An online method is presented for detecting and estimating unmodeled translational maneuvers of a target vehicle. Designed for relative navigation scenarios, the algorithm runs onboard the chaser vehicle and operates without communication from the target. By leveraging a buffer of observed pre-fit measurement innovations, the method eliminates the need for prior knowledge about the timing, magnitude, or direction of the target’s maneuvers. This method integrates adaptive process noise estimation with a splitting algorithm designed specifically for this type of unmodeled dynamics. The algorithm demonstrates rapid detection and estimation of unmodeled target maneuvers in a low Earth orbit scenario, without relying on inflated uncertainty bounds. Its performance surpasses that of state-of-the-art adaptive filters designed with prior knowledge of the maneuver. The algorithm also demonstrates competitive performance in detecting and estimating target maneuvers in a cislunar scenario, matching or exceeding state-of-the-art filters configured with prior knowledge of the maneuver. In both scenarios, the adaptive estimation of process noise is key to enable both rapid transient response to detected maneuvers and accurate steady-state performance; all without any prior knowledge of the target’s maneuver timing, magnitude and direction.
Long-term spacecraft motion in multi-body dynamical environments rarely remains strictly periodic; the phase space near periodic orbits is instead foliated by invariant tori supporting quasi-periodic motion, yet generic perturbations may equally destabilize trajectories along hyperbolic directions – making the systematic construction and characterization of these competing structures a central challenge in cislunar trajectory design. To meet this challenge, this paper develops a Fourier–collocation framework for computing families of quasi-periodic orbits (QPOs) in the Circular Restricted Three-Body Problem (CR3BP). Starting from a reference periodic orbit, fundamental frequencies are identified through frequency analysis and Floquet theory, enabling the construction of a full torus embedding expressed directly in angle coordinates. The torus is refined through a nonlinear optimization that enforces dynamical consistency with the CR3BP flow by minimizing Jacobi constant variation across the embedding, yielding a coherent quasi-periodic representation rather than a locally invariant curve. Arclength continuation in Fourier coefficient space then generates complete QPO families, including those surrounding unstable periodic orbits. To systematically improve accuracy, a novel harmonic addition algorithm identifies missing integer combinations of fundamental frequencies through spectral analysis of the Jacobi constant residual and incorporates them into the Fourier basis, reducing phase-point drift by over an order of magnitude for representative cases. Accuracy is assessed globally through phase-point drift analyses that compare the Fourier model against the true CR3BP flow across the full torus surface, providing a quantitative measure of dynamical consistency that is formulated over the entire manifold rather than localized to an invariant curve. Results for Lissajous, quasi-halo, and quasi-distant retrograde orbit families in the Earth–Moon system demonstrate the utility of the framework.
The Poincaré integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a numerical procedure for obtaining the state transition matrix (STM). Although phase-space volume is only preserved for conservative systems, we show how the invariants can be used to numerically compute the STM even when the system in question is modeled with nonconservative forces. The method is equivalent to a forward finite-difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. The new formulation allows the error in the linearization to be related to deviations in the modeled integral invariants. Numerical experiments using orbital motion and uncertainty propagation verify that linearization errors tend to be minimized when perturbation sizes correspond to minimal fractional error in the modeled integral invariants.
Space Situational Awareness (SSA) has become increasingly urgent as the need for reliable tracking and characterization of Resident Space Objects (RSOs) continues to grow. Progress in this area has been limited by the scarcity of community-accessible hyperspectral data. To address this gap, the United States Air Force Academy (USAFA) utilized its Falcon Telescope Network (FTN) to collect unresolved hyperspectral signatures of geosynchronous satellites. Prior studies using this dataset relied on nightly averaged spectra and one-dimensional (1D) time-series (TS) representations, often paired with complex deep learning (DL) classifiers. In contrast, this work investigates two methodological advances: the use of all individual observations without temporal averaging, and the transformation of spectral TS data into two-dimensional (2D) representations using Gramian Angular Summation Field (GASF) encoding. This approach is motivated by the ability of simpler DL classifiers, such as convolutional neural networks (CNNs), to effectively learn structured features. To address data scarcity and observational variability, physically motivated data augmentation strategies were applied, and conditional variational autoencoders (CVAEs) were explored for generating additional training samples. Models trained on GASF representations consistently outperformed TS baselines, achieving mean classification accuracies of approximately 80
Accurate characterization of the spectral Bidirectional Reflectance Distribution Function (BRDF) of spacecraft materials is critical for a wide-range Space Situational Awareness (SSA) tasks ranging from assessing the pose of spacecraft to modeling solar radiation influences on trajectories. Unfortunately, many goniometer systems that are used to measure the BRDF of materials are highly specialized, bulky, and costly to repair. These limitations mean that performing BRDF measurements within a small and potentially damaging space-weathering chamber is prohibitive in terms of both the cost-to-repair goniometer damage and overall volume-allowance. This is a major gap for BRDF characterization of spacecraft materials, as recent experiments have shown that BRDF can substantially differ when characterized in Earth’s atmosphere relative to when characterized under the influence of space weather factors such as Ultraviolet (UV) radiation and Atomic Oxygen (AO). To meet this need, we present the development of a Commercial Off The Shelf (COTS) goniometer system that enables broadband characterization of the BRDF of spacecraft material samples: the Georgia Tech Research Institute Goniometer (GT-RIG). This system has a volume-constrained design with easily swappable COTS components, enabling future BRDF characterization within space-weathering chambers. In this paper, we present a characterization of the prototype system, a modeling of the uncertainties of resultant BRDF measurements, and an initial set of BRDF measurements acquired by the system on Kapton material samples.
In-space assembly and servicing missions demand precise trajectory planning to prevent thruster plume impingement on sensitive components of the client spacecraft. In this paper we present a novel mathematical formulation for incorporating multiple ellipsoidal thruster-pointing constraints into the six-degree-of-freedom fuel-optimal rendezvous problem, using a target-relative Circular Restricted Three-Body Problem dynamical model. By analytically mapping thruster ray intersections with ellipsoidal exclusion zones onto a sphere, the method enables the construction of smooth activation functions that deactivate thrusters when violations would occur. This formulation is integrated into an indirect optimal control framework solved via single shooting, offering efficient convergence and satisfaction of the necessary conditions for optimality. The approach is validated through three simulation scenarios, including a servicing mission at the Sun–Earth L2 point, all demonstrating adherence to pointing constraints while achieving fuel-optimal trajectories. The method is flexible and scalable, making it well-suited to complex spacecraft geometries.
Compared to extensive studies on apparent magnitude and bi-directional reflectance functions (BRDFs) for Low Earth Orbit (LEO) satellites like Starlink, there has been a notable gap in the literature when it comes to spectral radiance characterization. Such characterization would be highly beneficial to the emerging Alternative Positioning, Navigation, and Timing (Alt-PNT) method of Terrestrial Optical Navigation, which involves collecting optical line-of-sight measurements to satellites in the presence of sky background, turbulence, and other atmospheric effects. Specifically, it could allow for careful design of optical filtering schemes to maximize signal-to-noise ratio (SNR) of the satellite measurements. To address the literature gap, the authors introduce a dataset resulting from a four-night observation campaign with the Magdalena Ridge Observatory’s 2.4-meter telescope. Spectra spanning 380–860 nm were collected for 50 satellites and orbital objects across LEO, Medium Earth Orbit (MEO), and Geostationary Orbit (GEO), with particular emphasis on all three generations of Starlink satellites. Analysis of the Starlink data reveals a local reflectance peak near 475 nm, a shape similar to the solar irradiance curve, and a distinct near-infrared spike for the v2 generation. Estimation of absolute spectral flux from relative flux density measurements is presented, as well as discussion on how near-infrared (NIR) or short wave infrared (SWIR) sensing could expand the operational envelope of terrestrial optical navigation. This dataset offers new insight into the feasibility of optical satellite tracking under challenging conditions, including daylight operations and onboard high-speed aerospace vehicles.
For perturbed two-body motion—such as small bodies in heliocentric orbits—the Cartesian state uncertainty alternates between near-Gaussian and strongly non-Gaussian regimes over the orbit. This behavior motivates hybrid estimators that adapt to the changing character of the uncertainty. Implementation of a hybrid filter hinges on the mechanisms that control the transitions between the two frameworks. In this paper, we introduce an unscented Kalman filter/particle filter (UKF/PF) hybrid prediction strategy that uses the normalized Euclidean distance to switch from the UKF (moment-based) to the PF (sample-based), and the Henze-Zirkler statistic to switch back, with dynamics sourced from ASSIST, an ephemeris-quality integrator. This autonomous switching technique requires only the abstractions propagated during prediction, enabling complete independence from measurement updates. We demonstrate the capability of the approach by propagating the state uncertainty of the asteroid 2024 YR_4 from its orbit solution in November 2025 to its close approach of the Moon in December 2032. The hybrid UKF/PF accurately and efficiently predicts the lunar impact probability, velocity, angle, and potential cratering of 2024 YR_4 , providing all the information necessary to assess the potential fallout of the ejecta created from such an impact event. The proposed hybrid prediction method effectively balances and integrates the complementary strengths of the moment- and sample-based approaches in a measurement-free environment.
Accurately characterizing spacecraft materials and the effects of aging is essential for space situational awareness. This study explores the use of a color index taxonomy, developed from laboratory data, as a tool for distinguishing satellite materials based on their optical signatures. The approach extends this taxonomy to include both pristine materials and their irradiated states. Samples from various chemical groups were exposed to high-energy (95 keV) electron irradiation, while their optical properties were monitored using Directional Hemispherical Reflectance (DHR) measurements. Signal intensity was analyzed using the Sloan Digital Sky Survey (SDSS) astronomical filter set. Both visual and quantitative assessments of color-color diagrams were conducted to evaluate the feasibility of differentiating materials through photometric measurements. The results demonstrate the potential of color indices as a remote sensing technique for identifying spacecraft materials and assessing material degradation in space environments
Relative motion between orbiting spacecraft is commonly modeled in the Hill frame due to its analytical first-order solutions and the intuitive geometry of the resulting trajectories. However, the Hill frame is not ideal for mission scenarios involving constraints defined in the body frame of a spinning chief, such as collision avoidance during close-proximity operations or docking within a keep-in zone. This paper investigates relative motion from the perspective of the rotating body frame of the chief, focusing on three fundamental spin cases. In each case, the body frame is initially aligned with the Hill frame and undergoes constant rotation about one of the Hill frame coordinate axes: radial, along-track, and cross-track direction. Closed-form solutions to the Clohessy-Wiltshire equations are used to derive analytical expressions for the relative motion in the chief body frame, assuming circular chief orbits and small separation distances. The resulting trajectories are described using geometrically meaningful invariants of motion, providing intuitive insights into the trajectory shapes and locations. These trajectories are characterized as parametric epitrochoid or hypotrochoid curves. The analysis considers both bounded and drifting motion, and includes both resonant cases, where the spin rate equals the orbital rate, and non-resonant spin cases.
This paper introduces a class of gravity-assist trajectories that enable low-altitude, ballistic flybys over Saturn’s main rings. An analytical framework is developed to construct conic orbits that intersect the ring plane at specified radii and altitudes, using closed-form relations between orbital elements and desired ring-pass geometry. By linking Titan flyby conditions to the resulting ring-skimming trajectories, families of feasible tours are identified that traverse the D, C, B, and F rings across a broad range of relative velocities and observation durations. To illustrate the method, a 162-day reference tour is designed featuring four Titan gravity assists, thirteen low-inclination ring passes, and additional opportunistic flybys of icy moons such as Enceladus and Rhea. This approach expands the mission design space for in situ ring science by enabling repeated close-range observations.
The Asynchronous One-Way Range (AOWR) scheme was developed by the authors, and the results of the field tests conducted to date have been reported. It works in a pair of transceivers. The Gravity Recovery and Climate Experiment (GRACE) mission adopted the Dual One-Way Range (DOWR) scheme to measure distance by referencing the phase difference, while clock synchronization is performed independently through the code correlation method known as Two-Way Time Transfer (TWTT). The clock synchronization has been conceived distinct from the range measurement. However, the mutual phase difference data inherently contain not only range information but also clock-difference information. This paper provides an overview of how the single AOWR scheme operates in real-time by integrating a simultaneous range measurement method with clock synchronization. This paper discusses how relativity is treated in the AOWR scheme enabling the simultaneous measurement through symmetric formulation, taking advantage of the duality. The symmetric formulation developed in this paper accounts strictly for special and general relativistic time dilation. While the current AOWR scheme relies on code correlation, which exhibits significant fluctuations and reduced accuracy, the paper further incorporates a mutual carrier-phase tracking scheme into the AOWR framework. The new estimator yields significantly more stable and accurate range and clock-difference data. The paper presents how the effects of tropospheric and ionospheric delays are effectively mitigated for the AOWR scheme in the configurations that include a ground station. Preliminary hardware-in-the-loop tests have been conducted, and their results are presented.
An efficient new framework for automating the search for multiple-body high-fidelity pump-down tours is presented. An existing pathfinding method for same-body transfer sequences is extended to include inter-moon transfers in patched conics. A separate algorithm analyzes each multiple-body sequence to determine how many legs can be efficiently converted to high-fidelity and optimized. The sequences are pruned, and patched conics searches are repeated from the terminal conditions of the high-fidelity trajectories. Frequent corrections in the high-fidelity model allow the optimization scheme to exploit, rather than fight, the high-fidelity perturbations. The process is automated and returns a Pareto optimal trade space of high-fidelity multiple-body pump-down tours. The method is used to create integrated trajectories starting at Titan arrival conditions and terminating with capture at Enceladus. The resulting Pareto front ranges from 900-1030 days time of flight and 410-550 m/s Δ v , and leads to a compelling case for sending an orbiter to Enceladus.
A computationally efficient approach is presented to propagate initial condition uncertainty, represented by a probability density function (PDF), through a nonlinear system. The log-PDF is assumed to be a linear combination of basis functions, and the amplitudes of these functions are computed by requiring the approximation to satisfy the Fokker-Planck-Kolmogorov equation (FPKE). Sparse approximation tools are utilized to trade off between FPKE error and the sparsity of the log-PDF model. The approach derives insights from known analytical stationary solutions of FPKE to construct multidimensional basis functions that accurately represent the state PDF. This judicious construction of basis functions helps alleviate the curse of dimensionality associated with the growth of basis functions in multidimensional space. Two nonlinear oscillators and a two-body problem are considered to demonstrate the efficacy of the proposed approach. Simulation results show that this approach effectively propagates uncertainty through both non-conservative and conservative systems.
A next-generation Mars Network is investigated to determine a configuration optimized for both communications and positioning performance for surface users. A previously proposed 6000 km altitude, 3-satellite equatorial constellation that was found to be optimal for communications to surface users located in the latitude range from 60°S to 60°N is shown to be deficient for surface positioning. Inclining the 3-satellite configuration between 30° and 50° improves positioning performance to users in this latitude range; however, due to a lack of coverage this improvement is primarily seen for positioning when using tracking data collected over long timespans. Moving to an inclined 6-satellite case and using a Walker 6/2/0 delta configuration, at selected inclinations and altitudes, greatly improves the positioning solution performance over shorter timescales, with the best performance obtained with orbits inclined at 50°. Also examined were continuous coverage global constellations that were compared to the Walker 50°: 6/2/0 configurations. The single fold continuous coverage Walker 55.7°:7/7/5 constellation slightly improves the positioning performance and provides more uniform and continuous coverage to the poles, which the Walker 50°:6/2/0 case cannot. Finally, a Walker 57.1°: 8/8/2 constellation that provides continuous twofold coverage was examined; however, the high altitude required for this case reduces its communication performance and yields poorer positioning performance relative to the Walker 55.7°:7/7/5. It is concluded that a next generation Mars Network with focused support to users between 60°S and 60°N that the Walker 50°: 6/2/0 is the best positioning and communications performance while, for continuous coverage global coverage, the Walker 55.7°: 7/7/5 is superior.
A fundamental astrodynamics problem is to map impulsive trajectories into finite- and low-thrust ones. We propose a thrust-continuation based mapping between minimum- Δ v impulsive and finite-thrust trajectories. Two notable features of the proposed method are: a) guessing the non-intuitive costates is completely circumvented, and b) multiple-impulse trajectories can be converted into multiple-revolution finite- and low-thrust fuel-optimal trajectories. A novel derivation is proposed to estimate the mass costate from extremal impulsive solutions, based on a high-thrust assumption. The method is tested on three trajectory design problems under two-body dynamics and one problem under the circular restricted three-body problem (CR3BP) dynamics of the Earth-Moon system. A remarkable result, under two-body dynamics, is the uniqueness of the fuel-optimal solutions for the specified total number of revolutions, when limited to a single orbital revolution on each potential phasing orbit. Results show the method applies successfully to extremal multi-impulsive trajectories under both two-body and CR3BP dynamics. If we consider incipient minimum- Δ v impulsive solutions, results indicate that impulsive maneuvers are mapped into local fuel-optimal trajectories. A fascinating heretofore unknown finding is the existence of a critical thrust value (for the same initial mass and specific impulse values) at which two completely different fuel-optimal trajectories result in the same final mass for the same total time of flight and number of orbital revolutions.
The study evaluates the atomic oxygen (AO) durability and surface stability of novel polymeric materials proposed for low Earth orbit (LEO) applications. The siloxane-, polyhedral oligomeric silsesquioxane (POSS)-, and polyimide (PI)-based films were exposed to ground-based AO conditions simulating up to six months of LEO-equivalent fluence. All three materials were systematically investigated through measurements of mass loss, surface roughness evolution, and defect formation to determine resistance to AO exposure. Results confirm the excellent capabilities of the PI-based film, a mature technology manufactured by DuPont, which exhibited the lowest mass loss at 0.35
Unmodeled forces and torques can cause significant variations in the desired position and attitude of a spacecraft in orbit. For the attitude part, disturbances are typically absorbed by reaction wheels, which have the ability to store external torques in the form of angular momentum. This paper investigates the use of a gimbaled solar electric propulsion thruster to manage reaction wheel momentum, in addition to its primary scope of providing low thrust to follow a heliocentric trajectory, with the aim to prevent the wheel momentum from growing excessively. The thruster is mounted on a dual-gimbaled platform attached to the spacecraft hub. The two degrees of freedom associated with the direction of the thruster are exploited to counteract the momentum buildup on the wheels and reduce the necessity of performing impulsive momentum management. The novelty of this work is the complete kinematic analysis of this system for general spacecraft configurations with such a gimbaled thruster. Large rotating solar arrays provide the required power for the electric thruster and are also used to leverage the solar radiation pressure torque to offload momentum. Emphasis is placed on the problem of determining how to align the thruster in the presence of uncertainties in the center of mass location. The steady-state integral feedback term of the attitude control law is used to inform a sequential least-squares estimator about the location of the center of mass, which is iteratively estimated. The results illustrate that even with small degree-level thruster platform orientation changes, the three-dimensional center-of-mass location can be estimated.
It is challenging to measure the mass of an asteroid in a high-speed spacecraft flyby, especially for the small 50-140 m diameter asteroids that are the primary concerns for planetary defense. Prior work on improving the mass measurement capability of flybys has focused on deploying single-use test-masses from a host spacecraft and tracking them using relative measurements. Instead of test-masses, this research studies the possible mass measurement performance from using multiple full spacecraft to perform the flyby. We find that with interspacecraft measurement accuracies of 0.1 mm/s for range-rate and 1 m for range, four spacecraft can measure the mass of 140 m asteroids to better than 15 % 1 σ for flyby speeds up to 20 km/s, or 50 m asteroids up to speeds of 5 km/s. With a better intersatellite range-rate measurement accuracy of 0.1 μ m/s, four spacecraft can measure the mass of 50 m asteroids for speeds up to 20 km/s as well. These results demonstrate the capabilities required to measure asteroid masses in most planetary defense scenarios.
