The availability of realistic covariance information for the orbit of every Resident Space Object (RSO) contained in a catalogue is crucial for Space Situational Awareness activities, e.g., collision avoidance services. The most comprehensive of these catalogues is the Special Perturbations Catalogue (SPCAT), maintained by the U.S. 18th Space Defense Squadron. The SPCAT is the high-precision ephemeris version of the Two Line Elements RSOs catalogue, publicly available on databases such as Space Track and Celestrak. However, covariance information is not provided with the mean state of the SPCAT ephemerides. So-called observed covariance values can be obtained via a comparison procedure between consecutive orbit information updates referring to the same SPCAT RSO. This paper proposes new methodologies for calculating covariance values for catalogues deprived of such information, including the application and adaptation of existing data-fusion methods from literature. The main final goal is to compute covariance matrices that are more realistic and reliable than those obtained with the currently available methods. Another key objective is the integration of the new methodology in an operational environment. Computational efficiency is then a relevant factor, and the baseline method to be developed is selected and improved taking into account such efficiency criterion. A new routine that considers the Orbit Determination epoch of each RSO ephemeris arc to coherently combine covariances based on their propagation time is developed and implemented. Two fusion methods are deployed, Covariance Intersection and Covariance Union, and the realism of the results is tested with a well-established metric, the Mahalanobis distance and its fitting of the Chi-square distribution according to appropriate Empirical Distribution Function tests such as Cramer-von Mises. The realism of the combined covariances is validated against precise ephemeris of LEO Sentinel satellites. While Covariance Intersection is proved inadequate as a stand-alone fusion method due to the characteristics of the SPCAT observed covariances, Covariance Union provides covariance values that are consistently more realistic than the ones obtained with the baseline method.

The increasing congestion of Earth's orbital environment necessitates advancements in traditional Space Surveillance and Tracking (SST) methods to ensure the safe and sustainable use of space. In this context, accurately estimating the attitude of uncontrolled space objects is essential for developing effective space debris mitigation strategies and improving key predictions, such as atmospheric reentries and collision probabilities. This study introduces the AISwarm-UKF method, a novel approach for attitude estimation of uncontrolled space objects with known geometric and optical characteristics using light curve data. The method integrates different estimation, optimisation and data analysis techniques, namely Adaptive Importance Sampling (AIS), Systematic Resampling, Particle Swarm Optimisation (PSO), Clustering and the Unscented Kalman Filter (UKF), to improve the performance of the Bayesian inference process. Applied to a realistic operational scenario, the AISwarm-UKF method demonstrates high accuracy, robustness, and computational efficiency, offering a viable solution for space situational awareness. (c) 2025 The Authors. Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

The efficiency and sustainability of spacecraft operations is a growing challenge due to the accelerated increase of the space objects population. Thus, the quality of Space Traffic Management (STM) and Space Situational Awareness (SSA) services is essential to ensure the sustainability of the space environment. The quality of such services relies not only on an accurate knowledge of the Resident Space Object (RSO) state, but also on its associated uncertainty. However, there is a lack of accurate and cost-effective methodologies for Uncertainty Quantification (UQ) in the context of SSA, where a large number of objects are maintained in the catalogues. The atmospheric drag is one of the largest sources of uncertainty in Low Earth Orbits (LEO). Stochastic models have been widely proposed in the literature to represent its aleatoric nature. However, the introduction of stochastic dynamics increases the complexity of orbit propagation and determination. On the other side, classical implementations to characterize the uncertainty from dynamical models in batch least-squares orbit determination such as the consider parameters theory fail to represent the stochastic nature of the atmospheric drag uncertainty, despite maintaining a tractable level of complexity. This work presents the validation with real data of the Stochastic Consider Parameters (SCP) model, a methodology developed for uncertainty quantification via covariance estimation applied to batch least-squares orbit determination and propagation that allows considering the effect of stochastic time-correlated errors to improve the covariance realism efficiently. To estimate the parameters that govern the stochastic noise, the SCP model is combined with a previously developed uncertainty quantification method. Such method receives as input estimated and propagated orbits, quantifying the uncertainty of the system offline of the orbit determination and propagation processes, not requiring modification of operational Space Surveillance and Tracking (SST) systems. In this work, real radar observations from the Spanish Space Surveillance Radar (S3TSR) are used to test the covariance realism improvement of the SCP method for several RSOs at different altitudes with respect to deterministic constant error models. The results analyse the physical interpretation of the estimated noise parameters with real data, while also evaluating key metrics to assess covariance realism such as Cramer-von-Mises metric and covariance containment. (c) 2025 The Authors. Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

Space debris proliferation in Low Earth Orbit (LEO) has heightened the urgency for effective Collision Avoidance Manoeuvres (CAMs). This work presents a pioneering framework aimed at devising a novel collision avoidance manoeuvre design for drag-augmentation small platforms. The framework facilitates the alteration of drag acceleration by adjusting the satellite's ballistic coefficient through cross-sectional area changes. This approach generates controlled deviations in the nominal trajectory, offering a feasible solution for collision avoidance without necessitating thrusters or fuel consumption. The paper introduces an analytical method for propagating drag augmentation manoeuvres and applies it for collision avoidance studies purposes. The formulation followed to implement this manoeuvre within a numerical propagator is presented, as well as the optimisation process developed for the application of drag augmentation manoeuvres in collision avoidance scenarios. Real-world applications showcase the suitability of these approaches, confirming the use of drag augmentation manoeuvres to avoid collisions in LEO. Additionally, the requirements and boundaries of the strategy, including altitude restrictions and satellite-specific properties, are discussed. (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

The unprecedented increase in the number of objects orbiting the Earth necessitates a comprehensive characterisation of these objects to improve the effectiveness of Space Surveillance and Tracking (SST) operations. In particular, accurate knowledge of the attitude and physical properties of space objects has become critical for space debris mitigation measures, since these parameters directly influence major perturbation forces like atmospheric drag and solar radiation pressure. Characterising a space object beyond its orbital position improves the accuracy of SST activities such as collision risk assessment, atmospheric re-entry prediction, and the design of Active Debris Removal (ADR) and In-Orbit Servicing (IOS) missions. This study presents a novel approach for the simultaneous estimation of the attitude and optical reflective properties of uncontrolled space objects with known shape using light curves. The proposed method also accounts for atmospheric effects, particularly the Aerosol Optical Depth (AOD), a highly variable parameter that is difficult to determine through on-site measurements. The methodology integrates different estimation, optimisation, and data analysis techniques to achieve an accurate, robust, and computationally efficient solution. The performance of the method is demonstrated through the analysis of a simulated scenario representative of realistic operational conditions.

The management of the finite capacity of near-Earth orbital space requires both scientific and technical as well as policy and regulatory approaches to deal with all the aspects of the issue. In this chapter these various aspects have been analysed. This paper summarises the activities carried out within the working group on Space capacity management mandated by the International Astronautical Federation Space Traffic Management Technical Committee.First, a scientific and technical understanding of what is meant by this limited capacity, how to quantify it, and how to measure its use is discussed. Several metrics are discussed to highlight the importance of a concerted framework for the definition, computation, monitoring, and allocation of the space environment capacity. Then need for a transparent methodology and a mechanism to ensure the review and approval of the proposed capacity is discussed. The policy and regulatory aspects of space capacity management, under the existing international legal framework for space activities, are also covered. The paper gives recommendations to reach a shared understanding on how space environment capacity should be uniquely defined as a first step towards the management of this capacity and to reach an international consensus about the metrics that should be used.

Collision avoidance, the process of planning and possibly executing a manoeuvre to mitigate the risk of a collision in orbit, is becoming increasingly important as the amount of space traffic increases. This paper discusses different types of conjunction events, the technical processes involved in identifying higher risk conjunctions and possible mitigation techniques, and gaps and limitations in the processes. Possible solutions to these gaps are addressed including improved communication and coordination, more accurate and precise data, and improved education of operators. Several recommendations are made to improve the collision avoidance process and effectiveness.

This paper reviews improved operational concepts for collision avoidance, addressing the challenges that electric propulsion introduce in Collision Avoidance operations, including during early and final phases of the satellite lifetime (orbit raising and end-of-life operations) as well as during routine operations already in the target orbit. First, those challenges are detailed, outlining how it impacts collision avoidance procedures, of which thruster uncertainty plays a dominant role due to its rapid accumulation during expected long-duration manoeuvres performed with electric propulsion systems (required to reach the desired delta-V). If the uncertainty accumulation is not addressed, conjunction events may appear in the dilution of probability region, where knowledge of the primary and secondary is too poor to take mitigation action. This situation, therefore, should be avoided as much as possible. The design of a collision avoidance manoeuvre becomes increasingly complex for lowthrust propulsion systems, where the thrust profile needs to be optimized throughout the duration of the manoeuvre. SpaceX's Starlink satellites, along with the OneWeb constellation, are a clear representation of the widespread use of low-thrust propulsion. Hence, the deployment of thousands of electric propulsion satellites fosters the development and introduction of new approaches to collision avoidance design and operations. An analysis of derived improved operational concepts is then detailed in this paper, focusing on improving the conjunction screening and collision avoidance manoeuvre operational concepts, explaining what area of collision avoidance (screening, mitigation) each concept improves, by how much (e.g., uncertainty reduction, Collision Avoidance Manoeuvre (CAM)decision delay and mission impact), and what operational scenarios such concepts apply to (electric orbit raising, Geostationary Orbit (GEO) station keeping manoeuvres etc.). The paper ends by presenting the results of a set of simulations carried out assessing the impact of improved operational concepts for different scenarios, compared to a baseline nominal operational concept, which is currently used in operations by satellite operators.

We develop a metric to evaluate the distance between two orbits in the perturbed two-body problem in terms of thrust-limited control. To this end, we make use of the Thrust Fourier Coefficients formulation and limit our approximation to secular (or averaged) variations. This allows us to express the orbital transfer as an ordinary differential equation that is linear with respect to the control parameters. Hence, by assuming a smooth transfer between the initial and final orbital states, obtaining the required control law simply consists in solving a linear system. Due to its computational efficiency, the developed metric is highly suitable for sampling and search-based computations, and we find reachability a particularly interesting application.

Numerous satellites with electric propulsion perform long duration maneuvers during their orbit acquisition phase. This poses a challenge to space object cataloging activities if no information regarding the maneuver plan is known a priori. Various works have been devoted to maneuver detection and tracking of space objects using radar and optical surveillance data, but the special case of unknown dynamics, analogous to a maneuver spanning several days or months, has received less attention. Herein, we propose a methodology to maintain custody of uncooperative low-thrust spacecraft under the special characteristics of surveillance radar observations. Based on the stochastic hybrid systems framework, a multi-hypothesis algorithm leverages information derived from measurements and the dynamical characteristics of the object. The latter is accomplished in an efficient manner by means of a low-thrust control metric that relies on the Thrust Fourier Coefficients approximation. To improve filter robustness, the maneuver transition density is assumed to be uniform within the set of reachable states, whose outer bound is approximated via the proposed control measure. The algorithm is applied to the orbit acquisition phase of a LEO satellite using synthetic data from a simulated surveillance radar network, and its shown to be capable of maintaining custody throughout the entire three-month transfer.

The reliability of the uncertainty characterization, also known as uncertainty realism, is of the uttermost importance for Space Situational Awareness (SSA) services. Among the many sources of uncertainty in the space environment, the most relevant one is the inherent uncertainty of the dynamic models, which is generally not considered in the batch least-squares Orbit Determination (OD) processes in operational scenarios. A classical approach to account for these sources of uncertainty is the theory of consider parameters. In this approach, a set of uncertain parameters are included in the underlying dynamical model, in such a way that the model uncertainty is represented by the variances of these parameters. However, realistic variances of these consider parameters are not known a priori. This work introduces a methodology to infer the variance of consider parameters based on the observed distribution of the Mahalanobis distance of the orbital differences between predicted and estimated orbits, which theoretically should follow a chi-square distribution under Gaussian assumptions. Empirical Distribution Function statistics such as the Cramer-von-Mises and the Kolmogorov–Smirnov distances are used to determine optimum consider parameter variances. The methodology is presented in this paper and validated in a series of simulated scenarios emulating the complexity of operational applications.

Break-up events represent the dominant source of objects in space catalogues, surpassing half of the overall population. These not so uncommon events include explosions, collisions or anomalous events resulting in fragmentations and their number is estimated to be higher than 630. The early cataloguing of the fragments generated during these events poses a complex challenge for space objects cat-alogue build-up and maintenance processes. The provision of Space Surveillance and Tracking products and services during the few first days after a break-up event can be crucial to avoid collisions between the fragments and other space objects, particularly in highly con-gested regimes, such as Low Earth Orbit. In this regard, reducing the time required to accurately estimate the trajectories of the frag-ments may enable the execution of collision avoidance manoeuvres, in the case of operational space objects with manoeuvre capabilities, and analyse potential collision cascade events, which may endanger the space environment. This paper studies the whole cataloguing process after a break-up event, starting from a catalogue with no fragments from the fragmentation under-analysis, and until a well-established orbit is obtained for all fragments, using a ground-based sensor network. First, the observations enter a multi-sensor multi-target track-to-track association algorithm in charge of grouping observations belonging to the same objects. To resolve the ambi-guity, particularly shortly after the event, hypotheses about tracks belonging to the same fragment are generated, scored, pruned, and promoted, only when there is enough confidence, leading to the initialisation of new objects in the catalogue. As soon as the catalogue is populated, a track-to-orbit correlation algorithm is responsible for the correlation of observations and already catalogued orbits. This alleviates the track-to-track association and enables the update of the orbital estimates, required for maintaining the catalogue.(c) 2023 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).

Due to the ever-increasing space objects population, space situational awareness products and services have become the cornerstone for the safety and sustainability of spacecraft operations. Most of these services rely on the characterization of the uncertainty of the system, which is known as uncertainty quantification. In many applications the uncertainty of the orbit state is represented by the covariance matrix, obtained from an orbit determination (OD) process. However, typical OD processes usually consider the measurements noise as the only source of uncertainty. An unrealistic characterisation of the uncertainty of dynamical and observations models leads to a degradation of the realism of the covariance, and jeopardizes spacecraft operations. In this work, we apply our recent methodology for covariance realism improvement, based on the consider parameter theory of batch least-squares methods, to a catalog scenario to derive the uncertainty of the atmospheric drag model. This methodology infers the variance of consider parameters based on the observed distribution of the Mahalanobis distances of the orbital differences between predicted and estimated orbits, which theoretically should follow a chi-square distribution under Gaussian assumptions. Empirical distribution function statistics such as the Cramer-von-Mises or the Kolmogorov-Smirnov distances are used to determine optimum variances of such parameters for covariance realism. The main objective of this work is to adapt and test the previously developed methodology to a LEO catalog scenario, in which the evolution of the density uncertainty for multiple objects can be analysed together by modelling such uncertainty as a consider parameter. Thus, instead of estimating the variances of the consider parameters tailored to a single object during a long period, the objective of this work is to determine variances of parameters of an parametric model for the atmospheric density uncertainty, improving the covariance realism for different clusters of cataloged objects (i.e. different altitudes or ballistic coefficient). Altitude-dependent models of the atmospheric density uncertainty, based on statistical analysis of historic space weather data, are applied for realistic simulations together with space-correlated density perturbations. Results are presented focusing on the physical interpretation of the determined consider parameter model variances and their effectiveness for improving the covariance realism of the considered catalog of objects.

The space environment is rapidly getting congested, inducing a growth of the risk of collision between Resident Space Objects (RSOs). The validity of collision risk assessment depends on the quality of the catalogs of RSOs, which shall be as accurate and up-to-date as possible. Maneuvers of operational satellites represent a problem, because, if not correctly detected and estimated, they could lead to catalog degradation or pollution. In this paper, a novel approach to tackle the maneuver detection and estimation problem is presented. The methodology, which is part of the association problem between tracks and objects, is intended to be included in real-time cataloging systems to increase their flexibility. This paper is a continuation, extension and improvement of a former work, where maneuver estimation was carried out with optical observations. The estimation algorithm is extended to radar observations with the inclusion of a new dynamical model. The joint detection and estimation scheme is tested in a simulated maintenance chain with tracks and orbits from a single satellite. In this scenario, the output of the maneuver estimation is then used as an a-priori guess in high-fidelity orbit determination, which is refined and used to compute a post-maneuver orbit. The results of the application of the detection and estimation algorithm within the simulated chain are presented, highlighting the advantages and validating the methodology, providing a basis for a wider multi-target multi-sensor association framework, with the final goal of solving the association problem with data from survey activities.

Maneuver detection and estimation is deemed crucial for maintaining catalogs of Resident Space Objects (RSOs) as it helps to avoid sets of duplicated objects and track correlation issues. In fact, maneuvers, along with launches and break-up events, are the main source of potential new object detections during RSOs cataloging activities. For the continuous and reliable provision of Space Situational Awareness (SSA) and Space Traffic Management (STM) services, a challenging trade-off between detection time and characterization accuracy of maneuvers needs to be performed. In this paper, two novel and operationally feasible methodologies are proposed for maneuver detection and estimation. The first, a track-to-orbit methodology, uses a pre-maneuver orbit to linearize the dynamics and estimate the single burn that minimizes the residuals of the post-maneuver tracks. The second, an orbit-to-orbit methodology, estimates the double burn that solves a minimization problem between the pre-maneuver and post-maneuver orbits. Both methods, based on an optimal control approach, are not only proposed to tackle the maneuver estimation problem but also to be integrated on operational and robust association frameworks. Results are presented for optical scenarios with both simulated and real data, providing insightful conclusions on the capabilities, performance and limitations of the proposed methods. Particular emphasis is given to the importance of the track association, since a single track is usually not enough to perform a reliable estimation of the maneuver. Besides, the capability of the methods to provide a solution to the association problem, even when not perfectly characterizing the true maneuver, is discussed.

The reliability of the uncertainty characterization, also known as uncertainty realism, is of the uttermost importance for Space Situational Awareness (SSA) services. Among the different sources of uncertainty related to the orbits of Resident Space Objects (RSOs), the uncertainty of dynamic models is one of the most relevant ones, although it is not always included in orbit determination processes. A classical approach to account for these sources of uncertainty is the consider parameters theory, which consists in including parameters in the underlying dynamical models whose variance aims to represent the uncertainty of the system. However, realistic variances of these consider parameters are not known a-priori. This work presents a method to infer the variance of the consider parameters, based on the distribution of the Mahalanobis distance of the orbital differences between predicted and estimated orbits, which theoretically shall follow a χ ^2 distribution under Gaussian assumption. This paper presents results in a simulated scenario focusing on Geostationary (GEO) regimes. The effectiveness and traceability of the uncertainty sources is assessed via covariance realism metrics.

The state space representation of active resident space objects can be posed in the form of a stochastic hybrid system. Satellite maneuvers may be accounted for according to control cost or heuristical considerations, yet it is possible to jointly consider a combination of both. In this work, Sequential Monte Carlo filtering techniques are applied to the maneuvering target tracking problem in an optical survey scenario, where the maneuver control inputs are characterized in a Bayesian inference process. Due to the scarcity of data inherent to space surveillance and tracking, model switching probabilities are not estimated but derived from the ability of the state representation to fit incoming measurements. A Markov Chain Monte Carlo sampling scheme is used to explore the region assumed accessible to the object in terms of the hypothesized post-maneuver observation and a novel and efficient control distance metric. Results are obtained for a simulated optical survey scenario, and comparisons are drawn with respect to a moving horizon least-squares estimator. The proposed framework is proved to allow for a capable implementation of an automated online maneuver detection algorithm, thus contributing to the reduction of uncertainty in the state of active space objects.

This paper proposes a novel track-to-track association methodology able to detect and catalogue resident space objects (RSOs) from associations of uncorrelated tracks (UCTs) obtained by radar survey sensors. It is a multi-target multi-sensor algorithm approach able to associate data from surveillance sensors to detect and catalogue objects. The association methodology contains a series of steps, each of which reduces the complexity of the combinational problem. The main focus are real operational environments, in which brute-force approaches are computationally unaffordable. The hypotheses are scored in the measurement space by evaluating a figure of merit based on the residuals of the observations. This allows us to filter out most of the false hypotheses that would be present in brute-force approaches, as well as to distinguish between true and false hypotheses. The suitability of the proposed track-to-track association has been assessed with a simulated scenario representative of a real operational environment, corresponding to 2 weeks of radar survey data obtained by a single survey radar. The distribution and evolution of the hypotheses along the association process is analysed and typical association performance metrics are included. Most of the RSOs are detected and catalogued and only one false positive is obtained. Besides, the rate of false positives is kept low, most of them corresponding to particular cases or objects with high eccentricity or limited observability.

The detection and identification of Resident Space Objects (RSOs) from survey tracks requires robust and efficient orbit determination methods for the association of observations of the same RSO. Both Initial Orbit Determination (IOD) and Orbit Determination (OD) methods perform the orbital estimation in which the association of tracks relies. The choice of proper IOD and OD methods is essential for the whole data association, since they are in charge of providing the estimation required to evaluate the figure of merit of the association. In this paper, we review the state of the art and propose a novel method that does not require initialisation, accounts for measurement noise and provides a full estimation (i.e., state vector and covariance) from an arbitrary number of optical observations. To do so, a boundary value problem is formulated to find a pair of ranges leading to a minimum residuals of the observations. The proposed methods are compared against classical alternatives simulated in scenarios representative of the current space debris environment. (C) 2021 COSPAR. Published by Elsevier B.V.