Mathematical Model and Method of Optimal Placement of Optical-Electronic Systems for Trajectory Measurements of AIr Objects at Test

To study the dynamic propertiesof the new generation of airplanes, helicopters, un-manned aerial vehicles, rocket and artillery weaponsand ammunition at test sites (polygons) use mobilelaser optical-electronic stations of the trajectory ofmeasurement (LOETMS). Each LOETMS providesthe detection of test air objects in the visible andinfrared spectral ranges, their high-precision tracking,measurement and delivery of the parameters of thecoordinates of the movement of air objects in realtime. In order to eliminate systematic and suppressrandom errors of trajectory measurements, LOETMSsare integrated into a unified polygon information-measuring system (UPIMS). Since the cost of eachLOETMS is high enough, when constructing theUPIMS, the problem arises of choosing the minimumnumber of LOETMSs and their location along thetest tracks of the polygon so that the dispersion ofestimates of the parameters of the coordinates ofthe movement of air objects is minimal or at leastless than or equal to a given threshold. The reportprovides a mathematical formulation and solution ofthe two-criterion problem of optimal placement ofLOETMS on the territory of the polygon. The mainattention is paid to the mathematical formulation andthe method of solving the problem of metrologicalcertification of the UPIMS for a fixed number andlocation of LOETMSs along the test tracks of thepolygon. It is shown that the solution of the UPIMSmetrological certification problem is reduced to lin-earizing the non-linear function of random arguments(model of the trajectory of air objects) and calculatingthe dispersions of dependent variables (parametersof motion coordinates) from known dispersions ofindependent variables. The results of solving theproblems of optimal placement of LOETMSs on theterritory of the polygon and metrological certificationof UPIMS are given. The studies are relevant not onlyfor field testing of aircraft, but also of scientific andpractical interest in the construction of monitoringsystems for airspace in the visible and infrared spectralranges and the study of the trajectories of objects ofartificial and natural origin in the Earth’s atmosphere.