Comprehensive Measurement of Position and Velocity in the Transverse Direction Using the Crab Pulsar

Traditional X-ray pulsar ranging and velocity measurement methods only estimate the radial position and velocity information of the pulsar. For non-linear orbits, errors in the transverse position and velocity of the pulsar lead to errors in the radial velocity of the pulsar, leading to distortion of the X-ray pulsar profile. Based on this, we propose using the distortion of the pulsar profile to infer the transverse position and velocity information of the pulsar. First, a model of the distortion of the pulsar profile due to errors in the transverse position and velocity is established, and the observable directions of the transverse position and velocity are given separately. Then, considering that the distortions in the pulsar profile caused by errors in the transverse position and velocity are indistinguishable, we establish a reactive motion state measure related to the observable directions for the transverse position and velocity errors as a new observable measure in X-ray pulsar navigation. The experimental results show that the precision of the reactive motion state measure reaches 0.57, equivalent to a position error of 284.50 m or a velocity error of 0.57 m/s.