem is reduced to lin- earizing the non-linear function of random arguments (model of the trajectory of air objects) and calculating the dispersions of dependent variables (parameters of motion coordinates) from known dispersions of independent variables. The results of solving the problems of optimal placement of LOETMSs on the territory of the polygon and metrological certification of UPIMS are given. The studies are relevant not only for field testing of aircraft, but also of scientific and practical interest in the construction of monitoring systems for airspace in the visible and infrared spectral ranges and the study of the trajectories of objects of artificial and natural origin in the Earth’s atmosphere.