Multi-satellite localization based on QR decomposition

Multi-satellite localization is a common localization method, which mainly uses time difference of arrival (TDOA) for localization. Many algorithms have been proposed for multi-satellite localization. However, due to the non-convex characteristics of the optimization problem, these algorithms tend to fall into local minima and degrade the localization accuracy. In this paper, we consider the position constraint that the target is located on the Earth surface, and convert the non-convex quadratic equation constraints to linear constraints in the iterative process. This paper proposed a localization algorithm based on QR decomposition, which can guarantee convergence to the global optimal solution. It is demonstrated through simulations that the algorithm can achieve the corresponding Cramer-Rao lower bound (CRLB), and the localization accuracy can be effectively improved by considering the position constraint of the target.