Initial Orbit Determination of a Space Object from Limited Angular Optical Measurements

Currently, the problem of initial orbit determination for space objects based on angular coordinate measurements (right ascension and declination) under limited data conditions is of significant practical value. The aim of this work was to develop a non-iterative estimation method for the slant range vector of an unknown space object relative to an observation site under conditions of limited angular optical measurement data, enabling near-real-time determination of orbital parameters (semi-major axis, inclination, eccentricity, longitude of the ascending node, and argument of latitude). This is particularly relevant for operational orbit determination of unknown space objects to prevent hazardous close approaches and potential collisions, especially given the increasing number of satellite launches and the growing density of space debris in low Earth orbit. A method for initial orbit determination (in the absence of prior orbital data) of an unknown space object is presented, based on angular optical measurements over a short observation arc (< 0.5°) in two detection regions. The proposed method allows for the estimation of the slant range vector of an unknown space object relative to the observation site using angular measurement data and computed values of the velocity projection onto the frame plane of a reference satellite (with known orbital parameters). To estimate the velocity projection onto the frame plane, a method for detecting space objects in optical surveillance system video data is employed. Experimental optical observations of the detected SL-12/RB rocket stage were performed, including angular measurements and orbital parameter calculations. The absolute errors in determining the semi-major axis of the SL-12/RB rocket stage did not exceed 19.71 km. The absolute errors in orbital inclination i, longitude of the ascending node Ω, and argument of latitude u were 0.033°, 0.083°, and 0.046°, respectively.

1. Lei X. [et al.]. Identification of uncatalogued LEO space objects by a ground-based EO array. Advances in Space Research. 2021;67(1):350-359. doi: 10.1016/j.asr.2020.07.030.

2. Herrick S. Astrodynamics: Orbit determination, space navigation, celestial mechanics. London: Van Nostrand Reinhold Company, 1971. 540 p.

3. Escobal PR. Methods of Orbit Determination. Huntington, N.Y.: R.E. Krieger Pub. Co., 1976. 479 p.

4. Vallado D. Fundamentals of Astrodynamics and Applications. Hawthorne: Microcosm Press, 2013. 1106 p.

5. Kazemi S. [et al.]. Orbit determination for space situational awareness: A survey. Acta Astronautica. 2024; 222:272-295. DOI: 10.1016/j.actaastro.2024.06.015

6. Gronchi GF. Dimare L. Orbit determination with the two-body integrals. Celest. Mech. Dyn. Astron. 2010; 107:299-318. DOI: 10.1007/s10569-010-9271-9

7. Milani A, Gronchi GF, Vitturi MDM, Knežević Z. Orbit determination with very short arcs. I admissible regions. 2004;90:57-85. doi: 10.1007/s10569-004-6593-5

8. Lei X. [et al.]. An Improved Range-Searching Initial Orbit-Determination Method and Correlation of Optical Observations for Space Debris. Appl. Sci. 2023; 13(24):13224. DOI: 10.3390/app132413224

9. Pastor A, Sanjurjo-Rivo M, Escobar D. Initial orbit determination methods for track-to-track association. Advances in Space Research. 2021;68(7):2677-2694. DOI: 10.1016/j.asr.2021.06.042

10. Cai H. [et al.]. Improved tracklet association for space objects using short-arc optical measurements. Acta Astronautica. 2018;151:836-847.

11. Lei X. [et al.]. A geometrical approach to association of space-based very short-arc LEO tracks. Advances in Space Research. 2018;62(3):542-553. doi: 10.1016/j.asr.2018.04.044

12. Baranova V, Spiridonov A, Ushakov D, Saetchnikov V. The Resident Space Object Detection Method Based on the Connection between the Fourier Domain Image of the Video Data Difference Frame and the Orbital Velocity Projection J. Astron. Space Sci. 2024;41(3):159-170. DOI: 10.5140/JASS.2024.41.3.159

13. Baranova VS, Saetchnikov VA, Spiridonov AA. Autonomous Streaming Space Objects Detection Based on a Remote Optical System. Devices and Methods of Measurements. 2021;12(4):272-279. doi: 10.21122/2220-9506-2021-12-4-272-279

14. Subbotin MF. Introduction to theoretical astronomy. Moscow, Nauka Publ., 1968. 800 p.

15. Spiridonov AA. [et al.]. Small satellite orbit determination using single pass Doppler measurements. IEEE Journal on Miniaturization for Air and Space Systems. 2022;3(4):162-170. doi: 10.1109/JMASS.2022.3188736

16. Stoker K. [et al.]. Angles-Only Orbit Determination Accuracies with Limited Observational Arc // Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS). 2020. [Electronic resource]. URL: https://amostech.com/TechnicalPapers/2020/Poster/Stoker.pdf (08.04.2025).