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

Анотація

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.