Mohammed Irfan Rashed, University of Hawaii Manoa
https://doi.org/10.64861/MAOC5669
Keywords: CR3BP, Cislunar Space, Space Situational Awareness, Observability Analysis, NRHO, Halo Orbits, Three-Body Dynamics, State Estimation, Constellation Geometry, Manifold Dynamics
Abstract:
The transition from Earth-centric operations to sustained activity in cislunar space necessitates a fundamental reassessment of Space Situational Awareness (SSA) architectures. Traditional SSA systems are derived from two-body orbital dynamics, Earth-fixed sensor geometries, and continuous or near-continuous line-of-sight tracking. These assumptions are incompatible with the dynamical structure of the Earth-Moon system, where spacecraft trajectories evolve under nonlinear multi-body gravitational interactions and where ground-based sensing is temporally intermittent and geometrically constrained. As operational concepts expand to include near-rectilinear halo orbits (NRHOs), halo families about libration points, distant retrograde orbits (DROs), and manifold-connected transfer trajectories, SSA must be reformulated as an astrodynamics-constrained observability problem rather than a perturbative extension of low-Earth orbit tracking.
This work defines cislunar SSA as a distributed nonlinear state estimation problem under Circular Restricted Three-Body Problem (CR3BP) dynamics. In contrast to classical orbit determination frameworks, where uncertainty growth is primarily influenced by atmospheric drag and geopotential harmonics, cislunar trajectories exhibit intrinsic sensitivity along unstable manifold directions. Using state transition matrix (STM) analysis in the synodic rotating frame, we examine the anisotropic growth of covariance associated with halo-class trajectories. Results show that estimation uncertainty expands preferentially along unstable eigendirections, producing exponential divergence during specific orbital phases even under moderate initial state dispersion.
These dynamical characteristics impose fundamental limits on Earth-based SSA architectures. Ground stations located on Earth experience limited visibility arcs for NRHO and L2 halo trajectories, particularly during lunar occultation or when geometry induces poor angular separation. Under such conditions, the observability matrix associated with classical angle-only tracking becomes ill-conditioned, leading to transient rank deficiency and amplified state reconstruction error. We demonstrate that even high-precision optical measurements cannot compensate for geometric degeneracy when measurement baselines collapse relative to unstable manifold alignment.
To address these structural limitations, we introduce a constellation-level observability framework that integrates inter-satellite measurements within the three-body dynamical environment. Rather than treating additional spacecraft as independent tracked objects, we model the constellation as a coupled sensing network that augments the global observability matrix. The formulation incorporates nonlinear relative motion, time-varying geometry, and manifold-driven phase evolution. Observability is evaluated using time-dependent rank analysis and singular value decomposition of the augmented measurement Jacobian, revealing how constellation topology directly influences estimation robustness.
A key contribution of this study is the definition of cislunar-specific observability metrics. First, we extend the classical geometric dilution of precision (GDOP) concept to a three-body rotating frame, introducing a three-body geometric dilution of precision (3B-GDOP) metric that accounts for synodic frame rotation and nonlinear relative motion. Second, we define a manifold-aligned sensitivity index that quantifies the projection of estimation covariance onto unstable eigenspaces. Third, we propose a time-windowed conditioning metric that evaluates transient observability degradation over finite measurement arcs, capturing dynamic geometric degeneracies that do not appear in static analysis.
High-fidelity numerical simulations are conducted for representative NRHO and L2 halo trajectories. Multiple constellation configurations are evaluated, including co-orbital phase-offset clusters, manifold-distributed relay architectures, and cross-plane halo geometries. Results indicate that specific phasing strategies can reduce covariance growth rates by aligning measurement geometry with unstable manifold directions, effectively suppressing exponential divergence. In particular, configurations that maintain persistent relative angular separation across unstable axes demonstrate improved estimation stability during periods of Earth occultation.
The analysis further reveals a coupling between invariant manifold transport pathways and optimal sensing geometry. By exploiting natural manifold flows, constellation elements can maintain favorable relative alignment without continuous station-keeping, thereby reducing propellant expenditure while preserving observability conditioning. This finding suggests that orbit design and SSA architecture cannot be decoupled in the cislunar regime; instead, dynamical systems structure should inform constellation geometry from inception.
Importantly, the framework developed here characterizes fundamental astrodynamical limits independent of specific sensor hardware or centralized processing assumptions. The emphasis is placed on geometric and dynamical constraints that bound achievable state estimation performance. While distributed autonomous estimation strategies may leverage these principles, the present contribution lies in establishing a rigorous observability foundation for cislunar SSA under nonlinear gravitational dynamics.
Comparative analysis against Earth-centric extrapolated SSA models demonstrates that neglecting manifold-aligned sensitivity can underestimate state uncertainty growth by significant margins in NRHO-class trajectories. Conversely, constellation-augmented architectures exhibit resilience against intermittent Earth visibility and maintain bounded covariance growth during dynamically sensitive orbital segments. These results provide quantitative design guidance for lunar gateway support missions, logistics traffic management, and long-duration cislunar infrastructure monitoring.
By reframing SSA as a nonlinear dynamical systems observability problem, this work advances an astrodynamics-driven methodology for sustainable situational awareness in the Earth-Moon system. The study establishes analytical and numerical tools for evaluating constellation geometry, defines metrics tailored to three-body motion, and identifies structural principles for estimation stability in weakly stable and unstable orbital regimes. As cislunar activity accelerates, such dynamical considerations will become foundational to scalable and resilient SSA architectures.
As cislunar operations transition from exploratory missions to sustained infrastructure, domain awareness must be grounded in the dynamical realities of the Earth-Moon system rather than extrapolated from low-Earth orbit paradigms. The framework presented in this study establishes quantitative links between three-body orbital structure, measurement geometry, and estimation stability, revealing architectural dependencies that are not evident in two-body analyses. By formalizing constellation-enhanced sensing within a CR3BP-based observability structure, this work provides a rigorous foundation for evaluating performance limits and resilience in future cislunar SSA systems. The results demonstrate that sustainable situational awareness in weakly stable and unstable orbital regimes requires deliberate integration of orbit design, dynamical systems analysis, and estimation theory. These findings offer practical guidance for the development of scalable tracking architectures supporting lunar gateway operations, logistics traffic, and long-duration cislunar assets, and define a pathway toward resilient domain awareness in the evolving Earth-Moon environment.
Date of Conference: September 15-18, 2026
Track: Cislunar SDA