Abstract
Probabilistic Admissible Region (PAR) is a technique to initialize the probability density function (pdf) of the states of a Resident Space Object (RSO). It combines apriori information about some of the orbital elements and a single partial-state observation to initialize the pdf of the RSO. A unified, geometrical solution to Probabilistic Admissible Region, G-PAR, is proposed. The proposed scheme gives a closed-form, clearly explainable solution for PAR particle mapping for the first time.
It is shown that the G-PAR can be posed as a Bayesian measurement update of the very diffuse pdf of the states given by the postulated statistics. The effectiveness of the proposed G-PAR will be shown on diverse combinations of sensors and apriori knowledge. Its unique advantages in resolving the data association problem inherent in initializing the pdf of the objects when tracking multiple objects will also be presented.
Supported by Air Force Office of Scientific Research.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
DeMars, K.J., Jah, M.K.: Initial orbit determination via gaussian mixture approximation of the admissible region. Adv. Astron. Sci. 143 (2012)
Faber, W., Chakravorty, S., Hussein, I.: Multi-object tracking with multiple birth, death, and spawn scenarios using a randomized hypothesis generation technique (RFISST). In: Proceedings of the 19th International Conference on Information Fusion, pp. 154–161. IEEE, Darmstadt (2016)
Gooding, R.H.: A new procedure for the solution of the classical problem of minimal orbit determination from three lines of sight. Celest. Mech. Dyn. Astron. 66(4), 387–423 (1997)
Hussein, I.I., Roscoe, C.W.T., Schumacher, Jr., P.W., Wilkins, M.P.: Probabilistic admissible region for short-arc angles-only observation. In: Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, Wailea, HI, 9–12 September 2014 (2014)
Hussein, I.I., Roscoe, C.W.T., Wilkins, M.P., Schumacher, Jr., P.W.: Probabilistic admissibility in angles-only initial orbit determination. In: Proceedings of the 24th International Symposium on Space Flight Dynamics, Laurel, MD, 5–9 May 2014 (2014)
Kelecy, T., Shoemaker, M., Jah, M.: Application of the constrained admissible region multiple hypothesis filter to initial orbit determination of a break-up. In: Proceedings of the 6th European Conference on Space Debris, Darmstadt, Germnay (2013)
Roscoe, C.W.T., Hussein, I.I., Wilkins, M.P., Schumacher, P.W., Jr.: The probabilistic admissible region with additional constraints. Adv. Astron. Sci. 156, 117–130 (2015)
Roscoe, C.W.T., Schumacher, P.W., Jr., Wilkins, M.P.: Parallel track initiation for optical space surveillance using range and range-rate bounds. Adv. Astron. Sci. 150, 989–1008 (2014)
Roscoe, C.W.T., Wilkins, M.P., Hussein, I.I., Schumacher, Jr., P.W.: Uncertain angles-only track initiation for SSA using different iod methods. Adv. Astron. Sci. 158 (2016)
Tommei, G., Milani, A., Rossi, A.: Orbit determination of space debris: admissible regions. Celest. Mech. Dyn. Astron. 97, 289–304 (2007)
Acknowledgements
The authors are thankful to Dr. Erik Blasch, AFOSR, and AFWERX for providing generous funding to support this research work via contract no. FA9550-21-P-0008.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Mishra, U.R., Faber, W., Chakravorty, S., Hussein, I., Sunderland, B., Hesar, S. (2024). Geometric Solution to Probabilistic Admissible Region Based Track Initialization. In: Blasch, E., Darema, F., Aved, A. (eds) Dynamic Data Driven Applications Systems. DDDAS 2022. Lecture Notes in Computer Science, vol 13984. Springer, Cham. https://doi.org/10.1007/978-3-031-52670-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-031-52670-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-52669-5
Online ISBN: 978-3-031-52670-1
eBook Packages: Computer ScienceComputer Science (R0)