This letter investigates the physical layer authentication (PLA) in dynamic environments, where the users have different mobility velocities. The performance of PLA in this scenario suffers from the inaccurate prediction of the channel statement information (CSI) owing to the Doppler shifts and multipath fading. To overcome the difficulty, a model-driven learning algorithm is developed to predict dynamic CSI. Specifically, the Bahdanau Attention Autoencoder (BAAE)-based PLA scheme is proposed to extract relevant channel features and mitigate inter-symbol interference and inter-carrier interference. Compared to existing deep learning-based PLA schemes, the proposed scheme addresses the core factors contributing to poor authentication accuracy at the algorithmic level, rather than brute-force learning from bigger datasets. Experiment results show that the proposed scheme presents more accurate predictions and lower complexity compared with the existing data-driven models across all tested signal noise ratio levels and velocities. Moreover, it is robust to maintain 99.6% authentication accuracy even when the users are moving with high velocities.