Conflict probability estimation for free flight

The safety and e ciency of free ight will bene t from automated con ict prediction and resolution advisories. Con ict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a con ict will occur, given a pair of predicted trajectories and their levels of uncertainty. This paper presents a method to estimate that con ict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single, equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and a Monte Carlo validation are presented.