X-ray pulsar-based navigation method using one sensor and modified time-differenced measurement

X-ray pulsar-based navigation method using one sensor (XNAVO) could fix the position of satellites by sequentially observing X-ray pulsars at the cost of loading one X-ray sensor, which drops the demand on the loading capability of satellite and is feasible for practice. However, subjected to the current research status of astronomical measure and the radiation mechanism of pulsar, there are unexpected systematic biases in XNAVO, which would greatly worsen the positioning performance of XNAVO. In addition, the systematic biases compensation methods previously proposed for X-ray pulsar-based navigation using three sensors would fail when being applied to XNAVO, due to the sequential observation strategy. In order to solve the problem, this paper introduces a positioning algorithm for XNAVO based on the modified time-differenced measurement. The propagation of systematic biases is analysed, revealing the systematic biases behave a quasi-periodical variation. Thus, a modified time-differenced measurement is proposed in accordance of the quasi-periodicity. A navigation filter that propagates sigma points to generate the improved time-differenced measurement model without linearisation has been given. The results of simulation have shown that the proposed method could reduce the major impact of investigated systematic biases.