Probabilistic Trajectory Prediction and Conflict Detection

To efficiently and safely accommodate the ever increasing air traffic, the concept of the Next Generation Air Transportation System has been proposed and studied in recent years. In this paper, we consider the problem of four-dimensional trajectory prediction and conflict detection, which is one of the key functions of the Next Generation Air Transportation System. 

Aircraft Dynamics

A stochastic linear hybrid system (SLHS) is proposed to describe the dynamics of an aircraft with changing flight modes. 

• The stochastic linear hybrid system can have two different discrete-state transition models depending on the availability of flight plans (or aircraft intent): the Markov transition model and state-dependent transition model. 

• The state-dependent transition model can incorporate the prior information about an aircraft’s intent. 

Trajectory Prediction

Based on the proposed model, an algorithm for the probabilistic reachability analysis of the stochastic linear hybrid system is proposed for aircraft four-dimensional trajectory prediction. 

Conflict Detection

To detect a midair conflict between aircraft, a computationally efficient algorithm is developed based on the cumulative distribution function approximation for the quadratic form of Gaussian random variables. 

Simulations

The performance of the proposed algorithms is validated through an illustrative air traffic scenario: two-aircraft terminal-area conflict detection scenario.

• aircraft 1 starts from point A1 heading toward the east.

• aircraft 2 starts from point B1 heading toward the north.

• They intend to follow the given terminal-area routes by passing a series of waypoints (illustrated by triangles) and then eventually land on the same runway (point C) at different times while keeping the safe clearance between them during the whole landing process.

• Due to some scheduling errors, there is a conflict between the two aircraft that both of them reach waypoint A3 almost at the same time, which violates the midair separation standard.

Related Publication

• W. Liu and I. Hwang, "Probabilistic Trajectory Prediction and Conflict Detection for Air Traffic Control," AIAA Journal of Guidance, Control and Dynamics, Vol. 34(6), p1779-1789, November-December 2011