An iterative method for short-wave source localization based on constrained weighted least squares

Short-wave source localization plays an important role in the military. Ionosphere reflection height has a significant impact on localization accuracy. In this paper, an iterative constrained weighted least squares algorithm is proposed to jointly estimate the source and ionosphere reflection height based on the ionospheric virtual height (IVH) reflection model using direction of arrival (DOA) measurements. The localization model containing two quadratic equation constraints is constructed based on the nonlinear relationship of auxiliary variables and the source position constraint. During the iteration process, the results of the previous iteration are utilized to convert the quadratic equation constraints to linear constraints, thus enabling the optimal solution to be given in closed form. Simulation results demonstrate that the accuracy of the proposed algorithm for both source and ionospheric ionosphere height is able to reach the corresponding constrained Cramér-Rao lower bound (CCRLB).