Leonardo Cament, Universidad de Chile; Martin Adams, Universidad de Chile; Elías Obreque, Northumbria University; Pablo Barrios, Universidad de Chile
Keywords: SSA, multi-object tracking, Poisson Labelled multi-Bernoulli Filter, Dynamic Orbit Model
Abstract:
The increasing number of resident space objects (SOs) in Earth’s orbit poses significant challenges for Space Situational Awareness (SSA). Accurate detection, tracking, and cataloging of these objects are critical to prevent potential collisions and ensure the sustainability of space operations. Over the past decades, the methods used for SO tracking have evolved, incorporating more sophisticated mathematical models and computational techniques to improve accuracy and efficiency.
The unpredictable nature of the various forces acting on SOs, such as atmospheric drag, gravitational perturbations, and solar radiation pressure, necessitates the need for advanced stochastic estimation techniques. These methods aim to update SO track catalogs accurately over time, mitigating the uncertainties associated with orbital dynamics. One approach is the use of Initial Orbit Determination, which can be performed with the Probabilistic Admissible Region (PAR) approach. This provides an initial, estimated distribution of an object’s trajectory based on the first observation. Subsequent observations refine this estimate using recursive Bayesian filters, enhancing the precision of orbital predictions.
This research explores new methodologies that leverage a combination of Random Finite Set-based Poisson Labelled Multi-Bernoulli (PLMB) filtering and advanced orbital motion models based on Lie algebra. The distribution used to model SO tracks is a Concentrated Gaussian Distribution (CGD) defined in a Lie Space SO(3).
The primary objectives are as follows:
The improvement of single SO dynamic motion propagation models. Specifically, the uncertainties in satellite mass and effective area affecting atmospheric drag and solar radiation pressure, which are significant in Low Earth Orbits (LEOs), will be modeled. Accurate estimation of these parameters is essential for refining orbit predictions and ensuring robust tracking performance.
The use of Lie algebra-based methods for dynamic motion modeling of single SO targets will be used. By leveraging Lie manifolds, it is possible to model motion uncertainties in directions that align more naturally with orbital trajectories than traditional Cartesian coordinate-based approaches, potentially improving computational efficiency and prediction accuracy.
We investigate the possibility of splitting CGDs when the sigma-points, which are deterministically chosen points used to approximate the statistical properties of a distribution, differ significantly from those of a single CGD after the propagation process.
In this study, we will use the High Precision Orbit Propagator (HPOP) software for the simulation and analysis of the orbital dynamics of the studied objects. The Earth’s gravitational field model will be based on the Earth Gravitational Model 2008 (EGM2008), which provides a high-resolution spherical harmonics expansion. The solar radiation pressure model will incorporate variations in the orientation and effective area exposed to the radiation flux. Atmospheric drag will be represented using the NRLMSISE-00 model, which estimates atmospheric density as a function of altitude, solar activity, and geomagnetic conditions. Additionally, gravitational perturbations due to the attraction of the Sun and Moon will be included, allowing us to capture third-body effects relevant to the dynamics of objects in Low Earth Orbit (LEO).
To develop and validate the proposed SO propagation models, reliable ground truth data is required. This research utilizes data from the Space and Planetary Exploration Laboratory (SPEL), University of Chile, which includes information from four CubeSats:
SUCHAI (Norad 42788)
SUCHAI-2 (Norad 52192)
SUCHAI-3 (Norad 52191)
PlantSat (Norad 52188).
Historical data analyzed from these satellites includes key parameters such as altitude, the drag coefficient, the ballistic coefficient, the BSTAR drag term, inclination, mean motion, position, and velocity. These parameters serve as the ground truth for evaluating the performance of various SO dynamic propagation motion models. This data was collected and calculated between September 2017 and February 2024. In previous studies, the atmospheric drag and solar radiation pressure parameters were assumed constant. However, these parameters are actually time varying and are therefore estimated in this article. Comparisons will be made between the proposed work and state of the art, showcasing improvements in uncertainty representation and computational efficiency.
The drag coefficient, the ballistic coefficient and BSTAR parameters used in the dynamic model atmospheric drag and solar radiation pressure equations will be utilized in various ways:
The parameters will be assumed constant during the whole filtering process.
The time varying historical parameters will be directly applied in the atmospheric drag and solar radiation pressure equations.
The parameters will be modeled with Normal distributions, using the mean and standard deviation derived from the historical data.
The parameters will be estimated, in the filtering process. This requires the augmentation of the SO state vector to addresses the variation in satellite physical characteristics, further refining the accuracy of the models. The exploration of different estimation techniques for these coefficients, including machine learning and Gauss-Markov models, will be applied for more reliable long-term tracking predictions.
The results of this study will demonstrate the effectiveness of Lie algebra-based state propagation in improving long-term SO tracking accuracy. Additionally, the incorporation of adaptive CGD splitting will be validated through simulated and real-world satellite data from the SUCHAI mission, illustrating its Impact on reducing estimation errors. The findings will highlight the advantages of integrating advanced filtering techniques with physics-based modeling for enhanced space object cataloging and prediction.
Date of Conference: September 16-19, 2025
Track: Astrodynamics