Pre-departure 4D trajectory modeling is fundamentally important to Trajectory Based Operations (TBO), identified as a key capability for the success of the Next Generation Air Transportation System (NextGen). Though there exists some research work on the in-flight 4D trajectory model, which typically predicts flight's positions with a short look-ahead time under the assumption that the flight velocity is constant, little work has been done to develop pre-departure 4D trajectory models or extend the in-flight model for the pre-departure application. Based on the prior work on in-flight 4D trajectory modeling, this paper addresses generating pre-departure 4D stochastic trajectory modeling along the predetermined 4D deterministic trajectory, taking into consideration a random departure delay and different planned along-track velocities on different trajectory segments. Due to the computational difficulty of solving the precise formulation, this paper proposes and calibrates the simplest model, which assumes a deterministic departure delay and a constant planned velocity along the whole trajectory, with recent operational aviation data using Maximum Likelihood Estimation, and then derives the expected flights' positions and their variances for trajectories with a random departure delay and different planned velocities. We evaluate the performances of the models, as well as their variants and present numerical examples to illustrate their applications.
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