cs.ROMar 21, 2026

Unified Orbit-Attitude Estimation and Sensor Tasking Framework for Autonomous Cislunar Space Domain Awareness Using Multiplicative Unscented Kalman Filter

Authors: Smriti Nandan Paul, Siwei Fan

Organizations: Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, 65409, MO, United States · Embry-Riddle Aeronautical University, 3700 Willow Creek Rd, Prescott, 86301, AZ, United States

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Abstract

The cislunar regime departs from near-Earth orbital behavior through strongly non-linear, non-Keplerian dynamics, which adversely affect the accuracy of uncertainty propagation and state estimation. Additional challenges arise from long-range observation requirements, restrictive sensor-target geometry and illumination conditions, the need to monitor an expansive cislunar volume, and the large design space associated with space/ground-based sensor placement. In response to these challenges, this work introduces an advanced framework for cislunar space domain awareness (SDA) encompassing two key tasks: (1) observer architecture optimization based on a realistic cost formulation that captures key performance trade-offs, solved using the Tree of Parzen Estimators algorithm, and (2) leveraging the resulting observer architecture, a mutual information-driven sensor tasking optimization is performed at discrete tasking intervals, while orbital and attitude state estimation is carried out at a finer temporal resolution between successive tasking updates using an error-state multiplicative unscented Kalman filter. Numerical simulations demonstrate that our approach in Task 1 yields observer architectures that achieve significantly lower values of the proposed cost function than baseline random-search solutions, while using fewer sensors. Task 2 results show that translational state estimation remains satisfactory over a wide range of target-to-observer count ratios, whereas attitude estimation is significantly more sensitive to target-to-observer ratios and tasking intervals, with increased rotational-state divergence observed for high target counts and infrequent tasking updates. These results highlight important trade-offs between sensing resources, tasking cadence, and achievable state estimation performance that influence the scalability of autonomous cislunar SDA.

Figures & tables

Figure 1: Reflection Geometry for a Representative Surface Facet. (quadrilateral facet shown for illustration purpose, triangular facet is used.)
Figure 2: Candidate Observer Orbit Set Consisting of 302 Periodic Trajectories Drawn from 13 Earth-Moon Orbit Families, Shown Together with Fixed Targets in the Rotating Frame (2000 Points).
ParameterValue or Description
Initial epoch2460584.5 JD (00:00:00 UT, October 1, 2024)
Orbit propagation methodRunge-Kutta order 5(4) ( Dormand and Prince, 1980 )
Integration tolerancesRelative and absolute tolerances =10−10=10^{-10}
Static target shape and dimensionSphere with 1 mm radius
Maximum number of architecture evaluations10,000
Optimization early stopping criterion500 iterations
Table 1: Simulation Settings for the Architecture Optimization
Orbit NumberOrbit Family Scenario A | B | CNumber of Satellites Scenario A | B | C
1 2 3 4 5 6 7 8 9 10L3L_{3} Halo north | Butterfly north | L1L_{1} Halo north L3L_{3} Halo south | L3L_{3} Halo south | L2L_{2} Halo south L2L_{2} Halo south | L1L_{1} Halo south | L3L_{3} Halo north L3L_{3} Halo north | L3L_{3} Halo north | L2L_{2} Halo north L3L_{3} Halo south | L2L_{2} Halo south | L2L_{2} Halo north L2L_{2} Halo south | L2L_{2} Halo south | L2L_{2} Halo south L3L_{3} Halo south | L2L_{2} Halo north | L3L_{3} Lyapunov L2L_{2} Halo north | Butterfly south | L2L_{2} Halo south L2L_{2} Halo south | Butterfly south | L2L_{2} Halo south L2L_{2} Halo south | L3L_{3} Lyapunov | L3L_{3} Lyapunov2 | 5 | 5 1 | 2 | 2 7 | 7 | 7 1 | 5 | 1 1 | 3 | 10 1 | 3 | 8 2 | 3 | 2 1 | 2 | 4 3 | 2 | 1 1 | 1 | 3
Table 2: Best-Performing Architectures Identified by the TPE-Based Optimizer for the Sparse-Opt (Scenario A), Moderate-Opt (Scenario B), and Dense-Opt (Scenario C) Cases
Figure 3: Observer Orbits Selected by the TPE-Based Optimizer for (a) Sparse-Opt (Scenario A), (b) Moderate-Opt (Scenario B), and (c) Dense-Opt (Scenario C).
Figure 4: Observer Orbits Selected by the Random Search-Based Optimizer for (a) Sparse-Opt (Scenario A), (b) Moderate-Opt (Scenario B), and (c) Dense-Opt (Scenario C).
ParameterValue or Description
Initial epoch2460584.5 JD (00:00:00 UT, October 1, 2024)
Orbit propagation methodRunge-Kutta 5(4) with relative/absolute tolerances: 10−1010^{-10}
Orbit propagation period1 day
Targets’ initial covarianceDiagonal with position variance 10−1×100000210^{-1}\times 100000^{2} m2m^{2}
 Velocity variance 10−1×(0.1)210^{-1}\times(0.1)^{2} (m/s)2(m/s)^{2}
 attitude error variance 525^{2} deg2deg^{2}
Table 3: Simulation Settings for the Dual Sensor Tasking-State Estimation Task
Figure 5: Scenario A-Based Estimation Performance for Different Target Counts from the Dual Sensor Tasking-Estimation Framework. (a), (b) Show the Fraction of Time Estimation Error is Within 3σ3\sigma Bounds. (c), (d) Show Component-Wise ANEES. (e), (f) Show RMSE Values.
Figure 6: Estimation Results for a Select Few Targets Corresponding to nT=20n_{T}=20 (for Scenario A-based Architecture).
Figure 7: Scenario A and B-Based Estimation Performance for Different Tasking Intervals from the Dual Sensor Tasking-Estimation Framework. (a), (b) Show the Fraction of Time Estimation Error is Within 3σ3\sigma Bounds. (c), (d) Show Component-Wise ANEES. (e), (f) Show RMSE Values.
Figure 8: Scenario A-Based Estimation Performance for Different Tasking Intervals from the Dual Sensor Tasking-Estimation Framework for a Higher Target-to-Observer Ratio (20 Observers, 50 Targets). (a) Shows Component-Wise ANEES, (b) Shows RMSE Values, and (c) Shows Estimation Results for a Representative Target.
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