Joint Posterior Reachable-Region Prediction via Local Markov Factor Graphs

Predicting the future occupied regions of non-cooperative space objects is critical for close-range situational awareness, on-orbit servicing, and collision risk assessment. Yet, conventional target-wise estimators discard the cross-target uncertainty correlations induced by a shared chaser state, whereas reachable-set propagation methods often prescribe disturbance bounds independent of current observations. With known target identities, this paper presents a joint multi-target state estimation and probabilistic reachable-region prediction method based on a local Markov factor graph. The graph unifies chaser and target states, relative-position measurements, equivalent maneuver variables, and history-supported behavior and pair-interaction factors. Schur complement analysis demonstrates how marginalizing the shared chaser state induces cross-target covariance and transfers information through common observations. The finite-graph posterior is then mapped to a corrected-dynamics inferred-control (CDIC) framework to produce target- and time-indexed probabilistic position regions for evaluating orbital safety. Monte Carlo simulations with common random numbers demonstrate that the joint formulation falls back to independent target estimation when relation evidence is absent, while persistent shared evidence improves prediction-center accuracy and empirical trajectory containment. Parameter-sensitivity and randomized-configuration tests delimit this evidence-conditioned benefit. These findings identify the operating regime where cross-target information improves multi-object state estimation, equivalent-maneuver inference, and probabilistic reachable set prediction.