Chaofan Tuo

The enhanced long-range navigation (eLoran) system serves as a reliable backup to the global navigation satellite system (GNSS) and holds strategic significance in critical applications. To address the limitations of the traditional eLoran system under cold start and incomplete chain conditions, this paper proposes a two-stage pseudorange positioning framework. First, this framework projects the Earth to a standard sphere, enabling the derivation of closed-form solutions based on measured pseudorange values. Second, a Newton-Raphson method is employed for iterative refinement, utilizing closed-form solutions as an initial position to obtain the accurate position. This framework requires less prior position information and supports flexible station combinations. Also, the framework is capable of positioning under cold start conditions and in areas beyond the coverage of the entire chain. Third, the framework is comprehensively validated through theoretical simulations and practical applications. The results demonstrate significant improvements in positioning availability and accuracy, compared to the traditional eLoran system that utilizes time difference of arrival (TDOA) and pseudorange-based local optimization methods. The proposed framework exhibits superior robustness and broader applicability, establishing a solid foundation for eLoran-based resilient navigation.

The long-range navigation (Loran) system serves as a reliable backup to the global navigation satellite system (GNSS) and holds strategic significance in critical applications. However, the Loran system faces positioning ambiguity and range limitation challenges due to its time difference positioning mechanism and the constraints of the station chain signal in the additional time difference ambiguity discrimination (ATDAD) approach. To address these issues, this paper proposes a received electric field strength ambiguity discrimination (REFSAD) approach based on the electric field strength (EFS) attenuation characteristics of the Loran signal. The research constructs a comprehensive attenuation model applicable to mixed sea-land propagation paths and designs an ambiguity resolution strategy that does not require additional station information, thus enabling reliable identification of the true position. Through comprehensive Monte Carlo simulations and field-based experimental validation, this study demonstrates that the REFSAD approach exhibits statistically significant performance advantages, with 98.5% of positioning results falling within the high success rate interval (80-100%), compared to 97.4% for the ATDAD approach. When the coverage area is expanded by a factor of 3.8, the REFSAD approach maintains robust performance, with 98.2% of results within the high success rate range. Field experiments conducted in the South China Sea further validated the efficacy of REFSAD in regions where ATDAD is inapplicable, yielding a 100% positioning success rate with a root mean square error (RMSE) consistently maintained below 20 meters, thereby satisfying maritime navigation accuracy requirements.