Application of the Method of Semidefinite Relaxation for Determining the Orientation of a Solid Body in Space

Abstract

In this paper, the semidefinite relaxation method is applied to the problem of determining the orientation of a solid body relative to the local horizon using satellite navigation. It is shown how the initial nonconvex quadratic programming problem is immersed in a wider class of convex optimization problems that allow an effective solution. Instead of the original computationally complex problem, a convex problem was solved, giving an approximate solution of the original problem. The proposed approach is applied to the processing of experimental data.