Pervasive and high-accuracy positioning has become increasingly important as a fundamental enabler for intelligent connected devices in mobile networks. Nevertheless, current wireless networks heavily rely on pure model-driven techniques to achieve positioning functionality, often succumbing to performance deterioration due to hardware impairments in practical scenarios. Here we reformulate the direction finding or angle-of-arrival (AoA) estimation problem as an image recovery task of the spatial spectrum and propose a new model-driven deep neural network (MoD-DNN) framework. The proposed MoD-DNN scheme comprises three modules: a multi-task autoencoder-based beamformer, a coarray spectrum generation module, and a model-driven deep learning-based spatial spectrum reconstruction module. Our technique enables automatic calibration of angular-dependent phase error thereby enhancing the resilience of direction-finding precision against realistic system non-idealities. We validate the proposed scheme both using numerical simulations and field tests. The results show that the proposed MoD-DNN framework enables effective spectrum calibration and accurate AoA estimation. To the best of our knowledge, this study marks the first successful demonstration of hybrid data-and-model-driven direction finding utilizing readily available commodity 5G gNodeB.