Jason Williams, Whipbird Signals; Vaughan Clarkson, Whipbird Signals; Ashwani Kumar, DSTG; Kruger White, DSTG
https://doi.org/10.64861/HPFX9672
Keywords: Space domain awareness, space situation awareness, sensor management, sensor tasking, dynamic programming, non-myopic planning, Monte Carlo tree search
Abstract:
The exponential growth of resident space objects (RSOs) in recent decades has made space domain awareness an increasingly challenging problem. Catalogue maintenance, i.e., maintaining orbital estimates of the full library of known RSOs, requires cooperative inputs of a large multinational set of distributed sensors, comprising both commercial and government assets. _x000D_
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Traditional methods for tasking sensors fall into three categories. The first operates on a fixed schedule, requiring observations from particular sensors at a fixed interval; this history is well-described in [1]. The second optimises based on an analysis of the probability of detection, scheduling for RSOs most likely to be observed under the forecast conditions [1]. The final category is based on information gain, observing RSOs to maximise the reduction in some measure of uncertainty [2]. In [3] the sensor tasking problem is posed as a receding horizon dynamic program, which is solved within the family of open loop stochastic policies. Closed loop stochastic control is examined in [4] using Monte Carlo tree search (MCTS) [5] for the problem of sensor tasking for cislunar catalogue maintenance._x000D_
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We propose a covariance cost performance measure to penalise estimation errors according to a user-tailorable specification, which allows little or no cost when accuracy is adequate, increasing cost as accuracy deteriorates, and saturation of cost when accuracy deteriorates beyond an upper threshold. Both position and velocity can be penalised depending on user requirements. The concept fits into the broader framework of [6]. We also recognise that there is a sensing cost when the uncertainty grows beyond a sensor’s field of view and so multiple observations are required. Using a cost function that combines the covariance cost and sensing cost, we devise a method that performs non-myopic optimisation over a fixed time horizon using MCTS. In our simulations, we consider optimisation over a four-day horizon, where new tasking commands are issued in four timeslots per day. _x000D_
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The basic single-object method is extended to multiple RSOs using Lagrangian relaxation [7], incorporating Lagrangian dual variables, which act as penalty multipliers for violating the constraints of each sensor within each timeslot. This allows policy optimisation to be parallelised over the RSOs between dual variable updates, permitting efficient solution in problems involving many RSOs. _x000D_
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Each single-object tree has an intractably large number of possible observation action sequences, and numerical prediction of orbits over a four-day period is computationally challenging. We develop a method that permits rapid evaluation of observation sequences, and a directed search which identifies promising sequences for consideration using MCTS. The evaluation method forms the joint covariance of each pair of states adjacent in time for each RSO, and the joint covariance of each measurement with its corresponding state. Conceptually, this representation permits evaluation of any sequence of measurements under a jointly Gaussian approximation (or a linear minimum mean square estimator), providing an estimated posterior covariance matrix and allowing evaluation of any associated performance measures. Nevertheless, the time sampling density of states remains computationally demanding. This is addressed by marginalising dense state variables to obtain the desired spacing (i.e., the timeslot interval). In this representation, the states remain a Markov chain, but measurements are related to the two states immediately before and after the original marginalised state. Numerical difficulties are addressed using square root matrix representations. Collectively, these approximations permit evaluation of a large number of candidate observation sequences for each RSO. _x000D_
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The MCTS method develops closed loop, non-myopic policies, which anticipate missed detection events according to the model of probability of detection, and plan alternative action sequences for later decision periods in the planning horizon depending on earlier outcomes. _x000D_
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We demonstrate our method though a simulation which plans observations of 200 RSOs comprising low earth orbit (LEO), geostationary (GEO) and other orbit types. Orbits are obtained through numerical propagation of two-line elements from space-track.org. Orbital covariance matrices are initialised based on a series of sensor observations. Dynamics noise is generated by uncertain drag for LEO objects and solar radiation pressure for other orbit types, for both truth and estimation. Orbital propagation is performed using Orekit’s unscented Kalman filter implementation [8, 9]. Observations are planned over a four-day period based on unclassified information for a network of 12 optical and radar sensors in the Space Surveillance Network, with four timeslots per day. _x000D_
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The results demonstrate the viability of the proposed approach for a problem with significant scale. This reinforces the feasibility of sensor management approaches that adaptively plan to achieve a desired performance level (incorporating user requirements, and with an understanding that exceeding the level has diminishing returns), and that form closed loop, non-myopic policies._x000D_
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[1] J. Miller, “A New Sensor Allocation Algorithm for the Space Surveillance Network,” Military Operations Research, vol. 12, no. 1, pp. 57–70, 2007._x000D_
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[2] K. Hill et al., “Dynamic Tasking of Networked Sensors Using Covariance Information,” presented at the Advanced Maui Optical Space Surveillance (AMOS) Technology Conference, Maui, HI, 2010._x000D_
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[3] Z. Sunberg, S. Chakravorty, and R. S. Erwin, “Information Space Receding Horizon Control for Multisensor Tasking Problems,” IEEE Trans. Cybern., vol. 46, no. 6, pp. 1325–1336, Jun. 2016, doi: 10.1109/TCYB.2015.2445744._x000D_
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[4] S. Fedeler, M. Holzinger, and W. Whitacre, “Sensor tasking in the cislunar regime using Monte Carlo Tree Search,” Advances in Space Research, vol. 70, no. 3, pp. 792–811, Aug. 2022, doi: 10.1016/j.asr.2022.05.003._x000D_
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[5] C. B. Browne et al., “A Survey of Monte Carlo Tree Search Methods,” IEEE Trans. Comput. Intell. AI Games, vol. 4, no. 1, pp. 1–43, Mar. 2012, doi: 10.1109/TCIAIG.2012.2186810._x000D_
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[6] N. K. Dhingra, C. DeJac, J. Neel, A. Herz, T. Wolf, and B. Jones, “The Impact of Orbit Accuracy-Based Tasking on Sensor Network Efficiency,” presented at the Advanced Maui Optical Space Surveillance (AMOS) Technology Conference, Maui, HI, 2022._x000D_
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[7] D. A. Castanon, “Approximate dynamic programming for sensor management,” in Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, USA: IEEE, pp. 1202–1207. doi: 10.1109/cdc.1997.657615._x000D_
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[8] maisonobe, CS-SI/Orekit. (2025). doi: 10.5281/zenodo.16694949._x000D_
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[9] maisonobe, Hipparchus-Math/hipparchus. (2025). doi: 10.5281/zenodo.15234468._x000D_
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Date of Conference: September 15-18, 2026
Track: Space Domain Awareness