Tomasz Zubowicz, Polish Space Agency; Krzysztof Arminski, Polish Space Agency; Mikolaj Kruzynski, Polish Space Agency; Krzysztof Szyszka, Polish Space Agency; Antoni Wojtala, Polish Space Agency; Mikolaj Karawacki, Polish Space Agency; Patrycja Ignaczak, Polish Space Agency; Weronika Przybyl, Polish Space Agency; Edwin Wnuk, Polish Space Agency; Mariusz Slonina, Polish Space Agency
https://doi.org/10.64861/GHXY1735
Keywords: Terminal Decay Orbit Determination, Joint State–Parameter Estimation, Ballistic Coefficient Estimation, Regime-Adaptive Filtering, Re-entry Prediction and Uncertainty Quantification
Abstract:
Accurate orbit determination (OD) of objects approaching atmospheric re-entry remains a critical capability within Space Situational Awareness (SSA) and Space Domain Awareness (SDA). In contrast to classical LEO orbit estimation problems, terminal decay is characterized by rapidly increasing atmospheric drag, strong state–parameter coupling, and elevated sensitivity to density model mismatch. Under such conditions, augmented-state estimation with a constant stochastic model for drag-related parameters becomes structurally inconsistent. This work addresses terminal decay OD as a non-stationary coupled state–parameter estimation problem and proposes a regime-adaptive formulation for joint state–drag estimation using heterogeneous sensor data (radar and optical). The core claim is that parameter observability evolves with altitude, and that stationary process-noise modeling of ballistic coefficient (or equivalent drag surrogate) is suboptimal across the decay timeline. Secondly, joint state–parameter estimation may benefit from fusing reduced optical observations with radar measurements to improve OD precision. The estimation problem is formulated by augmenting the Cartesian state vector with a drag-related parameter representing the effective ballistic coefficient. Rather than assuming constant parameter diffusion, the proposed approach introduces an altitude-dependent process model. Three dynamical regimes are defined: Regime I (h > 350 km): Weak drag influence; ballistic coefficient weakly observable. Regime II (250 km < h ≤ 350 km): Transitional regime; increasing drag sensitivity. Regime III (h ≤ 250 km): Drag-dominated dynamics; strong parameter identifiability. Within this structure, the parameter process covariance is scaled as a function of regime, thereby constraining diffusion when observability is weak and allowing rapid adaptation when drag dominates the dynamics. The adaptation law may be expressed as a piecewise or continuous altitude-dependent function, ensuring consistency with the evolving force model rather than heuristic tuning. Two experimental campaigns are designed to isolate and quantify the effect of regime-adaptive modeling. Experiment 1: Baseline LEO Case. A stable LEO object above significant drag influence is used to examine the behavior of augmented-state estimation under weak parameter observability. The experiment is set up to investigate whether constant process covariance leads to noise-driven parameter divergence and degradation of state estimates due to state–parameter correlation. Conversely, it examines whether overly restrictive covariance results in slow convergence and biased along-track predictions in the presence of drag mismodeling. This experiment is designed to confirm that ballistic coefficient estimation in high LEO is poorly conditioned. Experiment 2: Terminal Decay Case. A re-entry-approaching object is analyzed using radar range/range-rate and optical angular observations. Three filter configurations are compared: state-only estimation, joint state–drag estimation with constant parameter process noise, and regime-adaptive joint estimation. Performance is evaluated in terms of re-entry epoch prediction error, along-track uncertainty growth. The results are to investigate if the constant parameter diffusion produces either filter overconfidence (when too small) or instability (when too large). If confirmed, the regime-adaptive model may lead to improved re-entry time prediction, reduced along-track dispersion, and more realistic covariance evolution across the decay phase. From an SSA/SDA operational perspective, the method provides a structured framework for configuring OD filters during re-entry campaigns. Improved re-entry epoch prediction and uncertainty characterization directly enhance risk communication, sensor tasking decisions, and coordination within distributed tracking networks. The approach can be integrated into existing OD pipelines with minimal architectural modification. This study formalizes terminal decay orbit determination as a regime-dependent estimation problem and demonstrates that altitude-adaptive process modeling enhances both estimation robustness and operational prediction accuracy.
Date of Conference: September 15-18, 2026
Track: Astrodynamics