Accuracy of autonomous navigation by the mutual method in the case of a group flight of space vehicles

The article presents the results of an investigation of the accuracy of estimating errors in the determination of the motion parameters of the center of mass of a small spacecraft performing a group flight together with other small spacecraft, among which there is a small spacecraft that acts as the leader of the group.  The angles between the directions to the small spacecraft-leader, and navigational stars, one of which is in the plane of the orbit of the small spacecraft, and the direction to the second one coincides with the binormal of this plane are chosen as the primary navigation parameters measured by the onboard facilities of the small spacecraft. When estimating the errors in determining the parameters of the motion of the center of mass of a small spacecraft, assumptions are made about the central gravitational field of the Earth, the normal law of error distribution of on-board navigation measurements with known constant variances. The research was carried out on the basis of the method of analytical estimation of the accuracy of autonomous navigation of space vehicles. As a result of the studies, analytical expressions of covariance matrices are obtained that allow one to estimate the maximum achievable accuracy of the solution of the problem posed, depending on the altitude of the orbit of a group of small space vehicles, the displacement of the slave small spacecraft relative to the small spacecraft-leader by the latitude argument, the variances of measurement errors and the number of measurements during a navigation mode. The presented results can find application when it is necessary to substantiate ways of improving the accuracy of autonomous navigation of small spacecraft performing group flights.