Observability analysis of autonomous relative navigation system for small celestial body detection based on sequence images

The detection of small celestial bodies is significance for exploring the origin of universe and solving the problem of earth resources. Research about the small celestial body explorer and implementation of small celestial body detection has become the focus of the future space development of various nations. Affected by the command delay of the ground control network, the small celestial body explorers need to independently obtain the position and speed information of the small celestial body, which should have the ability of autonomous relative navigation. The autonomous relative navigation based on sequence images can not only provide the angle observations of small celestial bodies, which contain the relative motion information about the small celestial bodies, but also has the advantages of low cost and low power consumption. Since that, the autonomous relative navigation based on sequence images is an ideal method for the small celestial body detection, and it has been the research hotspots in the relative navigation field. Observability analysis can evaluate the observation ability of the system, which is the basis for studying the autonomous relative navigation system based on sequence images. For the problem of nonlinearity observability analysis of the small celestial body detection autonomous relative navigation system with sequence images, this paper proposes the observability matrix based on the derivation of the 0 to 2nd order Lie derivatives of the system by the differential geometry theory. The locally weak observability of the system under the typical orbital manifolds of small celestial body detection is realized based on the rank criterion of the observability matrix, and the results show that the small celestial body explorer can fully estimate the motion state of the small celestial body by the sequence images alone. In addition, the observability degree of the system is quantified according to the condition number method, and the influence of the varying of the relative orbital manifolds on the observability degree is analyzed. The conclusion can guide the orbit design of small celestial body detectors and have certain engineering values.