A stochastic approximation method for probability prediction of docking success for aerial refueling

Aerial refueling is capable of increasing the endurance and flight range of aircraft. However, during the docking phase of aerial refueling, the docking risk increases as the receiver aircraft approaches the tanker aircraft. A high docking risk indicates docking failure or even flight collision. In order to guarantee docking reliability and safety, a stochastic approximation method is proposed to predict the docking success probability during the docking phase of aerial refueling. If the success probability is lower than the specified value, the receiver aircraft needs to increase its relative distance from the tanker aircraft to reduce the risk. In our method, a stochastic differential equation is used to model the relative motion between the receiver and tanker aircrafts, where the receiver aircraft flies along a predefined flight path with influence of additive wind perturbations. The correlation between the magnitude of wind perturbations and the distance between the receiver and tanker aircrafts is considered. Then, based on the established relative motion model, the probability that the receiver aircraft enters the target set during a given time interval is predicted by the Markov chain stochastic approximation method. The docking success probability is computed by propagating the transition probabilities of the Markov chain backwards starting from the target set during the time interval. Comparing with the widely used Monte Carlo method in previous studies, our method demonstrates substantial effectiveness and efficiency.