M.A. Murzova1, V.E. Farber2

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

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

The problem of object tracking using both position and velocity measurements is discussed. The radar sensors measures position and velocity, and both of these measurements are utilized in the Kalman filter. In this work we consider the growing-memory filter and αβλγ-filter. Position and velocity measurements usage leads to the improvement of tracking accuracy. The analytical expressions for lag errors and tracking accuracy of αβλγ-filter and lag errors of growing-memory filter are derived. The gain determination strategy is proposed. This strategy is based on the equality of the tracking accuracy of αβλγ-filter to the tracking accuracy of growing-memory filter in the presence both position and velocity measurements. The tracking accuracy of the filters with and without additional velocity measurements is compared. Besides that the tracking accuracy of the αβλγ-filter is calculated by statistical simulation to ensure their conformity with the obtained analytical expressions.

Murzova M.A., Farber V.E. Tracking accuracy of αβλγ-filter using both position and velocity measurements. Radiotekhnika. 2026. V. 90. № 4. P. 23−35. DOI: https://doi.org/10.18127/j00338486-202604-04 (In Russian)

1. Farber V.E. Osnovy traektornoj obrabotki radiolokacionnoj informacii v mnogokanal'nyh RLS: Uchebnoe posobie. M.: MFTI. 2005 (in Russian).
2. Murzova M.A., Farber V.E. Ocenka dal'nostnoj sostavlyayushchej dvizheniya radiolokacionnyh ob"ektov v RLS s LChM-signalom: Uchebnoe posobie. M.: MFTI. Fiztekh. 2025 (in Russian).
3. Ryabova-Oreshkova A.P. Fil'try s effektivnoj konechnoj pamyat'yu, realizuemye na CVM posredstvom rekurrentnyh formul. Izvestiya AN SSSR. Tekhnicheskaya kibernetika. 1969. № 4. S. ?????? (in Russian).
4. Saho K., Masugi M. Automatic parameter setting method for an accurate Kalman filter tracker using an analytical steady-state performance index. IEEE Access. 2015. V. 3. P. 1919-1930.
5. Murzova M.A., Farber V.E. Skhodimost' α-β-fil'tra dlya razlichnyh znachenij koefficientov skorostnogo smeshcheniya. Radiotekhnika. 2018. № 10. S. 5−17 (in Russian).
6. 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.
7. Trofimenko M.A., Farber V.E. Ocenka vliyaniya nalichiya skorostnoj oshibki pri izmereniyah dal'nosti v RLS s LChM-signalom na granicy ustojchivosti algoritmov ocenki dal'nosti i radial'noj skorosti. Radiotekhnika. 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– 4.
9. Murzova M.A., Farber V.E. Vybor koefficientov sglazhivaniya α-β-fil'tra po kriteriyu minimuma dispersii summarnoj oshibki dlya RLS s LChM-signalom. Radiotekhnika. 2018. № 4. S. 5−16 (in Russian).
10. Kuz'min S.Z. Cifrovaya obrabotka radiolokacionnoj informacii. M.: Sovetskoe radio. 1967 (in Russian).
11. Castella F.R. Tracking accuracies with position and rate measurements. IEEE Transactions on Aerospace and Electronic Systems. 1981. V. AES-17. № 3. P. 433-437.
12. Ekstrand B. Analytical steady state solution for a Kalman tracking filter. IEEE Transactions on Aerospace and Electronic Systems. 1983. V. AES-19. № 6. P. 815-819.
13. Ramachandra K.V. Kalman filtering techniques for radar tracking. New York: Marcel Dekker. 2000.
14. Sudano J.J. The alpha-beta-eta-theta tracker with a random acceleration process noise. Proceedings of the IEEE National Aerospace and Electronics Conference (NEACON2000). Dayton. OH. USA. 10–12 October 2000. P. 165–171.
15. Saho K., Masugi M. Performance analysis and design strategy for a second-order, fixed-gain, position-velocity-measured (α-β-η-θ) tracking filter. Applied Science. 2017. V. 7. № 8. Р. 758.
16. Farina A., Pardini S. Multiradar tracking system using radial velocity measurements. IEEE Transactions on Aerospace and Electronic Systems. 1979. V. AES-15. P. 555-563.
17. Saho K., Masugi M. Performance analysis of α-β-γ-tracking filters using position and velocity measurements. EURASIP Journal on Advance in Signal Processing. 2015. 35.
18. Jahromi M.J., Bizaki, H.K. Target tracking in MIMO radar systems using velocity vector. Journal of Information Systems and Telecommunication. 2014. V. 2. № 3. P. 150–158.
19. Saho K. Steady-state performance analysis of tracking filter using LFM waveforms and range-rate measurement. Mathematical Problems in Engineering. 2018. V. 2018.
20. Gray J.E., Smith-Carroll A.S., Jordan L.A. The solution to the Lyapunov equation in constant gain filtering and some of its applications. Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory. Atlanta. GA. USA. 2004. P. 21-25.
21. Kuz'min S.Z. Osnovy proektirovaniya sistem cifrovoj obrabotki radiolokacionnoj informacii. M.: Sovetskoe radio. 1986 (in Russian).
22. Gray J.E., Smith-Carroll A.S., Murray W.J. What do filter coefficient relationships mean? Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory. Atlanta. GA. USA. 2004. P. 36-40.