Trajectory prediction is an essential component of the next generation national air transportation system. Reliable trajectory prediction models need to consider uncertainties coming from multiple sources. Environmental factor is one of the most significant reasons affecting trajectory prediction models and is the focus of this study. This paper propose an advanced Bayesian Deep Learning method for aircraft trajectory prediction considering weather impacts. A brief review of both deterministic and probabilistic trajectory prediction methods is given, with a specific focus on learning-based methods. Next, a deterministic trajectory prediction model with classical deep learning methods is proposed to handle both spatial and temporal information using a nested convolution neural network, recurrent neural network, and fully-connected neural network. Following this, the deterministic neural network model is extended to be …