Efficient Estimation of Probability of Conflict Between Air Traffic Using Subset Simulation

Abstract

This paper presents an efficient method for estimating the probability of conflict between air traffic within a block of airspace. Autonomous Sense-and-Avoid is an essential safety feature to enable Unmanned Air Systems to operate alongside other (manned or unmanned) air traffic. The ability to estimate probability of conflict between traffic is an essential part of Senseand-Avoid. Such probabilities are typically very low. Evaluating low probabilities using naive Direct Monte Carlo generates a significant computational load. This paper applies a technique called Subset Simulation. The small failure probabilities are computed as a product of larger conditional failure probabilities, reducing the computational load whilst improving the accuracy of the probability estimates. The reduction in the number of samples required can be one or more orders of magnitude. The utility of the approach is demonstrated by modeling a series of conflicting and potentially conflicting scenarios based on the standard Rules of the Air.

Data-Driven Probabilistic Methodology for Aircraft Conflict Detection Under Wind Uncertainty

“…In practice, the coefficients r * ij of the orthonormal polynomial (17) can be derived directly from the elements r ij of the matrix R, avoiding the inversion of the matrix R. The entries r ij are used to compute the coefficients a j and b j of the three-term recurrence relation (18) for 1 ≤ j ≤ p, where ψ −1 (ξ) = 0 and ψ 0 (ξ) = 1. More specifically, the coefficients a j and b j are written in terms of the elements r ij as a j = r j,j+1 r j,j − r j−1,j r j−1,j−1 and b j = r j+1,j+1 r j,j , for 1 ≤ j ≤ p, with r 0,0 = 1 and r 0,1 = 0.…”

“…The coefficients a j and b j can be used to efficiently calculate the nodes and weights used in the Gaussian quadrature (15). In particular, the threeterm recurrence relation (18) can be represented by means of the Jacobi matrix…”

Analytical Framework for Sensing Requirements Definition in Non-Cooperative UAS Sense and Avoid

“…In this framework, active lines of research involve the definition of sensing requirements [7], the development of ad-hoc obstacle detection and tracking techniques including data fusion [8][9][10], the derivation of effective conflict detection criteria [1], which can also be linked to recent developments in conflict probability estimation methods [11,12], the design of new sensors with low Size, Weight, and Power budgets [13], the assessment of risk, and the evaluation of separation minima [14]. These aspects are, indeed, tightly interconnected.…”

Machine-Learning-Aided Trajectory Prediction and Conflict Detection for Internet of Aerial Vehicles

“…According to civil aviation administration of China, more than 90% of accidents have occurred at low altitudes since the 21st century. Therefore, new techniques need be utilized to reduce probability of aerial vehicles collisions [5].…”