Abstract
We introduce an initial orbit determination technique that uses only sequential range-rate measurements along fixed lines of sight and time between measurements. Compared to existing velocity-based initial orbit determination methods which impose additional requirements such as concurrent observations, our method may reduce the number of sensors required for a spacecraft to perform autonomous, or onboard, initial orbit determination. The measurements required may be obtained by a single range-rate sensor, such as an X-ray detector observing X-ray pulsars, and an onboard clock. The accuracy of our algorithm is compared with existing techniques for a variety of orbits. Orbit determination errors, in terms of estimated position, are characterized with Monte Carlo simulation techniques. Results indicate that our method achieves better performance compared to an initial orbit determination method utilizing velocity vectors and time of flight. The position error of our technique increases for lower velocities and shorter measurement times, which is consistent with existing velocity-based initial orbit determination methods.
Similar content being viewed by others
References
Prussing, J.E., Conway, B.A.: Orbital Mechanics. Oxford University Press, Oxford (2012)
Branham, J.R.L.: Laplacian orbit determination. In: Teixeira, R., Leister, N.V., Martin, V.A.F., Benevides-Soares, P. (eds.) Astronomy in Latin America, vol. 1 (2003)
Taff, L.G.: On Initial Orbit Determination. Astron. J. 89, 1426–1428 (1984)
Curtis, H.D.: Chapter 5 - Preliminary orbit determination. In: Orbital Mechanics for Engineering Students, 2nd edn., pp. 255–317. Butterworth-Heinemann, Boston (2010)
Gooding, R.: A new procedure for orbit determination based on three lines of sight: angles only. NASA STI/Recon Technical Report N, vol. 94, p. 21224 (1993)
Sconzo, P.: The use of lambert’s theorem in orbit determination. Astron. J. 67, 19 (1962). https://doi.org/10.1086/108599
Hollenberg, C.L., Christian, J.A.: Geometric solutions for problems in velocity-based orbit determination. J. Astron. Sci. 67(1), 193–198 (2020). https://doi.org/10.1007/s40295-019-00170-7
Christian, J.A., Hollenberg, C.L.: Initial orbit determination from three velocity vectors. J. Guid. Control Dyn. 42(4), 894–899 (2019). https://doi.org/10.2514/1.G003988
Christian, J.A.: Starnav: autonomous optical navigation of a spacecraft by the relativistic perturbation of starlight. Sensors 19, 4064 (2019). https://doi.org/10.3390/s19194064
Sheikh, S.I., Pines, D.J., Ray, P.S., Wood, K.S., Lovellette, M.N., Wolff, M.T.: Spacecraft navigation using x-ray pulsars. J. Guid. Control. Dyn. 29(1), 49–63 (2006). https://doi.org/10.2514/1.13331
Gendreau, K.C., Arzoumanian, Z., Okajima, T.: The neutron star interior composition explorer (nicer): an explorer mission of opportunity for soft x-ray timing spectroscopy. In: Space Telescopes and Instrumentation 2012: Ultraviolet to Gamma Ray, vol. 8443, pp. 322–329. (2012). https://doi.org/10.1117/12.926396
Zhang, X., Shuai, P., Huang, L., Chen, S., Xu, L.: Mission overview and initial observation results of the x-ray pulsar navigation-i satellite. Int. J. Aerosp. Eng. (2017). https://doi.org/10.1155/2017/8561830
McKee, P.D.: Autonomous navigation in deep space using optical measurements of unresolved planets and stars. PhD thesis (2022). https://www.proquest.com/dissertations-theses/autonomous-navigation-deep-space-using-optical/docview/2769203240/se-2
Christian, J.A., Parker, W.E.: Initial orbit determination from bearing and range-rate measurements using the orbital hodograph. J. Guid. Control. Dyn. 44(2), 370–378 (2021). https://doi.org/10.2514/1.G005433
Christian, J., Ertl, C., Horneman, K., Lovell, A.: Doppler-only initial orbit determination for an orbiting transmitter. In: AIAA SCITECH 2022 Forum, p. 1000. (2022). https://doi.org/10.2514/6.2022-1000
Losacco, M., Armellin, R., Yanez, C., Lizy-Destrez, S., Pirovano, L., Sanfedino, F.: Robust initial orbit determination for short-arc doppler radar observations. arXiv preprint arXiv:2204.13966 (2022). https://doi.org/10.48550/arXiv.2204.13966
Holincheck, A., Cathell, J.: Single-pass, single-station, doppler-only initial orbit determination. In: AAS/AIAA Astrodynamics Specialist Conference, Charlotte, NC (2022)
Emadzadeh, A.A., Speyer, J.L.: Navigation in Space by X-ray Pulsars. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-8017-5
Anderson, K.D., Pines, D., Sheikh, S.: Investigation of x-ray pulsar signal phase tracking for spacecraft navigation. In: AIAA SCITECH 2022 Forum, p. 1589. (2022)
Hou, L., Lohan, K., Putnam, Z.R.: Comparison and error modeling of velocity-based initial orbit determination algorithms. In: AAS/AIAA Space Flight Mechanics Meeting, Virtual (2021)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hou, L., Putnam, Z.R. Autonomous Initial Orbit Determination Using Sequential Range-Rate Measurements. J Astronaut Sci 71, 24 (2024). https://doi.org/10.1007/s40295-024-00442-x
Accepted:
Published:
DOI: https://doi.org/10.1007/s40295-024-00442-x