Mathematical Model of Complex Radio-Location Portrait of Aim with a Final Number of Bright Points

Introduction. To form radio-location portrait (RLP) of aim - in the structures and algorithms of modern radar sets (RS), methods based on high identification signals are used. The hereinabove was established by the research analysis concerning the synthesis of RLP and existing approaches to the identification of unknown systems by adaptive methods. These methods imply high requirements for transmitters and prevents their implementation in pulse RS with low-frequency oscillators. This problem can be solved in another way, fit for use in RS with low-stability transmitters. In this case, the aim is regarded as a certain unknown system that brings certain known distortions in the deterministic signal that correspond to its transient response. At active location, the signal is fully known on both the transmitting and receiving sides (probing and echo signals), while spreading in a homogeneous medium, non-linear phase-frequency distortions are not introduced into it. When the adaptive filtering algorithm is applied, its transient feature is formed, to which the optimal weight vector of the synthesized adaptive filter will correspond. Thus, forming RLP in each probing period, it is possible to perform single-angle identification of aims and to realize coherent processing of echo signals, even when using incoherent sources of ultra-high frequencies of probe signals. This allowed us to formulate the purpose of the article, which is to increase the coherence of processing echo signals in pulsed RS with incoherent sources of probing signals. In order to achieve this research goal, the paper analyzes the existing methods of radio-location portrait of aim formation, on the basis of which mathematical models of signals reflected from aims with complex geometric surface shape are exploited, on which simulation work of the developed algorithms is carried out. Theoretical results. The mathematical model of the complex of radio-location portrait of aim image with a finite number of «bright points» has been improved pursuant to the analysis of existing methods of formation of radio-location portrait of aim and identified inconsistencies of existing methods with the modern requirements regarding the use in incoherent pulse radar stations. The model differs from the existing ones as it allows to take into account the amplitude-phase transformations of a complex circumflex of probing signal when reflected from a aim with a complex geometric shape in the azimuthal and longitudin