Вероятностный анализ требований к угломерной системе обнаружения смещения эллиптической орбиты

Юрий [Yuriy] Александрович [A.] Горицкий [Goritskiy]; Давид [David] Георгиевич [G.] Тигетов [Tigetov]; Екатерина [Ekaterina] Владимировна [V.] Китова [Kitova]

doi:10.24160/1993-6982-2020-6-101-109

Юрий [Yuriy] Александрович [A.] Горицкий [Goritskiy]
Давид [David] Георгиевич [G.] Тигетов [Tigetov]
Екатерина [Ekaterina] Владимировна [V.] Китова [Kitova]

DOI: https://doi.org/10.24160/1993-6982-2020-6-101-109

Keywords: elliptical and unfavorable orbits, angular measurements, displacement detection, information discrepancy, equations of motion, 2D model

Abstract

The article addresses the requirements for a goniometric system intended to detect displacements of the space body orbit, which measures angles at discrete moments of time with a random error. Two statistical hypotheses about the zero and specified nonzero displacement values are considered. The likelihood ratio statistics is obtained, and the information distance for it is determined, which characterizes the discrimination confidence level, and which depends on the measurement device accuracy s and discreteness Dt, and also on the orbit parameters. By specifying the orbits and discrimination confidence level, the accuracy s and discreteness Dt are determined through information discrepancy.

The information discrepancy is calculated on a family of orbits unfavorable for the observer, the plane of which touches the orbit of the moving observer, and the touching point is the intersection point of the corresponding trajectories.

To refine the information distance, a simple flat approximate motion-measurement model is substantiated, in which the true motion of the observer (outside the space body orbit plane) is replaced, without changing its speed, by motion in the space body orbit plane over the earth's sphere circumference. The justification is corroborated by calculating the errors. The obtained simple model is used for estimating the potential possibility of detecting the specified displacement.

Tables and graphs for practically determining the discreteness and accuracy of the system are given. The appendix contains all formulas necessary for carrying out similar calculations.

Examples show that from angular measurements it is possible to obtain quite reliable detection for the range of orbit parameters that are of practical interest.

Information about authors

Юрий [Yuriy] Александрович [A.] Горицкий [Goritskiy]

Dr.Sci. (Techn.), Professor of Mathematical and Computer Modeling Dept., NRU MPEI, e-mail: goritskiy@yandex.ru

Давид [David] Георгиевич [G.] Тигетов [Tigetov]

Ph.D. (Techn.), Head of the Moscow Radio Engineering Institute Sector, e-mail: David Tigetov@gmail.com

Екатерина [Ekaterina] Владимировна [V.] Китова [Kitova]

Student Mathematical and Computer Modeling Dept., NRU MPEI, e-mail: evkitova@bk.ru

References

1. Chang C.B. Optimal State Estimation of Ballistic Trajectories with Angle-only Measurements. Massachusetts: MIT Lincoln Laboratory, 1979.
2. Chang C.B., Tabaczynski J. Application of State Estimation to Target Tracking // IEEE Trans. Automatic Control. 1984. V. 29. No. 2. Pp. 98—109,
3. Саврасов Ю.С. Методы определения орбит космических объектов. М.: Машиностроение, 1981.
4. Саврасов Ю.С. Алгоритмы и программы в радиолокации. М.: Радио и связь, 1985.
5. Колесса А.Е., Пругло А.В., Равдин С.С. Восстановление орбит по угловым измерениям // Радиотехника. 2005. № 10. С. 5—9.
6. Колесса А.Е. Рекуррентные алгоритмы фильтрации для некоторых систем с нелинейностями кусочно-линейного типа // Автоматика и телемеханика. 1986. № 5. С. 61—69.
7. Колесса А.Е. Некоторые прикладные вопросы кусочно-линейной фильтрации // Автоматика и телемеханика. 1986. № 6. С. 61—69.
8. Колесса А.Е. Точные формулы оптимальной фильтрации для нестационарной кусочно-линейной задачи оценивания параметра // Автоматика и телемеханика. 1989. № 12. С. 69—80.
9. Булычев, В.Ю., Булычев Ю.Г., Ивакина С.С. Пассивная локация на основе угловых и мощностных измерений системы пеленгаторов // Известия РАН. Серия «Теория и системы управления». 2014. № 1. С. 65—73.
10. Булычев В.Ю. и др. Угломерно-энергетический метод нестационарной пассивной локации на базе однопозиционной системы // Известия РАН. Серия «Теория и системы управления». 2015. № 5. С. 122—136.
11. Farina A., Benvenuti D., Ristic B. Tracking a Ballistic Target: Comparison of Several Nonlinear Filters // IEEE Trans. Aerospace and Electronic Syst. 2002. V. 38. No. 3. Pp. 854—867.
12. Farina A., Ristic B., Timmoneri L. Cramer-Rao Bound for Nonlinear Filtering with Pd < 1 and Its Application to Target Tracking // IEEE Trans. Signal Proc. 2002. V. 50. No. 8. Pp. 1916—1924.
13. Ristic B., Farina A., Benvenuti D., Arulampalam M.S. Performance Bounds and Comparison of Non-linear Filters for Tracking a Ballistic Object on Re-entry // IEEE Proc. Radar, Sonar and Navigation. 2003. V. 150.No. 2.Pp. 65—70.
14. Кульбак С. Теория информации и статистика. М.: Наука, 1967.
15. Tigetov D, Goritsky Y, Anufriev A. Two-dimensional Model for Cramer-Rao Bounds of Angular Measurements on Elliptical Orbits // Proc. Intern. Russian Automation Conf. Sochy, 2019. Pp. 1—5.
---
Для цитирования: Горицкий Ю.А., Тигетов Д.Г., Китова Е.В. Вероятностный анализ требований к угломерной системе обнаружения смещения эллиптической орбиты // Вестник МЭИ. 2020. № 6. С. 101—109. DOI: 10.24160/1993-6982-2020-6-101-109.
#
1. Chang C.B. Optimal State Estimation of Ballistic Trajectories with Angle-only Measurements. Massachusetts: MIT Lincoln Laboratory, 1979.
2. Chang C.B., Tabaczynski J. Application of State Estimation to Target Tracking. IEEE Trans. Automatic Control. 1984;29;2:98—109,
3. Savrasov Yu.S. Metody Opredeleniya Orbit Kosmicheskikh Ob'ektov. M.: Mashinostroenie, 1981. (in Russian).
4. Savrasov Yu.S. Algoritmy i Programmy v Radiolokatsii. M.: Radio i Svyaz', 1985. (in Russian).
5. Kolessa A.E., Pruglo A.V., Ravdin S.S. Vosstanovlenie Orbit po Uglovym Izmereniyam. Radiotekhnika. 2005;10:5—9. (in Russian).
6. Kolessa A.E. Rekurrentnye Algoritmy Fil'tratsii dlya Nekotorykh Sistem s Nelineynostyami Kusochno-lineynogo Tipa. Avtomatika i Telemekhanika. 1986;5:61—69. (in Russian).
7. Kolessa A.E. Nekotorye Prikladnye Voprosy Kusochno-lineynoy Fil'tratsii. Avtomatika i Telemekhanika. 1986;6:61—69. (in Russian).
8. Kolessa A.E. Tochnye Formuly Optimal'noy Fil'tratsii dlya Nestatsionarnoy Kusochno-lineynoy Zadachi Otsenivaniya Parametra. Avtomatika i Telemekhanika. 1989;12:69—80. (in Russian).
9. Bulychev, V.Yu., Bulychev Yu.G., Ivakina S.S. Passivnaya Lokatsiya na Osnove Uglovykh i Moshch-nostnykh Izmereniy Sistemy Pelengatorov. Izvestiya RAN. Seriya «Teoriya i Sistemy Upravleniya». 2014;1:65—73. (in Russian).
10. Bulychev V.Yu. i dr. Uglomerno-energeticheskiy Metod Nestatsionarnoy Passivnoy lokatsii na Baze Odnopozitsionnoy Sistemy. Izvestiya RAN. Seriya «Teoriya i Sistemy Upravleniya». 2015;5:122—136. (in Russian).
11. Farina A., Benvenuti D., Ristic B. Tracking a Ballistic Target: Comparison of Several Nonlinear Filters. IEEE Trans. Aerospace and Electronic Syst. 2002;38;3:854—867.
12. Farina A., Ristic B., Timmoneri L. Cramer-Rao Bound for Nonlinear Filtering with Pd < 1 and Its Application to Target Tracking. IEEE Trans. Signal Proc. 2002;50;8:1916—1924.
13. Ristic B., Farina A., Benvenuti D., Arulampalam M.S. Performance Bounds and Comparison of Nonlinear Filters for Tracking a Ballistic Object on Reentry. IEEE Proc. Radar, Sonar and Navigation. 2003;150;2:65—70.
14. Kul'bak S. Teoriya Informatsii i Statistika. M.: Nauka, 1967. (in Russian).
15. Tigetov D, Goritsky Y, Anufriev A. Two-dimensional Model for Cramer-Rao Bounds of Angular Measurements on Elliptical Orbits. Proc. Intern. Russian Automation Conf. Sochy, 2019:1—5.
---
For citation: Goritskiy Yu.А., Tigetov D.G., Kitova Е.V. Probabilistic Analysis of the Requirements for an Elliptical Orbit Displacement Goniometric Detection System. Bulletin of MPEI. 2020;6:101—109. (in Russian). DOI: 10.24160/1993-6982-2020-6-101-109.