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. A stochastic linear hybrid system 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. 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. 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. The performance of the proposed algorithms is validated through an illustrative air traffic scenario.
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