A Waterfall-Plot-Based Multi-Criteria Framework for X-Ray Pulsar Time-Delay Estimation in Multi-Scenario Celestial Remote Sensing and Navigation

To improve the accuracy and stability of X-ray pulsar time-delay estimation for multi-scenario celestial remote sensing and navigation, this paper proposes a time-delay estimation method based on a waterfall-plot multi-criteria framework and develops an end-to-end simulation framework for multi-scenario applications. First, a pulsar profile waterfall-plot model is built, and principal component analysis is performed to characterize candidate periodic structures. The contribution rate of the principal eigenvalue is used to describe the overall significance of the candidate period, and the projection variance of the first principal component is used to measure the prominence of the candidate pattern in the principal subspace. Second, support vector regression is used to fit the peak track of the waterfall plot, and a regression slope is used to describe the geometric stability of the candidate period. These three indicators are fused for pulsar period and time-delay estimation. Tests based on Insight-HXMT satellite observation data show that, compared with the (Formula presented.) and (Formula presented.) test methods, our method improves time-delay estimation accuracy by 68.68% and 50.43%, respectively. Multi-scenario navigation simulations indicate positioning improvements of approximately 0.83 km, 3.04 km, and 1.05 km in the Earth-orbiting, Earth–Moon transfer, and Mars approach scenarios, respectively. These results suggest that the proposed framework can improve pulsar time-delay estimation and may provide useful measurement support for celestial remote sensing and navigation.