V.E. Farber1, M.A. Murzova2

1,2 PJSC “Radiofizika” (Moscow, Russia)

1 Moscow Institute of Physics and Technology (National Research University) (Dolgoprudny, Russia)

1 vladeffar@mail.ru; 2 mariya.trofimenko@phystech.edu

In this paper, features of a tracking filter using linear frequency modulated (LFM) waveforms are studied. The use of LFM waveforms results in that the range measurements of moving objects are biased due to the range-Doppler coupling in the signal. Thus, the range-Doppler coupling error is taken into account in developing tracking filter.

An influence of diffusion process (or process noise) parameters on the tracking accuracies of diffusion filter is studied. The diffusion filter is defined as a three-state Kalman filter with introduction of additional term into covariance matrix of extrapolation errors. Besides that, an observation matrix includes a range-Doppler coupling coefficient. The additional term is determined by transition and covariance matrices of diffusion process. The expressions for transition and covariance matrices are derived from the equivalence of tracking accuracies of the diffusion filter in steady state and a fixed memory least squares filter.

Murzova M.A., Farber V.E. Influence of the range Doppler coupling error on the characteristics of second-order diffusion filters.
Radiotekhnika. 2024. V. 88. № 4. P. 5−23. DOI: https://doi.org/10.18127/j00338486-202404-01 (In Russian)

1. Shirman Ja.D., Manzhos V.N. Teorija i tehnika obrabotki radiolokacionnoj informacii na fone pomeh. M.: Radio i svjaz'. 1981 (in Russian).
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. Mehra R.K. Sravnenie neskol'kih nelinejnyh fil'trov dlja sistemy slezhenija za vhodjashhimi v atmosferu letatel'nymi apparatami. Voprosy raketnoj tehniki. 1973. № 1. S. 3-23 (in Russian).
4. Konovalov A.A. Osnovy traektornoj obrabotki radiolokacionnoj informacii. V 2-h chastjah. Ch. 2. SPb: Izd-vo SPbGJeTU «LJeTI». 2014 (in Russian).
5. Li X. R., Jilkov V. P. Survey of maneuvering target tracking. Part I. Dynamic models. IEEE Transactions Aerospace Electronic Systems. 2003. V. 39. № 4. P. 1333-1364.
6. Rjabova-Oreshkova A.P. Fil'try s jeffektivnoj konechnoj pamjat'ju, realizuemye na CVM posredstvom rekurrentnyh formul. Izvestija AN SSSR. Ser. Tehnicheskaja kibernetika. 1969. № 4 (in Russian).
7. Volochkov E.B. Izmerenie dal'nosti LChM-signalom pri neizvestnoj doplerovskoj chastote. Radiotehnika. 1991. T. 55. № 11. S. 17-19 (in Russian).
8. Murzova M.A., Farber V.E. Shodimost' α-β-fil'tra dlja razlichnyh znachenij kojefficientov skorostnogo smeshhenija. Radiotehnika. 2018. № 10. S. 5−17. DOI: 10.18127/j00338486-201810-01 (in Russian).
9. Murzova M.A., Farber V.E. The α-β Filter for Tracking Maneuvering Objects with LFM Waveforms. 2017 IVth International Conference on Engineering and Telecommunication. IEEE. 2017. P. 104-107.
10. Murzova M.A., Farber V.E. Vybor kojefficientov sglazhivanija α-β fil'tra po kriteriju minimuma dispersii summarnoj oshibki dlja RLS s LChM-signalom. Radiotehnika. 2018. № 4. S. 5−16 (in Russian).
11. Farber V.E. Analiz harakteristik algoritmov opredelenija parametrov dvizhenija kosmicheskih apparatov po informacii radiolokacionnyh sredstv, ispol'zujushhih zondirujushhie signaly s linejnoj chastotnoj moduljaciej. Kosmicheskie issledovanija. 1995. T. 33. № 1. S. 31−35 (in Russian).
12. Trofimenko M.A., Farber V.E. Influence of range-Doppler coupling on the tracking stability of reentering space objects. 2015 International Conference on Engineering and Telecommunication. IEEE. 2015. P. 40-44.
13. Trofimenko M.A., Farber V.E. Ocenka vlijanija skorostnogo smeshhenija v radiolokacionnyh stancijah s LChM-signalom na granicy ustojchivosti soprovozhdenija vhodjashhih v atmosferu kosmicheskih ob’ektov. Trudy MFTI. 2015. T. 7. № 2. S. 156−166 (in Russian).
14. Murzova M.A., Farber V.E. Analiz atmosfernogo fil'tra, adaptirovannogo k nalichiju skorostnoj oshibki po dal'nosti. Radiotehnika. 2017. T. 81. № 4. S. 5−14 (in Russian).
15. Murzova M.A. Ocenka vlijanija skorostnoj oshibki po dal'nosti na tochnostnye harakteristiki fil'tra pervogo porjadka. Materialy XI Vserossijskoj nauchno-tehnicheskoj konferencii «Radiolokacija i radiosvjaz'». 2017. S. 57-61 (in Russian).
16. Trofimenko M.A., Farber V.E. Ocenka vlijanija nalichija skorostnoj oshibki pri izmerenijah dal'nosti v RLS s LChM-signalom na granicy ustojchivosti algoritmov ocenki dal'nosti i radial'noj skorosti. Radiotehnika. 2015. T. 79. № 10. S.7−16 (in Russian).
17. 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.
18. Saho K. Steady-State Performance Analysis of Tracking Filter Using LFM Waveforms and Range-Rate Measurement. Mathematical Problems in Engineering. 2018. V. 2018.
19. 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.
20. Trofimenko M.A., Farber V.E. Ocenka vlijanija skorostnoj oshibki na ustojchivost' fil'trov vtorogo porjadka. Radiotehnika. 2016. T. 80. № 4. S. 5−17 (in Russian).
21. Murzova M.A., Farber V.E. Sravnenie sposobov kompensacii skorostnoj oshibki po dal'nosti v algoritmah ocenki dal'nosti i radial'noj skorosti. Radiotehnika. 2019. T. 83. № 4. S. 5−18. DOI: 10.18127/j00338486-201904-01 (in Russian).
22. Murzova M.A. Vybor kojefficientov diffuzii dlja fil'tra Kalmana s kompensaciej skorostnoj oshibki po dal'nosti. Radiotehnika. 2019. T. 83. № 10. S. 32−42. S. 5−18. DOI: 10.18127/j00338486-201910(15)-06 (in Russian).
23. Murzova M.A., Farber V.E. Ocenka vlijanija skorostnoj oshibki na harakteristiki fil'trov 2-go porjadka s rastushhej pamjat'ju. Radiotehnika. 2023. T. 87. № 9. S. 5-23. DOI: https://doi.org/10.18127/j00338486-202309-01 (in Russian).
24. Farber V.E. Osnovy traektornoj obrabotki radiolokacionnoj informacii v mnogokanal'nyh RLS: Ucheb. posobie. M.: MFTI. 2005 (in Russian).
25. Kuz'min S.Z. Osnovy proektirovanija sistem cifrovoj obrabotki radiolokacionnoj informacii. M.: Sovetskoe radio. 1986 (in Russian).
26. Eli Brookner. Tracking and Kalman Filtering Made Easy. John Wiley & Sons, Inc. 1998.
27. Barnett S. Simplification of the Lyapunov matrix equation A'PA - P= -Q. IEEE Transactions on Automatic Control. 1974. V. AC-19. P. 446–447.