Pulsars are neutron stars with high rotation speeds and have extraordinary long-term rotational stability. X-ray pulsar-based navigation (XNAV) is a navigation method that estimates the position and velocity of a spacecraft using the X-ray radiation from pulsars. Flight experiments on Insight-Hard X-ray Modulation Telescope (Insight-HXMT) and Neutron Star Interior Composition Explorer (NICER) have successfully verified the feasibility of using XNAV for a single spacecraft. For spacecraft in formation, a pulsar-based navigation method that uses the pulse phase delay between spacecraft is derived. Moreover, a direct estimation method for pulse phase delay, which is independent from the pulsar template, is proposed. The proposed method is verified with simulation data of the Crab pulsar and real data of the same pulsar obtained from Insight-HXMT and NICER.
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