Radar Method for Estimating the Average Size of a Swarm of Space Debris

The task of ground-based radar monitoring of single small-sized objects of space debris (SD) with a size of about 10 cm or less even in low-Earth orbits is extremely difficult due to the requirements for high energy and radar resolution. However, the appearance of small-sized objects is associated with the destruction of larger fractions of SD and, therefore, as a rule, these are not single objects. Therefore, it is proposed to pay attention to monitoring not a single small element of SD, but a “swarm” of such small-sized objects. As a first approximation, we can limit ourselves to determining the values of the parameters characterizing the structure of the swarm of small-sized SD objects “on average”. The work uses a multi-point model of an extended group target with random statistically independent partial reflectors that fill a certain region of space with small-sized objects randomly distributed over the volume of the SD swarm. In the radial direction, the distribution of small-sized SD fractions corresponds to the normal law with respect to some average value located at the orbital altitude H. In the longitudinal direction, the distribution of SD elements is equiprobable. It is proposed to estimate the average sizes of the SD swarm by the variance of the altitude (radial) spread of small-sized SD elements, which is determined by the mutual two-frequency correlation function of radar echo signals reflected from the swarm of small-sized SD fractions. It is shown that with a high angular resolution of the ground-based radar antenna operating in the beam-park mode of vertical sounding, the required sensitivity to the radial extent of the cloud of small-sized SD fractions is achieved.