Nonlinear Parameter Estimation Model for Dynamic Stability Analysis and Uncertainty Quantification of Six-Degree-of-Freedom Atmospheric Entry Capsules

As atmospheric entry vehicles descend through planetary atmospheres, they encounter complex, nonlinear aerodynamic phenomena and uncertain dynamic behaviors, making accurate estimation of dynamic stability coefficients critical for reliable entry, descent, and landing. This study addresses these challenges by introducing a novel Bayesian framework integrated with a six-degrees-of-freedom (6-DOF) dynamic model to determine stability coefficients and their associated uncertainties. A Markov Chain Monte Carlo (MCMC) inference technique, initialized via a nonlinear least squares approach, is employed to obtain posterior distributions of the stability parameters rather than relying solely on deterministic estimates. The 6-DOF equations of motion are first validated against two established 6-DOF simulation benchmarks, demonstrating excellent agreement and confirming the model’s credibility. Synthetic time series of aerodynamic angle data generated for a reference (Genesis) vehicle model serves as input for the inference process, enabling the recovery of original stability coefficients and the reconstruction of trajectories with rigorously quantified uncertainties. These results highlight the potential of the proposed Bayesian methodology to enhance the fidelity and robustness of dynamic stability analyses, ultimately supporting more reliable atmospheric entry mission design and execution.