Ellipsoid‐Based Integral Probability Model for Vehicle Position and Dynamic State Evaluation During Parachute Deployment in Mars <scp>EDL</scp> Missions

ABSTRACT The uncertainty in a vehicle's position and dynamic state at the end of the Mars atmospheric entry significantly influences the successful deployment of the parachute. This uncertainty is primarily driven by measurement uncertainties, including those associated with the vehicle's initial state and model parameters. These uncertainties propagate through the dynamic system, thereby contributing to the overall uncertainty in the vehicle's terminal state. Traditionally, errors in the vehicle's position and dynamic state are evaluated separately using different indicators. However, successful parachute deployment depends on both the vehicle's position and dynamic state. This paper presents a method that integrates errors in both the vehicle's position and dynamic state to quantify the uncertainty in the terminal state of Mars entry vehicles, considering various contributing factors. The method also assesses the probability of successful parachute deployment. First, a covariance matrix representing the vehicle's terminal state error is derived by propagating measurement uncertainties through the dynamic system using linear covariance analysis. A terminal state ellipsoid model is developed. Subsequently, an altitude‐velocity‐downrange parachute feasible deployment box is defined, considering the constraints in altitude, Mach number, dynamic pressure, and deployment position accuracy. By integrating the terminal state ellipsoid with the feasible deployment box, an integral probability model is constructed to estimate the maximum probability of successful parachute deployment within the predefined box. Numerical simulations validated the effectiveness of the terminal state ellipsoid and the integral probability model in quantifying uncertainty and demonstrating their capability to assess the vehicle's terminal position and to ensure deployment safety.