A two‐stage iterative method for short‐wave source localisation

Abstract

Short‐wave source localisation has an important role in many fields. A two‐stage iterative algorithm is proposed based on the ionospheric virtual height (IVH) model using the direction of arrival (DOA) and time difference of arrival (TDOA) measurements, which is divided into DOA stage and TDOA stage. The optimisation problem of the TDOA stage can be obtained by using the result of DOA stage and TDOA measurements. During the solution process, the non‐convex quadratic equation constraints are converted to linear constraints, which can lead to the algorithm converges to the global optimal solution and the optimal solution can be analytically solved. The theoretical analysis demonstrates that the localisation accuracy of both stages can reach the corresponding constrained Cramér‐Rao lower bound (CCRLB). And the accuracy of TDOA stage achieves the CCRLB of hybrid localisation. Finally, the performance of the proposed method is demonstrated by simulations.