Effect of X-ray energy band on the X-ray pulsar based navigation

The X-ray energy band, which has a direct impact on the detector configuration and the estimation accuracy of the pulse time of arrival (TOA), is an important physical parameter for X-ray pulsar based navigation (XPNAV). Despite nearly five decades of work, there is still no convincing quality analysis for the effect of the X-ray energy on the XPNAV. In this paper, the impacts of the X-ray energy on the XPNAV are quantified for the first time through the Cramér-Rao lower bound (CRLB) theory. A lower bound on the variance of the pulse TOA is derived, and the indicators of the geometric factor and signal to noise ratio (SNR) are presented as the basic selection criteria. The RXTE observations of the Crab pulsar about 11 years (2001–2011) are applied to subdivide the entire 2–60 keV into finer energy windows of 2–10 keV, 10–20 keV, 20–30 keV, 30–40 keV, 40–50 keV and 50–60 keV to obtain pulse profiles in different energy bands. Discrepancies of these pulse profiles are investigated, and their impacts on the navigation accuracy are evaluated. The results demonstrate that the estimation accuracy of the pulse TOA applying the energy band 2–30 keV is improved by 15.54% compared with 2–10 keV, while an improvement of about 15.95% can merely be achieved applying 2–60 keV than 2–10 keV for the Crab pulsar.