Two-dimensional positioning of the crab pulsar with avoidance of non-sensitive direction

In the surrounding orbits, the position error of the spacecraft causes the distortion of the accumulative pulsar profile. Through theoretical analysis, a non-sensitive direction exists in three-dimensional space. Specifically, the initial position error in the non-sensitive direction hardly causes the large distortion of the accumulative pulsar profile, and can easily cause the search algorithm to fall into a local optimum. To significantly reduce the risk of falling into local optima, we propose a two-dimensional positioning method using the distortion of the accumulative Crab pulsar profile. This method combines coarse and fine searches, optimizing orbital recursive error and the chi-square value of the profile, respectively. By exploring two-dimensional positioning on a plane perpendicular to the non-sensitive direction through multiple epoch folds, we achieve precise positioning of the Crab pulsar. Furthermore, to reduce repeated computations, we utilize the dictionary folding method to achieve fast epoch folding. The simulation results demonstrate an approximately 13% improvement in the accuracy of the two-dimensional positioning method with avoidance of non-sensitive direction, compared to the traditional two-dimensional positioning method, although the angle of the search planes of two two-dimensional positioning methods is small. Additionally, its computational time is approximately 3 min. These results indicate that the proposed method has high precision and real-time performance.