Fabian Dallinger, Universität der Bundeswehr München; Benedikt Aigner, Universität der Bundeswehr München; Thomas Andert, Universität der Bundeswehr München
https://doi.org/10.64861/FVUM2724
Keywords: Physics-informed machine learning, Extreme learning machines, Orbit determination, Covariance estimation, Uncertainty quantification, High-fidelity force modeling, Low Earth orbit, SSA/SDA
Abstract:
Accurate orbit determination (OD) is foundational to Space Situational Awareness (SSA) and Space Domain Awareness (SDA), yet many operational decisions depend as much on uncertainty as on the best-estimate trajectory. In routine operations, OD must often be performed from short arcs, sparse sampling, and tracking geometries that provide limited information, and it is frequently stressed by force-model uncertainty (e.g., imperfect atmospheric density, attitude assumptions, or solar radiation pressure modeling). Classical batch OD and filtering typically compute covariance via linearization of the dynamics and measurements, propagating sensitivities with a state transition matrix (STM) about a nominal trajectory. In short-arc or poorly initialized regimes—and especially when the force environment is mismodeled—this STM-based linearization can become fragile, leading to slow convergence, divergence, or covariance products that are difficult to trust when the nominal orbit remains far from the truth. _x000D_
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This paper investigates physics-informed orbit determination with Physics-Informed Extreme Learning Machines (PIELMs) and focuses on covariance estimation under high-fidelity Low Earth Orbit (LEO) dynamics. The physics-informed formulation estimates a continuous trajectory representation by fitting tracking measurements while explicitly enforcing the equations of motion as a regularizer. Unlike conventional iterative OD that repeatedly integrates an STM around an evolving nominal orbit, the PIELM approach is designed to reduce sensitivity to initialization by learning a globally consistent trajectory subject to physics constraints. What is new is a statistically validated, time-resolved covariance estimation method for physics-informed OD in a perturbation-rich LEO environment, together with a calibration benchmark against standard STM-based covariance products under matched and mismodeled forces._x000D_
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We consider a representative ground-based tracking scenario using common SSA observables (e.g., range/azimuth/elevation) in an operationally relevant LEO setting with deliberate force-model mismatch. The OD problem is formulated with a high-fidelity force environment, including spherical-harmonic Earth gravity, third-body perturbations, solar radiation pressure with eclipse handling, and atmospheric drag driven by a density model with realistic uncertainty. For fair benchmarking, both the PIELM estimator and an STM-based batch weighted least squares (WLS) baseline use identical measurement and force models; differences arise from the trajectory representation and optimization strategy (continuous physics-informed trajectory versus iterative linearization and STM propagation). To obtain covariance in the PIELM setting, we evaluate uncertainty strategies that combine residual structure from the physics-informed fit with sensitivity of the learned trajectory to measurement noise and modeling assumptions, producing time-tagged covariance and correlation information aligned with the learned solution._x000D_
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Two controlled LEO studies assess robustness and covariance realism. Study 1 benchmarks OD robustness and failure modes as a function of initial orbit quality and compares convergence behavior and solution quality against the STM-WLS baseline in regimes where a weak initial guess is expected to challenge linearized OD. Study 2 isolates covariance calibration under matched truth-model conditions and deliberate perturbation mismatch (with emphasis on drag/SRP sensitivity), and evaluates whether predicted uncertainty levels and correlations match empirical error behavior over time. Calibration is assessed using a set of consistency diagnostics commonly used for OD validation, focusing on Mahalanobis distance and NEES-style tests, with residual-consistency checks where applicable. The analysis focuses on direct comparison of predicted covariance behavior to observed error statistics in a controlled setting._x000D_
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Overall, the paper provides a benchmark for PIELM-based OD with uncertainty quantification under realistic LEO conditions, identifies regimes where physics-informed covariance products are well-calibrated versus systematically miscalibrated, and offers practical guidance on modeling choices and measurement regimes where additional constraints or data types are required for trustworthy SSA/SDA decision support._x000D_
Date of Conference: September 15-18, 2026
Track: Astrodynamics