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.

The results of comparative estimation of the accuracy of autonomous navigation of small spacecraft in formation flying are presented. To carry out the research, the “zenith” method and the method of navigation by orbital references were chosen. These methods are based on measurements of the angular position of the Earth and an orbital reference point relative to navigational stars. Assumptions concerning the central terrestrial gravitational field and the normality of errors of the on-board navigation measurements with known constant variability were introduced in the studies. The studies were carried out using the theory of analytical estimation of the accuracy of spacecraft autonomous navigation methods. The use of this theory makes it possible to obtain the covariance error matrix of the required vector of navigation parameters and to estimate the potential (maximum achievable) characteristics of the accuracy of the navigation methods used. A dimensionless navigation error coefficient was chosen as an indicator of the accuracy of small spacecraft navigation method. The coefficient is associated with the elements of the main diagonal of the covariance matrix, it characterizes the precision properties of the method, is integrated by nature and does not depend on the volume and accuracy of the results of navigation measurements. The criterion of expediency of applying the method of determining the parameters of motion of the spacecraft center of mass is based on the comparison of navigation error rates. The presented results allow us to make reasonable choice of the method of autonomous navigation and of the composition of the onboard control of small spacecraft in formation flying.

The article presents the results of an analytical study of the accuracy of estimating systematic optical errors of onboard navigation measurements that, along with the vector characterizing the motion of the center of mass of the space robot, are included in the vector of the parameters to be specified. The range to the orbital reference point, the relative speed of its motion and the angles between the directions to the orbital landmark and to the navigational stars, one of which is in the plane of the space robots orbit, and the direction to the second one coincides with the normal to this plane are chosen as the primary navigation parameters to be measured by the space robot onboard facilities. The conditions that make it possible to specify the augmented vector of the parameters to be determined are defined. Estimating the systematic errors of measurements we make assumptions about the central gravitational field of the Earth, the normal law of measurement errors with known variances and the constancy of the unknown systematic errors. Analytical expressions of the covariance matrices that make it possible to estimate the maximum achievable accuracy of solving the task depending on the kind of navigational measurements, variances of measurement errors and the number of measurements during a selected measuring interval are obtained. The presented results can be applied to justify the ways of improving the accuracy of the autonomous navigation of a space robot in diagnosing the technical condition of an orbital object.