Abstract
A critical challenge in Space Domain Awareness (SDA) is gaining custody of newly detected or maneuvering objects. The dynamically feasible location of one such object may be represented as an admissible region or reachable set. This paper proposes techniques for exploring search sets using sample-based planning. Several methods for sampling feasible regions of measurement space are developed, and Monte Carlo Tree Search (MCTS) is applied over a limited horizon to determine time-optimal sets of actions. Tree search aids in overcoming local minima in solutions found with traditional optimization methods. With tasking methodologies in place, a second contribution of this paper explores estimation methodologies in the presence of null detections; these developments are critical to the search and recovery problem, in which the target probability density projected to measurement space is generally much larger than the sensor field of view. A special focus is applied to the admissible region, and given a Gaussian mixture representation of the admissible region, a novel methodology for splitting mixands in an arbitrary measurement space is presented. A mixand weight update is derived for the key scenario in which no detection is made at a measurement epoch. Merging methodologies are applied, and the resultant Gaussian sum filter is demonstrated for a representative case in which follow-on tracking of a geostationary object is desired.
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References
Holzinger, M.J., Jah, M.K.: Challenges and potential in space domain awareness. J. Guid. Control. Dyn. 41(1), 15–18 (2018). https://doi.org/10.2514/1.G003483
ESA Space Debris Office: ESA’s Annual Space Environment Report, No. July, 2019, pp. 1–78
Erwin, R.S., Albuquerque, P., Jayaweera, S.K., Hussein, I.: Dynamic sensor tasking for space situational awareness. In: Proceedings of the 2010 American Control Conference, ACC 2010, pp. 1153–1158 (2010). https://doi.org/10.1109/acc.2010.5530989
Williams, P.S., Spencer, D.B., Erwin, R.S.: Coupling of estimation and sensor tasking applied to satellite tracking. J. Guid. Control. Dyn. 36(4), 993–1007 (2013). https://doi.org/10.2514/1.59361
Sunberg, Z., Chakravorty, S., Erwin, R.S., Member, S.: Information space receding horizon control for multisensor tasking problems. IEEE Trans. Cybern. 46(6), 1325–1336 (2016). https://doi.org/10.1109/TCYB.2015.2445744
Linares, R., Furfaro, R.: Dynamic sensor tasking for space situational awareness via reinforcement learning. In: Advanced Maui Optical and Space Surveillance Technologies Conference, pp. 1–10 (2016)
Fedeler, S., Holzinger, M., Whitacre, W.: Sensor tasking in the cislunar regime using Monte Carlo Tree Search. Adv. Space Res. 70, 1–19 (2022). https://doi.org/10.1016/j.asr.2022.05.003
Africano, J., Schildknecht, T., Matney, M., Kervin, P., Stansbery, E., Flury, W.: A geosynchronous orbit search strategy. Space Debris 2, 357–369 (2000). https://doi.org/10.1023/B:SDEB.0000030025.04930.08
Frueh, C., Fielder, H., Herzog, J.: Heuristic and optimized sensor tasking observation strategies with exemplification for geosynchronous objects. J. Guid. Control. Dyn. 41(5), 1036–1048 (2018). https://doi.org/10.2514/1.G003123
Milani, A., Sansaturio, M.E., Tommei, G., Arratia, O., Chesley, S.R.: Multiple solutions for asteroid orbits: computational procedure and applications. Astron. Astrophys. 431(2), 729–746 (2005). https://doi.org/10.1051/0004-6361:20041737
Worthy, J.L., Holzinger, M.J.: Use of uninformative priors to initialize state estimation for dynamical systems. Adv. Space Res. 60(7), 1373–1388 (2017). https://doi.org/10.1016/j.asr.2017.06.040
Gehly, S., Jones, B.A., Axelrad, P.: Search-detect-track sensor allocation for geosynchronous space objects. IEEE Trans. Aerosp. Electron. Syst. 54(6), 2788–2808 (2018). https://doi.org/10.1109/TAES.2018.2830578
DeMars, K.J., Jah, M.K.: Probabilistic initial orbit determination using Gaussian mixture models. J. Guid. Control. Dyn. 36(5), 1324–1335 (2013). https://doi.org/10.2514/1.59844
Fujimoto, K., Alfriend, K.T.: Optical short-arc association hypothesis gating via angle-rate information. J. Guid. Control. Dyn. 38(9), 1602–1613 (2015). https://doi.org/10.2514/1.G000927
Schumacher, P.W., Gaebler, J.A., Roscoe, C.W., Wilkins, M.P., Axelrad, P.: Parallel initial orbit determination using angles-only observation pairs. Celest. Mech. Dyn. Astron. 130(9), 1–20 (2018). https://doi.org/10.1007/s10569-018-9852-6
Hobson, T.A., Clarkson, I.V.L.: A particle-based search strategy for improved space situational awareness. In: 2013 Asilomar Conference on Signals, Systems and Computers, pp. 898–902 (2013). https://doi.org/10.1109/ACSSC.2013.6810418
Murphy, T.S., Holzinger, M.J.: Generalized minimum-time follow-up approaches applied to tasking electro-optical sensor tasking. In: Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference (2017)
Fränken, D., Schmidt, M., Ulmke, M.: “Spooky action at a distance" in the cardinalized probability hypothesis density filter. IEEE Trans. Aerosp. Electron. Syst. 45(4), 1657–1664 (2009). https://doi.org/10.1109/TAES.2009.5310327
Chang, H.S., Fu, M.C., Hu, J., Marcus, S.I.: An adaptive sampling algorithm for solving Markov decision processes. Oper. Res. 53(1), 126–139 (2005). https://doi.org/10.1287/opre.1040.0145
Coulom, R.: Efficient selectivity and backup operators in Monte-Carlo tree search. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) Machine Learning: ECML 2006. ECML 2006. Lecture Notes in Computer Science, vol. 4212, pp. 282–293. Springer, Berlin, Heidelberg (2006). https://doi.org/10.1007/11871842_29
Kocsis, L., Szepesvari, C.: Bandit based Monte-Carlo Planning. Lect. Notes Comput. Sci. 4212, 282–293 (2006). https://doi.org/10.1109/scc.2004.1358005
Silver, D., Veness, J.: Monte-Carlo planning in large POMDPs. In: Advances in Neural Information Processing Systems (NIPS), pp. 1–9(2010)
Sunberg, Z., Kochenderfer, M.J.: Online algorithms for POMDPs with continuous state, action, and observation spaces. In: Twenty-Eighth International Conference on Automated Planning and Scheduling (2018)
Ross, S.: Introduction to Stochastic Dynamic Programming. Academic Press, New York (1983)
Pineau, J., Gordon, G., Thrun, S.: Point-based value iteration: an anytime algorithm for POMDPs. In: IJCAI International Joint Conference on Artificial Intelligence, pp. 1025–1030 (2003)
Genz, A., Trinh, G.: Numerical computation of multivariate normal probabilities using bivariate conditioning. J. Comput. Graph. Stat. 1, 141–149 (1992)
Cunningham, J.P., Hennig, P., Lacoste-Julien, S.: Gaussian probabilities and expectation propagation. arXiv e-prints. arXiv:1111.6832 (2011)
Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47, 235–256 (2002)
Auger, D., Couëtoux, A., Teytaud, O.: Continuous upper confidence trees with polynomial exploration - consistency. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 194–209(2013)
Wang, Y., Audibert, J.Y., Munos, R.: Algorithms for infinitely many-armed bandits. In: Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference, pp. 1729–1736(2009)
Couetoux, A., Hoock, J.-B., Sokolovska, N., Teytaud, O.: Continuous upper confidence trees. In: Coello, C.A.C. (eds.) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683, pp. 433–445. Springer, Berlin, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25566-3_32
Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: On triangulations of a set of points in the plane. IEEE Trans. Inf. Theory 29(4), 228–240 (1983)
Alspach, D.L., Sorenson, H.W.: Nonlinear bayesian estimation using Gaussian sum approximations. IEEE Trans. Autom. Control 17(4), 439–448 (1972). https://doi.org/10.1109/TAC.1972.1100034
Julier, S.J., Uhlmann, J.K.: New extension of the Kalman filter to nonlinear systems. In: Signal Processing, Sensor Fusion, and Target Recognition VI. Proc. SPIE 3068 (1997). https://doi.org/10.1117/12.280797
Havlak, F., Campbell, M.: Discrete and continuous, probabilistic anticipation for autonomous robots in Urban environments. IEEE Trans. Robotics 30(2), 461–474 (2014). https://doi.org/10.1109/TRO.2013.2291620
Runnalls, A.R.: Kullback-Leibler approach to Gaussian mixture reduction. IEEE Trans. Aerosp. Electron. Syst. 43(3), 989–999 (2007). https://doi.org/10.1109/TAES.2007.4383588
Milani, A., Gronchi, G.F., Vitturi, M.D.M., Knežević, Z.: Orbit determination with very short arcs. I admissible regions. Celest. Mech. Dyn. Astron. 90(1–2), 59–87 (2004). https://doi.org/10.1007/s10569-004-6593-5
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Research on this project has been supported by the National Science Foundation Graduate Research Fellows Program Grant Number DGE 1650115 and the Draper Scholars.
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Fedeler, S.J., Holzinger, M.J. & Whitacre, W.W. Tasking and Estimation for Minimum-Time Space Object Search and Recovery. J Astronaut Sci 69, 1216–1249 (2022). https://doi.org/10.1007/s40295-022-00332-0
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DOI: https://doi.org/10.1007/s40295-022-00332-0