Bayesian framework for estimating dynamic stability derivatives in 6-DoF blunt-body entry vehicles

Abstract

As atmospheric entry vehicles traverse planetary atmospheres, they encounter strongly nonlinear and unsteady aerodynamic loads, leading to uncertain dynamic behavior. Accurate estimation of dynamic stability coefficients is critical for ensuring reliable entry, descent, and landing. This study introduces a Bayesian inference framework coupled with a six-degree-of-freedom dynamic model to estimate these coefficients and quantify their uncertainties using trajectory data. The six-degree-of-freedom model is validated against two benchmark cases, demonstrating strong agreement and establishing its reliability. A two-stage estimation process is employed: (1) Bayesian inference of stability derivatives using Markov Chain Monte Carlo with the No-U-Turn Sampler, based on training cases (${\alpha }_{T_0}=1^{\circ },5^{\circ },{10}^{\circ },{30}^{\circ }$), to recover both static ($C_{m_{\alpha }},C_{n_{\beta }}$) and damping ($C_{m_q},C_{n_r},C_{l_p}$) coefficients; and (2) prediction at untrained test angles (${\alpha }_{T_0}=2^{\circ },{20}^{\circ }$), via Akima spline interpolation of aerodynamic parameters. Applied to the Genesis sample return capsule, the framework accurately reconstructs training trajectories and captures nonlinear damping effects. Predictions at unobserved conditions maintain strong consistency, with only minor discrepancies near the simulation horizon. These results demonstrate the framework's potential as a robust, uncertainty-aware tool for dynamic stability analysis in atmospheric reentry applications.