Sensor Tasking for Low Earth Orbit Objects: Leveraging Space Sensor Data for Ground-Based Optical Observations

Because of recent advancements in space technologies, easier and more economical access to space, and an increase in commercial interests, the near-Earth space environment has witnessed an exploding number of objects being put into orbit. In particular, the low Earth orbit (LEO) region is at an increased risk of orbital collisions from large satellite constellation projects. Thus, monitoring LEO objects for space situational awareness and space traffic management has become increasingly imperative. In this paper, we use the concept of limited-CDF (cumulative distribution function) surface and mutual information for designing sensor tasking algorithms focusing on regular observation of known catalog LEO objects (follow-up). Observations are carried out using a simulated ground-based optical telescope. The simulations are representative of realistic observation processes. We investigate how data from passive space-based sensors can be used to improve the follow-up performance of the telescope. A sensor-tasking framework is developed in which we conduct a comparative study to assess how different types of satellite constellation patterns such as Walker-delta and Walker-star affect the overall sensor tasking performance. Several case studies are carried out to address the following points: (1) what are the appropriate characteristics of the parameters to be optimized and how does it impact the evolution of orbital state uncertainties?, (2) compare different traditional and non-traditional algorithms for sensor tasking problem, (3) investigate the effect of measurements from different constellation configurations of passive space-based sensor, and (4) what is an appropriate coordinate system for the limited-CDF surface

Advancing Cislunar Space Domain Awareness Through Robust Optimization Framework for Optical Sensors-Based Autonomous Satellite Systems

The number of cislunar resident space objects is expected to proliferate rapidly because of strategic interests targeting long-term presence on the Moon and exploration of other planets (e.g., Artemis Accords) and liberalization of space through the entry of private space players (e.g., Intuitive Machines). It necessitates expanding current near-Earth space domain awareness (SDA) operation systems and knowledge to the relatively unexplored cislunar region. Besides the traditional complexities, xGEO orbits (orbits beyond the geosynchronous Earth orbit (GEO) region) face additional challenges because of highly non-linear and non-Keplerian dynamics, which results in inaccuracies in uncertainty propagation and state estimation. Further challenges include varying degrees of stability or instability in different orbits and observation challenges due to large distances (detection difficulties), sensor/target geometric and illumination constraints, enormous volume to be covered, and the vast number of space/ground-based possibilities for sensor placement. Motivated by these challenges, the current paper presents an advanced optimization framework for cislunar SDA, which includes the following two tasks: (1) perform observer architecture optimization involving a realistic multi-objective cost function utilizing the Tree of Parzen Estimators (TPE) algorithm and (2) using the optimized architecture, solve a mutual information-based sensor tasking optimization problem, while simultaneously carrying out orbital and angular state estimation at a cadence smaller than the tasking cadence

Correction: Advancing Cislunar Space Domain Awareness Through Robust Optimization Framework for Optical Sensors-Based Autonomous Satellite Systems (American Institute of Aeronautics and Astronautics Inc, AIAA)

Correction Notice • Page 8: $\lambda_2$: It represents the cardinality-weighted corrected to $\lambda_2$: It represents the inverse of cardinality-weighted. Equation $\lambda_2=\sum_{i=1}^{10}(n_i\Xi_i)$ corrected to $\lambda_2=1/(\sum_{i=1}^{10}(n_i \Xi_i))$ • Page 11: Table 1 is updated with new orbital families and number of satellites & 1 & $L_2$ Halo south|$L_1$ Halo north|Butterfly south & 1|2|3\\ & 2 & $L_1$ Halo north|$L_2$ Halo south|Dragonfly south & 5|10|3\\ & 3 & Butterfly south|$L_2$ Halo south|$L_2$ Lyapunov & 3|10|4\\ & 4 & $L_1$ Halo south|$L_2$ Halo north|$L_1$ Halo north & 5|3|1\\ A|B|C & 5 & $L_2$ Halo south|$L_1$ Lyapunov|$L_2$ Halo north & 2|8|9\\ & 6 & $L_3$ Lyapunov|Butterfly north|$L_1$ Lyapunov & 1|3|9\\ & 7 & $L_1$ Halo south|Dragonfly north|Dragonfly north & 1|1|3\\ & 8 & $L_2$ Halo south|$L_1$ Lyapunov|$L_1$ Lyapunov & 1|10|8\\ & 9 & $L_1$ Lyapunov|Butterfly south|$L_1$ Halo north & 10|2|2\\ & 10 & $L_1$ Halo north|Dragonfly south|Butterfly north & 1|9|1\\ Corrected to & 1 & $L_3$ Halo north|Butterfly north|$L_1$ Halo north & 2|5|5\\ & 2 & $L_3$ Halo south|$L_3$ Halo south|$L_2$ Halo south & 1|2|2\\ & 3 & $L_2$ Halo south|$L_1$ Halo south|$L_3$ Halo north & 7|7|7\\ & 4 & $L_3$ Halo north|$L_3$ Halo north|$L_2$ Halo north & 1|5|1\\ A|B|C & 5 & $L_3$ Halo south|$L_2$ Halo south|$L_2$ Halo north & 1|3|10\\ & 6 & $L_2$ Halo south|$L_2$ Halo south|$L_2$ Halo south & 1|3|8\\ & 7 & $L_3$ Halo south|$L_2$ Halonorth|$L_3$ Lyapunov & 2|3|2\\ & 8 & $L_2$ Halo north|Butterfly south|$L_2$ Halo south & 1|2|4\\ & 9 & $L_2$ Halo south|Butterfly south|$L_2$ Halo south & 3|2|1\\ & 10 & $L_2$ Halo south|$L_3$ Lyapunov|$L_3$ Lyapunov & 1|1|3\\• Page 12: Figures 3a (left), 3b (middle), 3c (right) are updated with the new orbits. (Image presented)

Sensor Tasking Strategies for Space-Based Observers in the Cislunar Environment

The cislunar space environment has witnessed an increase in activities, and future projections indicate significant growth in object population. Consequently, it becomes crucial to monitor these objects for space domain awareness (SDA) purposes. As the number of objects surpasses the available observers, meticulous sensor tasking becomes essential. This paper focuses on designing and exploring strategies for observing and keeping custody of known objects in cislunar space. Optical space-based telescopes, combined with lunar ground-based telescope, are employed for sensor tasking of cislunar objects residing in valuable orbits. The proposed research aims to address the following key points: (1) examination of the feasibility and efficacy of Moon-based optical observer for sensor-tasking, (2) investigation of the selection of space-based observer orbits for sensor-tasking and benefit of coupling space and (lunar) ground-based observers, (3) utilization of non-product quadrature methods to propagate the covariance for the objects of interest, and (4) development and comparison of probability density-based and information-gain-based methods for optimizing the sensor-tasking framework in cislunar space. The outcomes of this research will contribute to enhanced monitoring and situational awareness in the evolving cislunar region

Advanced Ensemble Modeling Method For Space Object State Prediction Accounting For Uncertainty In Atmospheric Density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed HASDM-ML, CHAMP-ML, and MSIS-UQ machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called consider covariance sigma point (CCSP) filter that can account for the density uncertainties during orbit propagation. As a testbed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions

Stochastic Modeling Of Physical Drag Coefficient – Its Impact On Orbit Prediction And Space Traffic Management

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space domain awareness (SDA). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of SDA. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. (2021), we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch ∈ (-90°, +90°) and satellite yaw ∈ (0°, +360°)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known Challenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, along-track, and cross-track orbital errors caused by drag coefficient uncertainty. The key takeaways of this paper are - (a) a constant drag coefficient cannot be used for reliable SDA purposes, and (b) stochastic machine learning models allow for the computation of drag coefficients in a timely manner while providing reliable uncertainty estimates

Updates And Improvements To The Satellite Drag Coefficient Response Surface Modeling Toolkit

For satellites in the Low Earth Orbit (LEO) region, the drag coefficient is a primary source of uncertainty for orbit determination and prediction. Researchers at the Los Alamos National Laboratory (LANL) have created the so-called Response Surface Modeling (RSM) toolkit to provide the community with a resource for simulating and modeling satellite drag coefficients for satellites with complex geometries (modeled using triangulated facets) in the free molecular flow (FMF) regime. The toolkit fits an interpolation surface using non-parametric Gaussian Process Regression (GPR) over drag coefficient data computed using the numerical Test Particle Monte Carlo (TPMC) method. The fitted response surface provides a substantial computational benefit over numerical approaches for calculating drag coefficients. In this work, the RSM toolkit is further developed into a versatile software with extended capabilities. The capabilities are specifically expanded to include uncertainty quantification and adaptation for automatic development of regression models for satellites with non-stationary components (e.g., rotating solar panels). Furthermore, the toolkit uses Python 3.x and C programming languages to provide an open-source software package with a OSI approved GPL license. To assist the end user, the new RSM toolkit has been developed to have a user-friendly installation process and is provided with extensive documentation. The analysis of two different conceptual satellites is performed during this work: a simple cube and a CubeSat consisting of a simple cube body with 2 rotating solar panels. During the creation of the regression model for each satellite for different atmospheric species, it is found that the cube\u27s minimum Root Mean Squared Error (RMSE) is 0.00211 and the maximum RMSE is 0.00350. The CubeSat has a minimum RMSE of 0.00304 and the maximum is 0.00498. These results are overall conducive of a well performing regression model

Orbital Perturbations for Space Situational Awareness

Because of the increasing population of space objects, there is an increasing necessity to monitor and predict the status of the near-Earth space environment, especially of critical regions like geosynchronous Earth orbit (GEO) and low Earth orbit (LEO) regions, for a sustainable future. Space Situational Awareness (SSA), however, is a challenging task because of the requirement for dynamically insightful fast orbit propagation models, presence of dynamical uncertainties, and limitations in sensor resources. Since initial parameters are often not known exactly and since many SSA applications require long-term orbit propagation, long-term effects of the initial uncertainties on orbital evolution are examined in this work. To get a long-term perspective in a fast and efficient manner, this work uses analytical propagation techniques. Existing analytical theories for orbital perturbations are investigated, and modifications are made to them to improve accuracy. While conservative perturbation forces are often studied, of particular interest here is the orbital perturbation due to nonconservative forces. Using the previous findings and the developments in this thesis, two SSA applications are investigated in this work. In the first SSA application, a sensor tasking algorithm is designed for the detection of new classes of GEO space objects. In the second application, the categorization of near-GEO objects is carried out by combining knowledge of orbit dynamics with machine learning techniques

Space debris charging and its effect on orbit evolution

With the increasing number of debris in the space environment surrounding Earth, it has become important to keep track of the orbits of these defunct objects so as to avoid collisions with active satellites, transiting spacecrafts or other important space assets. In this paper, attention has been paid to trajectory evolution of debris in low Earth orbit and geosynchronous orbit regions. One of the forces effecting the trajectory of a space debris is the Lorentz force, which acts when a charged body moves through the Earth\u27s magnetosphere. Because of continuous bombardment of plasma particles, a space debris is often subject to charging. Correct modeling of Lorentz force requires correct modeling of magnetosphere and the body charge, which in turn depends on correct modeling of body currents, space-plasma environment and body capacitance. This research involves modeling of in-space charging for space debris, which are modeled as spherical conductors. Simulations incorporating Lorentz force as an additional perturbation force have been run to evaluate propagation of low area-to-mass ratio and high area-to-mass ratio objects