Solar Frequency Shift-Based Radial Velocity Difference Measurement for Formation Flight and Its Integrated Navigation

The solar spectrum can be obtained by a spectrometer on a spacecraft. The velocity of a spacecraft with respect to the Sun can be calculated according to the solar frequency shift. However, small-scale activities on the solar surface can cause spectral line drift, which results in a large and varying bias in the velocity measurement. This makes it difficult for a single spacecraft to exploit the solar frequency shift. To resist the interference of solar surface activities effectively, this paper develops a solar frequency shift-based radial velocity difference measurement method to enhance the accuracy of relative navigation for formation flight. In this method, each spacecraft in a formation observes the solar frequency shift and obtains a radial velocity measurement which includes the velocity bias caused by the solar surface activities. The difference in these radial velocities is immune to the varying velocity bias. Therefore the difference is utilized as the navigation measurement in this method. However, this navigation system cannot work alone because of unobservability. To make the navigation system observable and improve the accuracy of both absolute and relative navigation for formation flight, this paper combines it with X-ray pulsar navigation and proposes a radial velocity difference/pulsar integrated navigation method with observability. This autonomous integrated navigation scheme adopts the extended Kalman filter to deal with the radial velocity difference measurement and the pulsar time of arrival (TOA), providing absolute and relative navigation information for formation flight. The simulation results demonstrate that both the absolute and relative navigation accuracies of the proposed method are higher than those of X-ray pulsar navigation, especially relative navigation.