METHOD AND ALGORITHMS FOR CALCULATING HIGH-PRECISION ORIENTATION AND MUTUAL BINDING OF COORDINATE SYSTEMS OF SPACECRAFT STAR TRACKERS CLUSTER BASED ON INACCURATE MEASUREMENTS

Abstract

The problem of increasing the accuracy of determining the orientation of a spacecraft (SC) using a system of star trackers (ST) is considered. Methods are proposed that make it possible to use a joint field of view and refine the relative position of ST to improve the accuracy of orientation determination. The use of several star trackers leads to an increase in the angle between the directions to the stars into the joint field of view, which makes it possible to reduce the condition number of the matrices used in calculating the orientation parameters. The paper develops a combinatorial method for interval estimation of the SC orientation with an arbitrary number of star trackers. To calculate the ST orientation, a linear problem of interval estimation of the orthogonal orientation matrix for a sufficiently large number of stars is solved. The orientation quaternion is determined under the condition that the corresponding orientation matrix belongs to the obtained interval estimates. The case is considered when the a priori estimate of the mutual binding of star trackers can have an error comparable to or greater than the error in measuring the angular coordinates of stars. With inaccurately specified matrices of the mutual orientation of the star trackers, the errors in the mutual orientations of the STs are added to the errors of measuring the directions to the stars, which leads to an expansion of the uncertainty intervals of the right-hand sides of the system of linear algebraic equations used to determine the orientation parameters. A method is proposed for solving the problem of refining the mutual reference of the internal coordinate systems of a pair of ST as an independent task, after which the main problem of increasing the accuracy of spacecraft orientation is solved. The developed method and algorithms for solving such a complex problem are based on interval estimates of orthogonal orientation matrices. For additional narrowing of the intervals, the property of orthogonality of orientation matrices is used. The numerical simulation carried out made it possible to evaluate the advantages and disadvantages of each of the proposed methods.