Over‐the‐Horizon Direct Positioning With Ionospheric Heights Priors

ABSTRACT This study addresses positioning errors in high‐frequency (HF) over‐the‐horizon (OTH) localisation that arise from inaccuracies in ionospheric virtual height measurements. We propose a direct localisation algorithm based on the direct position determination (DPD) model in which the initial search range of the target is estimated using HF single‐station direction‐finding (SSDF). To enhance accuracy, the International Reference Ionosphere (IRI) model is combined with ionosonde data to provide priors on ionospheric virtual heights. These priors are incorporated into a single‐layer mirror reflection model of the ionosphere to establish a more accurate signal propagation path, thereby mitigating errors caused by variations in virtual heights across different transmission paths. The algorithm leverages the global search capability of particle swarm optimisation (PSO) to generate high‐quality initial solutions, followed by localised refinement through the Gauss–Newton method to further improve positioning accuracy. Experimental results show that, compared with traditional direct localisation methods that assume fixed virtual heights, the proposed approach reduces positioning errors by 5–25 km in typical scenarios and increases computational efficiency by more than 40% compared to the conventional exhaustive grid search method (measured in terms of computational complexity). Overall, the method provides a balanced solution for HF OTH localisation systems, effectively improving both accuracy and efficiency.