Online failure probability estimation under state estimation error and its application to angle of attack control of a reentry vehicle

Knowing the probability of failure in real-time i.e. the probability that a system violates some constraints is decisive for aerospace applications in the presence of state uncertainty. However, it often involves stochastic prediction of the constraints on the upcoming system's trajectory, which is computationally demanding. In addition, the trajectory prediction depends on the accuracy of the current state estimate, e.g. the navigation system, whose errors are usually not accounted for. This paper studies the impact of the state estimate error on the failure probability calculation, obtained by Monte Carlo trajectory sampling. The failure probability error is first shown to be made of two terms depending on the current state estimation error and the number of Monte Carlo samples. Then, an iterative Least Square estimator is introduced to refine the failure probability estimation without significantly increasing the computational load. It is theoretically shown to converge and lowers the failure probability estimation error of 33% in simulation. The approach is illustrated on a constrained stochastic control application: the atmospheric reentry of a vehicle inspired from SpaceX's Starship (SXS). The proposed method allows the failure probability estimate to be more accurate despite the unavoidable disturbances yielded by the state estimation algorithm and the Monte Carlo discrete sampling, in particular when the available computational load is limited onboard.