1 Relative velocity measurement with spectrometer and 2 its integrated navigation 3

In order to enhance the accuracy of the relative velocity measurement for the Mars 13 explorer formation flight, we develop a relative velocity measurement method. In this method, the 14 spectrometers at two Mars explorers are adopted to measure the starlight frequency shift and to 15 estimate the velocity with respect to the star. Unfortunately, the instantaneous velocity of star can 16 not be predicted accurately, which results in a large error in the velocity measurement. The 17 difference of these two velocities, which does not include the proper motion of star, is the relative 18 velocity between a pair of Mars explorers at the direction of the star. However, this navigation 19 method can not work alone because of unobservability. To make the navigation system observable 20 and improve the accuracy of both absolute and relative navigation for the Mars explorer formation 21 flight, we combine it with X-ray pulsar navigation and the inter-satellite links, and propose an 22 autonomous integrated navigation method with observability. In this integrated navigation scheme, 23 the extended Kalman filter is adopted to deal with the relative velocity, the inter-satellite links and 24 the pulse time-of-arrival, and estimate the absolute and relative navigation information for the Mars 25 explorer formation flight. The simulation results demonstrate that both absolute and relative 26 navigation accuracy of the proposed method are higher than that of the pulsar navigation, especially 27 the relative one. 28