Evangelina Evans, University of Colorado Boulder; Marcus Holzinger, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder
Keywords: cislunar, covariance analysis, visibility
Abstract:
Cislunar space domain awareness (SDA) relies on our ability to detect and track the movement of objects in the Earth-Moon system. To maintain custody of a target and estimate its state, it must be both visible and observable. Visibility is a binary condition determined by observer constraints, such as field-of-view limitations and exclusion zones surrounding celestial bodies. [4] For ground-based observers, the visibility of cislunar objects is governed by two periods: the lunar phase cycle and Earth’s daily rotation. Modeling the dynamics of a spacecraft in the rotating frame of the Earth-Moon system, these cyclic periods impose dynamic viewing constraints defined by the time-variation of angular geometries between the Sun, Earth and Moon. The epoch of an observation campaign can be mapped to an angle pairing which describes the time-of-month and time-of-day based on the relative orientations of the Sun and Earth. The collection of all angle pairings forms a month-by-day-long grid search, where each node represents a possible epoch. By iterating over a finite set of angle pairings, we can evaluate the visibility of cislunar periodic orbits across all epochs.
Visibility is a prerequisite for observability, which has traditionally been defined as a binary outcome based on the rank of the observability matrix, as described in [1]. However, recent works by [2] and [3] introduce observability metrics to quantify “how” observable an object is. In [2], a covariance-based approach integrates the information gained from a set of observation measurements over discrete time intervals to compute the information matrix, which, when inverted, produces the covariance matrix. If the information matrix is singular following an observation campaign, the object is considered unobservable.
This work provides comprehensive covariance analysis for cislunar periodic orbits across all epochs by computing heuristic, covariance-based metrics at each node in the angle-pairing grid. The epoch of an observation campaign is initialized as a node corresponding to a specific lunar phase angle and time-of-day angle. When the spacecraft is visible, collected measurements contribute to the information matrix, reducing state uncertainty. The traces of the position and velocity covariance components serve as heuristic metrics to quantify the spacecraft’s state uncertainty. If the spacecraft is unobservable or if its state uncertainties exceed an acceptable threshold, that node is excluded from further analysis. As a supplementary meta-heuristic, the percentage of total observable nodes is used to assess overall observability of the orbit. At the end of the grid search, position and velocity uncertainty contours are plotted to visualize state covariance trends for the observation campaigns along the orbit as a function of initial epoch. Ideally, orbits should be observable across all nodes; however, the most favorable epochs for an observation campaign are indicated by contours of minimum state uncertainty.
This work will simulate month-long observation campaigns from an equatorial ground station collecting angle-only optical measurements (azimuth and elevation) of a target placed on a periodic orbit defined by the circular restricted three-body problem (CR3BP). The orbits analyzed will include members of the Lyapunov, halo (e.g., L1 NRHO 9:2), vertical Lyapunov, and axial families around the collinear Lagrange points; short and long-period orbits around the triangular Lagrange points; and distant retrograde orbits around the Moon.
In the context of SDA, this work provides a method for assessing how the lunar phase and Earth’s daily rotation cycle impact the visibility of spacecraft on cislunar periodic orbits. By systematically sampling the grid and performing covariance analysis, we can identify optimal observation windows where viewing conditions align with mission constraints, such as allowable state uncertainties. The resulting observability metrics can then inform mission planning, ensuring consistent coverage and maximizing data collection opportunities throughout the lunar cycle.
References:
[1] Justin Kruger, Simone D’Amico. “Observability analysis and optimization for angles-only navigation of distributed space systems.” Advances in Space Research, Volume 73, Issue 11. 2024. Pages 5464-5483. ISSN 0273-1177. https://doi.org/10.1016/j.asr.2023.08.055.
[2] Dianetti, Andrew D., Ryan M. Weisman, and John L. Crassidis. “Application of observability analysis to space object tracking.” AIAA Guidance, Navigation, and Control Conference. 2017.
[3] Fowler, E.E., Paley, D.A., “Observability Metrics for Space-Based Cislunar Domain Awareness,” J Astronaut Sci 70, 10 (2023). https://doi.org/10.1007/s40295-023-00368-w.
[4] Klonowski, M., et al. “Analysis of Persistent Detection Corridors for Cislunar Space Situational Awareness.” Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference. 2024.
Date of Conference: September 16-19, 2025
Track: Cislunar SDA