K.K. Vasilev – Dr. Sc. (Eng.), Professor, Head of Department «Telecommunications», Ulyanovsk State Technical University
N.V. Luchkov – Ph. D. (Eng.), Leading Research Engineer, FRPC OJSC «RPA «Mars» (Ulyanovsk)
O.V. Saverkin – Post-graduate Student, Ulyanovsk State Technical University; Research Engineer, FRPC OJSC «RPA «Mars» (Ulyanovsk)
The results of mathematical modeling of three algorithms of trajectory filtration based on the use of Kalman linear and nonlinear filters are presented. The nonlinear character of the data is related to observations of radar marks from the target in spherical coordinates in the construction of its trajectory in a rectangular system. It is established that a nonlinear filter and a filter that takes into account the correlation of the errors of the linearized observations have a close efficiency. At the same time, the nonlinear filter has more computational costs. The mathematical modelling of operation two-coordinate radar is carried out. The results of simulation of the proposed algorithms have shown that Kalman nonlinear and linear filters are more effective if a target moves along one of the axes more quickly, at that linear filter has less computational costs. However, the use of the simplest linear filter with separate estimation can lead to significant errors. The standard deviation of these errors depends on the difference between the speed values of each axis: the greater the speed of the target's motion along one of the axes, the greater the standard deviation. At the same time if the target has close speeds along both of the axes, all of three algorithms have similar efficiency, at that the simplest linear filter has the smallest computational cost. The conclusions reached in the course of the research are described; the advantages and disadvantages of the proposed algorithms are described. Based on the results obtained, we can conclude that the nonlinear filter is more appropriate for radar data processing. However, in conditions of limited computing resources, it is preferable to use a linear filter that takes into account the correlation of the errors of the linearized observations. Furthermore, such approach can have efficiency close to the nonlinear filter.
The article is recommended for postgraduate students and engineers whose work is related to the statistical processing of radar in-formation. The results of the simulation will allow the researchers to carry out further studies on the optimization of existing methods for processing radar information at various levels.
- Kazarinov Yu.M. i dr. Radiotexnicheskie sistemy': uchebnik dlya studentov vuzov / Pod red. Yu.M. Kazarinova. M.: Izdatel'skij czentr «Akademiya». 2008. 592 s.
- Bar-Shalom Y., Li X.R. Estimation and Tracking: Principles, Techniques, and Software. Artech House, Boston, MA. 1993. 30 p.
- Sejdzh E'.P., Mels Dzh. Teoriya oczenivaniya i ee primenenie v svyazi i upravlenii: Per. s angl. / Pod red. B.R. Levina. M.: Svyaz'. 1976. 495 s.
- Konovalov A.A. Osnovy' traektornoj obrabotki radiolokaczionnoj informaczii. Ch. 1. SPb.: Izd-vo SPbGE'TU «LE'TI». 2013. 164 s.
- Vasil'ev K.K. Bajesovskoe razlichenie i oczenivanie sluchajny'x posledovatel'nostej // Radiotexnika i e'lektronika. 1985. T. 30. № 3. S. 476−485.
- Vasil'ev K.K. Optimal'naya obrabotka signalov v diskretnom vremeni: Ucheb. posobie. M.: Radiotexnika. 2016. 288 s.
- Vasil'ev K.K., Luchkov N.V. Traektornaya obrabotka na osnove nelinejnoj fil'traczii // Avtomatizacziya proczessov upravleniya. 2017. № 1(47). S. 4−9.
- Saverkin O.V. O nekotory'x princzipax sovmestnoj obrabotki danny'x ot neskol'kix radiolokaczionny'x stanczij // Integrirovanny'e sistemy' upravleniya. Ul'yanovsk: FNPCz AO «NPO «Mars». 2016. S. 182−187.