Casey Heidrich, University of Colorado Boulder; Marcus Holzinger, University of Colorado Boulder
Keywords: Initial Orbit Determination, Astrodynamics, Maneuver Estimation, Optimization
Abstract:
Initial orbit determination (IOD) is a continuing challenge in cislunar space situational awareness (SSA). A reliable SSA architecture must accurately compute orbits of observed spacecraft from optical or radio frequency measurements to predict future motion. Traditional IOD methods, such as Gauss or double-r methods [1], were developed exclusively for the application of two-body orbital mechanics. The highly chaotic and complex orbits of cislunar space necessitate considerable advances in reliable computing methods for IOD problems in these regions (where two-body assumptions are invalid). This challenge has precipitated a considerable effort in the literature [2-7] to develop novel and effective methods for cislunar IOD. Prior work includes machine learning aided strategies and iterative numerical methods, with the goal of improving the accuracy of reconstructed orbits. A key limitation of many current approaches is prediction of motion over increasingly long observing windows. Over time, multi-body orbital mechanics introduce chaotic behavior that becomes difficult to predict within optimization-based algorithms. Furthermore, an observed object may perform unknown maneuvers between observations, leading to divergence of assumed dynamics models. Continuing work must focus on improving methods for non-Keplerian IOD with dynamical inconsistency and inherent chaos.
In this work, we focus on a class of IOD algorithms built using sparse grid collocation methods [8,9]. Unlike explicit integration methods that “march” a solution forward or backward in time, the collocation IOD approach implicitly enforces system dynamics through transcription constraints. The resulting solution can be rapidly computed using nonlinear programming solvers. One of the primary benefits of the approach is the elimination of the requirement for a close initial guess to the true solution. Solver convergence is sufficient for a wide range of orbits beginning with an initial guess at one of the Earth-Moon Lagrange points, for example. Recent applications to agile spacecraft trajectories [9] have demonstrated reliability for IOD with impulsive or continuous low-thrust maneuvers. Control reconstruction is a highly valuable tool for understanding spacecraft thrust capability and predicting future motion.
Collocation-based IOD methods have shown promise for solving complex IOD problems, but their applications have largely been limited to simplified dynamics models, such as the circular restricted three-body problem (CR3BP). Although CR3BP dynamics are widely used and validated in cislunar SSA, they can be inaccurate for realistic observing applications. For example, the small eccentricity of the Earth-Moon orbit gradually changes the relative distance between the two bodies over the course of one synodic period, violating circular assumptions. External perturbations including the sun’s gravity and solar radiation pressure will also influence spacecraft motion. Generalizations such as the elliptic three-body problem [10] and bi-circular four-body problem [11] can offer some improvements to model accuracy, at the expense of computational complexity and geometric insight of the CR3BP. However, NASA’s SPICE toolbox [12] is widely considered the gold standard in modeling planetary ephemerides for space mission design and observation geometry. Given the need for operational reliability of IOD algorithms, we are motivated to develop an approach taking advantage of both: a) high-fidelity ephemeris models offered by SPICE for realistic observation geometry and physics modeling, and b) computational reliability and efficiency of collocation-based IOD algorithms to perform spacecraft tracking and maneuver reconstruction.
This work seeks to develop an accurate and efficient IOD method for cislunar space directly leveraging planetary ephemeris models. First, we discuss relevant reference frames and SPICE configuration data. Next, we outline models for three-body dynamics in the inertial J2000 frame to generate truth simulation trajectories. We then develop rotating frame dynamics from SPICE data, without relying on planar or circular orbit assumptions from the CR3BP. A collocation approach is applied to the ephemeris-derived rotating frame dynamics to model motion of cislunar spacecraft. The resulting solution can then be transformed back into an inertial frame for comparison. Initial results show accurate reconstruction from simulated measurements for realistic spacecraft orbits, using archival data from the NASA JPL Horizons interface. Data for spacecraft with known, documented historical maneuvers will be used to further validate the approach. Ephemeris-based IOD methods have significant potential to improve cislunar SSA capabilities by leveraging high-fidelity models for tracking and orbit determination of realistic spaceflight applications.
References
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Date of Conference: September 16-19, 2025
Track: Cislunar SDA