Sensor Scheduling for Space Object Tracking and Collision Alert
Given the increasingly dense environment in both low-earth orbit (LEO) and geostationary orbit (GEO), a sudden change in the trajectory of any existing resident space object (RSO) may cause potential collision damage to space assets. With a constellation of EO/IR sensor platforms and ground radar surveillance systems, it is important to design optimal estimation algorithm for updating nonlinear object states and allocating sensing resources to effectively avoid collisions among many RSOs. We consider N space objects being observed by M sensors whose task is to provide the minimum mean square estimation error of the overall system subject to the cost associated with each measurement. To simplify the analysis, we assume that sensors can switch between objects instantaneously subject to additional resource and sensing geometry constraints. We first formulate the sensor scheduling problem using the optimal control formalism and then derive a tractable relaxation of the original optimization problem, which provides a lower bound on the achievable performance. We propose an open-loop periodic switching policy whose performance can approach the theoretical lower bound closely. We also discuss a special case of identical sensors and derive an index policy that coincides with the general solution to restless multi-armed bandit problem by Whittle. Finally, we demonstrate the effectiveness of the resulting sensor management scheme for space situational awareness using a realistic space object tracking simulator with both unintentional and intentional maneuvers by RSOs that may lead to collision. Our sensor scheduling scheme outperforms the conventional information gain and covariance control based schemes in the overall tracking accuracy as well as making earlier declaration of collision events.
KeywordsSensor management Sensor scheduling Nonlinear filtering Kalman filter Restless multi-armed bandit Space object tracking Collision alert Situational awareness
H. Chen was supported in part by ARO through grant W911NF- 08-1-0409, ONR-DEPSCoR through grant N00014-09-1-1169 and Office of Research & Sponsored Programs at University of New Orleans. The authors are grateful to the anonymous reviewers for their constructive comments to an earlier draft of this work.
- 8.Chang, C., Chen, W., Huang, H.: Birkhoff-von Neumann input buffered crossbar switches. In: Proc. IEEE INFORCOM. 3, 1614–1623 (2000)Google Scholar
- 9.Chen, H., Chen, G., Blasch, E.P., Pham, K.: Comparison of several space target tracking filters. In: Proceedings of SPIE Defense, Security Sensing, vol. 7730, Orlando (2009)Google Scholar
- 10.Chen, H., Chen, G., Shen, D., Blasch, E.P., Pham, K.: Orbital evasive target tracking and sensor management. In: Dynamics of Information Systems: Theory and Applications. Hirsch, M.J., Pardalos, P.M., Murphey, R. (eds.), Lecture Notes in Control and Information Sciences. Springer, New York (2010)Google Scholar
- 14.Evensen, G.: Data Assimilation: The Ensemble Kalman Filter. Springer, New York (2006)Google Scholar
- 16.Gittins, J.C., Jones, D.M.: A dynamic allocation index for the sequential design of experiments. In: Progress in Statistics (European Meeting of Statisticians) (1972)Google Scholar
- 17.Gordon, N., Salmond, D., Smith, A.F.: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc. F 140(2), 107–113 (1993)Google Scholar
- 18.Guha, S., Munagala, K.: Approximation algorithms for budgeted learning problems. In: Proceedings ACM Symposium on Theory of Computing (2007)Google Scholar
- 25.Li, X.R., Jilkov, V.P.: A survey of maneuvering target tracking: approximation techniques for nonlinear filtering. In: Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, vol. 5428–62, Orlando (2004)Google Scholar
- 26.Maus, A., Chen, H., Oduwole, A., Charalampidis, D.: Designing collision alert system for space situational awareness. In: 20th ANNIE Conference, St. Louis, MO (2010)Google Scholar
- 29.Ru, J., Chen, H., Li, X.R., Chen, G.: A range rate based detection technique for tracking a maneuvering target. In: Proceedings of SPIE Conference on Signal and Data Processing of Small Targets (2005)Google Scholar