Relaxation methods for navigation satellites set optimization

Convex relaxation methods are commonly used to solve nonconvex mathematical optimization problems. These methods transform the original nonconvex problem in such a way that effective methods of solving convex optimization problems become applicable. Thus, a convex problem giving the approximate solution of the original task can be solved instead of the original computationally complex problem. Presented is the application of semidefinite relaxation to the task of determining the optimal set of Global navigation satellite systems signals that are selected for processing while solving the positioning problem. The need for signals set optimization is due to large number of navigation satellites accessible for the customers on the ground level. This binary optimization problem is hard to solve in real time. Two approaches are proposed to reduce the initial problem to the convex problem allowing the effective solution.