Traditional magnetic tracking approaches based on mathematical models and optimization algorithms are computationally intensive, depend on initial guesses, and do not guarantee convergence to a global optimum. Although fully-supervised data-driven deep learning can solve the above issues, the demand for a comprehensive dataset hampers its applicability in magnetic tracking. Thus, we propose an annular magnet pose estimation network (called AMagPoseNet) based on dual-domain few-shot learning from a prior mathematical model, which consists of two sub-networks: PoseNet and CaliNet.