Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Uncertainty Propagation based on an Ancestor Transform (AT) for Clustering Space Debris Fragments Considering Orbital Reachability SU DANDAN, JI YUNPENG, K.A. NEUSYPIN, M.S. SELEZNEVA This paper considers the problem of space debris clustering for planning active debris removal (ADR) missions in low-Earth orbits under multi-level uncertainty caused by errors in two-line ephemeris parameters (TLEs), variations in the upper atmosphere density (15–27 %), and temporal variability of reachability under the J2 perturbation. It is shown that deterministic clustering methods, including the k-means method and density-based algorithms, do not take into account the uncertainty, whereas standard probabilistic models such as Gaussian mixtures with the Dirichlet process (GMDP) under uninformative a priori assumptions lead to 3–8% violations of probabilistic constraints. A three-level uncertainty propagation technique is proposed that sequentially maps TLE errors to the distribution of proper orbital elements and then to the distribution of fl ight costs; an ancestor transform is used at all levels, ensuring second-order accuracy without calculating analytical Jacobians. The resulting distributions are incorporated into a physically informed Bayesian nonparametric clustering model, in which the reachability kernel accounts for both the expectation and variance of the flight cost, and probabilistic fuel constraints are specified through priors of the "distance to the feasible set" type, preserving full a posteriori quantification of uncertainty. Numerical experiments on space debris catalogs in low-Earth orbits have shown that the use of a unifi ed ancestor transform provides a 21.8-fold acceleration of computations while maintaining accuracy comparable to full Monte Carlo simulations (relative error < 0.01 %). The average relative error of the three-level scheme at the first and third layers is approximately 1.2 %, confirming its effectiveness for clustering with reachability constraints. Keywords: active debris removal (ADR), ancestor transform (AT), uncertainty propagation, proper orbital elements, reachability, Bayesian nonparametric clustering, probabilistic (chance-) constraints, Gibbs sampling. DOI: 10.25791/pribor.5.2026.1676 Pp. 45-58.