Differential-geometry-based multi-dimensional joint position-velocity estimation using Crab pulsar profile distortion

The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit. However, the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge. To solve this problem, the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation (MJPVE) using Crab pulsar profile distortion is proposed in this paper. Firstly, through theoretical analysis, it is found that the pulsar profile distortion caused by the initial state error in some joint position-velocity directions is very small. In other words, the accuracies of estimation in these directions are very low. Namely, the search dimension can be reduced, which in turn greatly reduces the computational load. Then, we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion. Finally, we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation. The experimental results show that compared with the grouping bi-chi-squared inversion method, MJPVE has high precision and extensive navigation information.