M.A. Murzova1, V.E. Farber2

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

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

This paper mainly considers a growing-memory filter for tracking an object moving with constant acceleration and detected by chirp radar. Chirp radars employ linear frequency modulated (LFM) waveforms for object tracking which yields a displacement of measured position from a true range of moving objects. This effect may enable better track accuracy in range. The second order degree polynomial describes coordinates law for a constantly accelerating maneuvering object. The issues of lag errors, covariance matrix of the filtered state vectors, impulse responses and Kalman gains are discussed. For example, the growing-memory filter is most often used for initiating track. The growing-memory filter is derived in recursive and non-recursive form based on least-squares. It is shown that the growing-memory filter estimating a true object range (with the range-Doppler coupling coefficient) can be represented by the growing-memory filter estimating a biased object range (without the range-Doppler coupling coefficient) and compensating the estimated biased range by the estimated the range-Doppler coupling error. Expressions giving an interrelation between lag errors, covariance matrix of the filtered state vectors, impulse responses and Kalman gains of growing-memory filters estimating true and biased range of moving objects are derived.

Murzova M.A., Farber V.E. Influence of the range Doppler coupling error on the characteristics of second-order filters. Radiotekhnika. 2023. V. 87. № 9. P. 5−23. DOI: https://doi.org/10.18127/j00338486-202309-01 (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. 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).
3. Farber V.E. Osnovy traektornoj obrabotki radiolokacionnoj informacii v mnogokanal'nyh RLS: Ucheb. posobie. M.: MFTI. 2005. (in Russian).
4. Livshic N.A., Farber V.E., Shapiro E.I. Reshenie zadachi nelinejnoj fil'tracii pri nalichii neinformativnyh rezul'tatov nabljudenij. Radiotehnika i jelektronika. 1984. T. 29. № 7. S. 1362-1367 (in Russian).
5. Farber V.E. Sravnitel'nyj analiz form zapisi kvazioptimal'nyh algoritmov fil'tracii pri nalichii anomal'nyh i neinformativnyh rezul'tatov izmerenij. Izvestija Rossijskoj akademii nauk. Teorija i sistemy upravlenija. 1992. № 3. S. 71-77 (in Russian).
6. Farber V.E. Analiz harakteristik algoritmov opredelenija parametrov dvizhenija kosmicheskih apparatov po informacii radiolokacion-
   nyh sredstv, ispol'zujushhih zondirujushhie signaly s linejnoj chastotnoj moduljaciej. Kosmicheskie issledovanija. 1995. T. 33. № 1. S. 31−35 (in Russian).
7. 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. № 10. S. 7−16 (in Russian).
8. 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.
9. 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).
10. 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.
11. 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).
12. 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.
13. Saho K. Steady-State Performance Analysis of Tracking Filter Using LFM Waveforms and Range-Rate Measurement. Mathematical Problems in Engineering. 2018. V. 2018.
14. 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.
15. 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. № 4. S. 5−16. DOI: 10.18127/j00338486-201904-01 (in Russian).
16. 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).
17. Murzova M.A., Farber V.E. Analiz atmosfernogo fil'tra, adaptirovannogo k nalichiju skorostnoj oshibki po dal'nosti. Radiotehnika. 2017. № 4. S. 5−14 (in Russian).
18. Trofimenko M.A., Farber V.E. Ocenka vlijanija skorostnoj oshibki na ustojchivost' fil'trov vtorogo porjadka. Radiotehnika. 2016. № 4. S. 5−17 (in Russian).
19. Rjabova-Oreshkova A.P. Fil'try s jeffektivnoj konechnoj pamjat'ju, realizuemye na CVM posredstvom rekurrentnyh formul. Izvestija
    AN SSSR. Tehnicheskaja kibernetika. 1969. № 4 (in Russian).
20. Kuz'min S.Z. Osnovy proektirovanija sistem cifrovoj obrabotki radiolokacionnoj informacii. M.: Sovetskoe radio. 1986 (in Russian).