A Time-Sequence Bayesian Framework for Attitude Dynamics Model Calibration with Sparse Measurements

A precise spacecraft attitude dynamics model is essential for accurately predicting a satellite’s orientation in orbit, with such predictions being centerpiece to mission safety, operational control, and long-term risk management. However, the highly nonlinear nature of spacecraft dynamics, compounded by uncertain and varying space perturbations such as atmospheric drag, solar radiation pressure, and magnetic torques, poses a substantial challenge to model fidelity. The problem is further exacerbated by the limited availability of in-orbit attitude measurements, which constrains direct calibration efforts. This work proposes a Bayesian stochastic model updating framework to systematically calibrate complex attitude dynamics models under epistemic and aleatory uncertainties. The methodology leverages approximate Bayesian computation with Euclidean and Bhattacharyya distance-based likelihoods, integrated within a transitional Markov chain Monte Carlo sampling scheme. A pseudo-online updating process is developed to incorporate sparse, sequential attitude measurements, enabling continual refinement of uncertain model parameters and improved characterization of stochastic dynamics. A numerical case study involving a rigid-body satellite subject to hybrid perturbations is presented to demonstrate the effectiveness of the proposed approach. The results show successful convergence of posterior distributions around true values, a significant reduction in epistemic uncertainty, and an improved predictive capability for attitude propagation in data-sparse scenarios. This framework offers a promising direction for enhancing attitude modeling reliability in the context of increasingly congested and observation-limited space environments.