M.A. Murzova – Post-graduate Student, Moscow Institute of Physics and Technology (State University); 

Engineer, PJSC «Radiofizika» (Moscow)

E-mail: mariya.trofimenko@phystech.edu

V.E. Farber – Dr.Sc.(Eng.), Professor, Head of Department, PJSC «Radiofizika» (Moscow);  Professor, Moscow Institute of Physics and Technology (State University) E-mail: vladeffar@mail.ru

In this paper, the features of an α-β filter that is typically used for tracking objects are studied. A chirp radar station detects these objects. Chirp radar uses linear frequency modulated (LFM) waveforms that produce biased measurements of target range due to the range-Doppler coupling in the signal. Convergence of α-βfilter is analyzed for different range-Doppler coupling coefficients by the impulse responses of the α-β filter. Tracking accuracies of α-β filter with alternating range-Doppler coupling coefficients and rangeDoppler coupling coefficients of a constant sign are compared. Stability boundaries of α-β filter with alternating range-Doppler coupling coefficients are derived

1. Shirman Ya.D., Manzhos V.N. Teoriya i texnika obrabotki radiolokaczionnoj informaczii na fone pomex. M.: Radio i svyaz’. 1981.
2. Fitzgerald R.J. Effect of Range-Doppler Coupling on Chirp Radar Tracking Accuracy // IEEE Transactions on Aerospace and Electronic Systems. 1974. V. AES-10. № 4. P. 528−532.
3. Farber V.E. Analiz xarakteristik algoritmov opredeleniya parametrov dvizheniya kosmicheskix apparatov po informaczii radiolokaczionny’x sredstv, ispol’zuyushhix zondiruyushhie signaly’ s linejnoj chastotnoj modulyacziej // Kosmicheskie issledovaniya. 1995. T. 33. № 1. S. 31−35.
4. Wong W., Blair W.D. Steady-state tracking with LFM waveforms // IEEE Transactions on Aerospace and Electronic Systems. 2000. V. 36. № 2. P. 701−709.
5. Murzova M.A., Farber V.E. Analiz atmosfernogo fil’tra, adaptirovannogo k nalichiyu skorostnoj oshibki po dal’nosti // Radiotexnika. 2017. № 4. S. 5−14.
6. Trofimenko M.A., Farber V.E. Oczenka vliyaniya nalichiya skorostnoj oshibki pri izmereniyax dal’nosti v RLS s LChM-signalom na graniczy’ ustojchivosti algoritmov oczenki dal’nosti i radial’noj skorosti // Radiotexnika. 2015. № 10. S. 7−16.
7. Jain V., Blair W.D. Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms // IEEE Transactions on Aerospace and Electronic Systems. 2009. V. 45. № 2. P. 765−773.
8. Murzova M.A., Farber V.E. The α-β Filter for Tracking Maneuvering Objects with LFM Waveforms // IEEE IVth International Conference on Engineering and Telecommunication. 2017. P. 104−107.
9. Murzova M.A. Oczenka vliyaniya skorostnoj oshibki po dal’nosti na tochnostny’e xarakteristiki fil’tra pervogo poryadka // Materialy’ XI Vseros. nauchno-texnich. konf. «Radiolokacziya i radiosvyaz’». 2017. S. 57−61.
10. Murzova M.A., Farber V.E. Vy’bor koe’fficzientov sglazhivaniya α-β fil’tra po kriteriyu minimuma dispersii summarnoj oshibki dlya RLS s LChM-signalom // Radiotexnika. 2018. № 4. S. 5−16.
11. Trofimenko M.A., Farber V.E. Influence of range-Doppler coupling on the tracking stability of reentering space objects // IEEE International Conference on Engineering and Telecommunication. 2015. P. 40−44.
12. Trofimenko M.A., Farber V.E. Oczenka vliyaniya skorostnogo smeshheniya v radiolokaczionny’x stancziyax s LChM-signalom na graniczy’ ustojchivosti soprovozhdeniya vxodyashhix v atmosferu kosmicheskix ob’‘ektov // Trudy’ MFTI. 2015. T. 7. № 2. S. 156−166.
13. Trofimenko M.A., Farber V.E. Oczenka vliyaniya skorostnoj oshibki na ustojchivost’ fil’trov vtorogo poryadka// Radiotexnika. 2016. № 4. S. 5−17.
14. Farber V.E. Osnovy’ traektornoj obrabotki radiolokaczionnoj informaczii v mnogokanal’ny’x RLS: Ucheb. posobie. M.: MFTI. 2005.
15. Ryabova-Oreshkova A.P. Fil’try’ s e’ffektivnoj konechnoj pamyat’yu, realizuemy’e na CzVM posredstvom rekurrentny’x formul // Izvestiya AN SSSR. Texnicheskaya kibernetika. 1969. № 4.
16. Tuzlukov V. Signal processing in radar systems. Tailor & Francis Group. 2013.
17. Kalata Paul R. The Tracking Index: A Generalized Parameter for α-β and α-β-γ Target Trackers // IEEE Transactions on Aerospace and Electronic Systems. 1984. V. AES-20. № 2. P. 174−182.
18. Mexra R.K. Sravnenie neskol’kix nelinejny’x fil’trov dlya sistemy’ slezheniya za vxodyashhimi v atmosferu letatel’ny’mi apparatami // Voprosy’ raketnoj texniki. 1973. № 1. S. 3−23.
19. Farber V.E. Analiz xarakteristik algoritmov oczenki e’ffektivnosti ae’rodinamicheskogo tormozheniya vxodyashhix v atmosferu kosmicheskix ob’‘ektov // Radiotexnika. 2007. № 10. S. 81−87.
20. Goroxov A.V., Farber V.E. Reshenie zadachi ob optimal’nom by’strodejstvii nablyudeniya za snizhayushhimisya v atmosfere kosmicheskimi ob’‘ektami // Izvestiya RAN. Teoriya i sistemy’ upravleniya. 1992. № 2. S. 197−205.
21. Volochkov E.B. Izmerenie dal’nosti LChM signalom pri neizvestnoj doplerovskoj chastote // Radiotexnika. 1991. № 11. S. 17−19.
22. Eli Brookner. Tracking and Kalman Filtering Made Easy. John Wiley & Sons, Inc. 1998.
23. Kuz’min S.Z. Osnovy’ proektirovaniya sistem czifrovoj obrabotki radiolokaczionnoj informaczii. M.: Sov. radio. 1986.
24. Blair W.D. Fixed-gain, two-stage estimators for tracking maneuvering targets. Naval Surface Warfare Center, Dahlgren Divison, Dahlgren, VA 22448-5000. 1992.