Conflict probability estimation for free flight

Abstract

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.

Simulating Collision Probabilities of Landing Airplanes at Nontowered Airports

“…A similar class of models are geometric conflict models (e.g., Paielli and Erzberger 1997, 1999, Irving 2002. In these models, the velocities of the airplanes are fixed as before, but their initial positions (in three dimensions) are random.…”

Aircraft conflict prediction and resolution using Brownian motion

“…However, since the prediction error can be modeled as the sum of a large number of independent random perturbations in disjoint time intervals, it is expected to be Gaussian. This hypothesis was indeed verified by empirical data in [2], which also suggested that the uncertainty can be decomposed into two components: an along track component whose variance grows with time, and a cross track component whose variance remains roughly constant. Based on this model, a number of methods have been proposed to predict the probability of conflict (PC) for aircraft pairs over horizons of the order of 20 minutes.…”

“…A conflict occurs if the intruder enters the protected zone of radius 5 nmi around aircraft 1 or vice versa. (2) where C = diag(o,,c,). c,,u, model the variance growth rate in the along track and cross track component respectively (no > oc typically).…”

“…Based on this model, a number of methods have been proposed to predict the probability of conflict (PC) for aircraft pairs over horizons of the order of 20 minutes. In [2] the notion of uncertainty ellipse is used to obtain a closed form over-approximation for PC. In [3], a randomzzed estimation algorithm is proposed for computing PC.…”

“…For the current system, a conflict is defined as a situation'where two aircraft come within 5 nauti- cal miles (nmi) of one another horizontally and within 1000 or 2000 feet (ft) vertically, depending on whether the flight level is below or above 29,000 ft respectively (see [2]). Conflict avoidance typically consists of two stages: conflict detection and conflict resolution.…”