A method for phase estimation of X-ray pulsar signals: Combining a transformer network structure and a two-dimensional profile map

The high-precision phase estimation of X-ray pulsar signals is crucial for X-ray pulsar navigation. This paper introduces a novel feature modeling method named Two-Dimensional Profile Map (2D-PM), which enhances the time-domain information of the period axis using the epoch folding algorithm. Compared to traditional profiles, the newly proposed 2D-PM model exhibits richer information content, and greater robustness in terms of folding period precision. Furthermore, a new time-series neural network structure, inspired by groundbreaking advancements in the field of Natural Language Processing (NLP), is developed using the TensorFlow framework. This structure is designed to learn the proposed features and achieve precise phase estimation. The paper also outlines training schemes and debugging strategies for hyperparameters. To test the method, sample sets were created using simulated data and Rossi X-ray Timing Explorer (RXTE) observational data. These samples are specifically designed to enhance feature consistency and the generalization capability of the network. The effectiveness of the proposed method is demonstrated through a comparative analysis with traditional cross-correlation algorithms. The results confirm a high degree of alignment between the network outputs and the feature model, highlighting the significant potential of the proposed method for application in X-ray pulsar navigation.