V.K. Klochko – Dr.Sc.(Eng.), Associate Professor, Professor, 

Department «Automatic and Information Technologies in Control», Ryazan State Radio Engineering University named after V.F. Utkin

E-mail: klochkovk@mail.ru

Cong Hoai Nguyen – Post-graduate Student, 

Department «Radio Engineering Devices», Ryazan State Radio Engineering University named after V.F. Utkin E-mail: nguyenconghoaikqh31891@gmail.com

Proposed is a mathematical model of multi-position Doppler observation system consisting of two or more mutually remote and space-oriented radio receivers with antenna arrays and external transmitter arranged arbitrarily in space. The system operates in «Silent Sentry System» mode to detect and evaluate spatial coordinates of moving objects group resolved by Doppler frequency. The developed model differs from systems of TDA (Time Differential of Arrive) type by its applicability in mobile systems of low distance for moving objects detection, easily and quickly deployed on unfamiliar terrain, absence of time moments fixation of signals reception, taking into account Doppler frequency shift and simple computational procedure of solving the system of linear equations. Two approaches to solving the problem of detection and determination of spatial coordinates are considered in the work. Accordingly, two algorithms have been developed. 

The first algorithm determines angular coordinates of moving objects resolved by Doppler frequency by phase method in angular coordinate systems of each receiver. Using angular coordinates there basis vectors of directions to objects are defined. The second algorithm detects a group of objects and finds their spatial coordinates by distributing the set of basis vectors found by the first algorithm by belonging to objects using the criterion of conjugation of vectors in stereo pairs. Analytical study of coordinates estimates accuracy is given. An approach to finding a velocity vector of each detected object based on solving a system of linear equations taking into account Doppler frequency shifts in stereo pairs of receivers is proposed. It is shown that in conditions of model experiment errors of objects spatial position estimations at a range of 1000 m are 0.5 m. Analytically it is proved that these errors can be reduced by several times due to selection of directions to objects taking into account orthonality.

The results of the work can be used for detection of moving objects and their trajectory tracking in multi-position radio systems of low distance operating in «Silent Sentry System» mode.

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11. Klochko V.K., Gudkov S.M., Nguen K.Kh. Sravnitelnyi analiz metodov otsenivaniya koordinat ob’ektov v passivnoi sisteme radiovideniya. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2018. № 2. № 64. S. 23−28. DOI: 10.21667/1995-45652018-64-2-23-28. (in Russian)
12. Klochko V.K., Nguen K.Kh. Algoritmy traektornogo soprovozhdeniya neskolkikh ob’ektov v passivnykh sistemakh radiovideniya. Radiotekhnika. 2019. № 6. S. 168−173. DOI: 10.18127/j00338486-201905(6)-18. (in Russian)