Jonathon Hope, Pennsylvania State University; Puneet Singla, The Pennsylvania State University; Roshan Eapen, Pennsylvania State University; Peter Kent, Peraton; Michael Goodman, Peraton; Joseph Diamond, Peraton
Keywords: Cislunar, Astrodynamics, Orbit Determination, Multi-Order Shooting Correction Schemes, XGEO, SDA
Abstract:
The growing number of Resident Space Objects (RSOs) has led to an increase in close approaches and the potential for conjunction events across regions from Low Earth Orbit (LEO) to Geostationary Orbit (GEO). Recently, the area beyond GEO, referred to as xGEO, has gained heightened strategic significance as both governmental and private entities make investments in what is being termed New Space Race 2.0. The task of determining the orbits of satellites using contemporary methodologies—such as initial orbit determination, batch least-squares estimation, and Kalman filtering—poses a range of distinctive challenges, particularly in regard to the performance of the traditional algorithms. In the xGEO space, the fundamental structure of space trajectories can be radically different. Potential orbits and trajectories are not limited to the conic sections anymore. The primary challenge that limits the transferability of tools and techniques from the GEO to xGEO region is non-Keplerian dynamics, data sparsity from limited coverage and frequent unavailability of sensors for absolute and relative navigation. While conic section geometry of the orbit in the two-body problem enables relatively straightforward initial orbit determination (IOD) for a variety of measurement types, there is no known IOD analog for the cislunar regime even for the foundational circular restricted three body problem (CR3BP). Gravitational acceleration in cislunar space in typically and order of magnitude smaller than in low Earth orbit. In some perspectives, this is a positive since less propulsion is needed to make large state changes. However, this simple fact also results in increased sensitivity to state errors. This high sensitivity to state error pose challenges in developing IOD algorithms which are robust to initial guess.
Methodology: This paper will utilize recently developed Multi-Order Shooting Scheme (MOSS) to develop robust IOD method to determine the trajectory of a cislunar object from optical observations. Traditional IOD methods uses first order Taylor series expansion of system dynamics and measurement model to arrive at an iterative scheme to estimate the spacecraft states (position and velocity) at an initial time. Such a method suffer requires a “good” guess to arrive at an accurate solution. Alternatively, the stringent requirement of a good initial guess could be reduced by employing correction schemes that use higher-order sensitivities. Higher-order sensitivities of any function at a given point capture more information about the function’s surface in a larger neighborhood around that point. This additional information about the function can be exploited in the shooting method to achieve better convergence. However, methods using sensitivities higher than second-order are rarely investigated, primarily due to the computational cost associated with computing higher-order derivatives. To address this, a derivative-free, non-intrusive approach has been employed to determine higher-order sensitivities. This approach makes extensive use of a non-product quadrature method called the Conjugate Unscented Transform (CUT). The utility of the CUT method as an optimal quadrature scheme has been demonstrated for several applications with great success. Higher-order correction schemes in the shooting method, enabled by sensitivities supplied by the CUT approach, is expected to fare better than a traditional IOD methods for cislunar domain.
Expected Outcomes: The main contribution of the work corresponds to developing a robust initial orbit determination (IOD) algorithm which utilizes the higher-order sensitivity of the underlying dynamics and measurement model. The secondary contribution of the work corresponds to computation of these sensitivities in a derivative free manner. The developed approach is expected to be more robust to initial guess for spacecraft position and velocity at an epoch point. Extensive simulations will be performed to assess the performance of the developed approach compared to traditional nonlinear least squares algorithm. Both periodic orbits around the Lagrange points and transfer trajectories will be considered to quantify the performance of the developed approach. The developed approach will enable a robust data association enabling cislunar space domain awareness.
SDA Applicability: Initial orbit determination is an essential component of space domain awareness (SDA) operations. The proposed IOD framework can be used to start tracks from optical observations of cislunar objects without any a-priori information. The position and velocity estimates can be used as an initial point for sequential state estimation algorithms and to accurately associate measurements with catalog objects.
Date of Conference: September 16-19, 2025
Track: Cislunar SDA