To improve the positioning accuracy of the Loran system and meet the requirements of Loran/BDS integrated positioning and timing, it is necessary to enhance the traditional Loran hyperbolic positioning method, making its pseudorange calculation consistent with the BDS positioning and timing solution. The existing pseudorange algorithm based on the Andoyer-Lambert formula has issues such as strict initial value selection range and susceptibility to singularities during calculations. This study proposes a new Loran pseudorange calculation method based on the Vincenty distance formula and conducts a simulation analysis of it. The results show that, in the absence of noise interference, the positioning and timing errors of this pseudorange algorithm are close to zero, demonstrating high accuracy. When subjected to random noise with a standard deviation of less than 100 ns, the latitude and longitude errors are both less than 10 m, and the timing error is less than 10⁻⁴ ns, meeting the requirements of Loran positioning and timing. Compared to the pseudorange algorithm based on the Andoyer-Lambert formula, the one based on the Vincenty formula has comparable positioning longitude accuracy but superior timing accuracy. Moreover, the latter offers a wider range of initial value selection and can avoid more singularity issues during calculations.

Loran is a crucial maritime navigation system and is also considered a key backup for satellite navigation systems. To enhance positioning and timing services, improving the accuracy of the Loran system is essential. This paper discusses the factors affecting Loran’s positioning and timing performance, with a focus on ASF (additional secondary factor) measurement techniques and filtering methods. This study specifically addresses challenges in maritime navigation and employs a first-order Gauss–Markov process to simulate ASF+SF values. This approach eliminates the need for precise geodetic distances or real-time GNSS corrections. The research included experimental tests conducted along the eastern coast of China, evaluating environmental conditions and the positioning station’s location data. Positioning calculations were performed under maritime navigation conditions. The experimental results demonstrate that when satellite navigation systems are unavailable, the proposed model significantly enhances navigation accuracy. The accuracy, previously at the level of several hundred meters, was improved to approximately 40 m, making Loran a more reliable alternative for maritime applications.

Satellite navigation and positioning systems have become an essential component of modern infrastructure, supporting a wide range of civil and industrial applications. However, satellite-based positioning systems are vulnerable to interference, spoofing, and equipment failures, making reliance on a single system increasingly risky. To enhance system availability and continuity, the concept of resilient Positioning, Navigation, and Timing (PNT) has therefore been proposed. This paper presents a unified BDS (BeiDou Navigation Satellite System)–eLoran (enhanced Loran) fusion framework for positioning under reduced satellite observability. The framework systematically integrates BDS and eLoran measurements across different observability conditions, ranging from full satellite availability (≥ 4 satellites) to degraded scenarios with three, two, or a single satellite. Experimental results show that incorporating eLoran measurements significantly improves the robustness and availability of BDS positioning under limited satellite visibility. In particular, when the number of available BDS satellites is insufficient for conventional GNSS positioning, eLoran-assisted fusion enables continuous positioning with meter-level horizontal accuracy under favorable geometric conditions. Overall, the proposed approach demonstrates a practical fusion strategy that supports graceful performance degradation and rapid recovery under satellite-degraded conditions, especially in maritime environments.

This study evaluates GeoClock under a raw-hour-disjoint protocol designed to avoid reuse of nominal observation epochs across source training and validation. The model maps variable-cardinality GNSS observations to 80 physical statistical features and processes causal 60-epoch windows using a multi-task temporal convolutional network. BDS_2I, BDS_7I, BDS_6I, and GPS_1C provide source training, validation, and a source lockbox; all GPS_2W hourly files are held out. Across five paired masked-pretraining seeds with seed-specific source-selected thresholds, direct GPS_2W transfer has a mean AUROC of 0.999377 ± 0.001246 and recall of 0.999990 ± 0.000022, but a mean FPR of 0.537431 ± 0.337510. An independently acquired cross-site and cross-domain validation set from Site B (20 one-hour injected files spanning four signal domains and five fault realizations per domain; 14,180 windows and 81 events) yields a frozen direct-transfer AUROC of 0.999983 and an FPR of 0.1108. Under the stated 240 s clean-start assumption, the FPR falls to 0.000545 with recall 0.9721. This experiment evaluates geographically distinct acquisition conditions using the same frozen model and source-selected threshold; because the fault patterns remain injected, it does not establish field integrity or generalization to arbitrary sites. Five-seed GRU and TCN comparisons, residual-threshold diagnostics, feature-family ablations, and component ablations do not resolve threshold portability. A radial ECEF sensitivity analysis shows severe degradation at 3 and 10 m coordinate offsets. The results support controlled recovery of the stated injected observables and expose calibration and position-reference limitations; they do not establish field integrity.

Global Navigation Satellite Systems (GNSS) provide essential positioning, navigation, and timing (PNT) services for a wide range of safety-critical applications. However, GNSS performance degrades significantly in satellite-deficient or interference-prone environments. To address this limitation, this study proposes a hybrid GNSS/eLoran integrity monitoring framework based on a simplified Receiver Autonomous Integrity Monitoring (RAIM) architecture. In the proposed method, GNSS observations from satellite constellations and range-equivalent measurements from the enhanced Loran (eLoran) terrestrial system are jointly processed using a weighted least-squares estimator. Integrity monitoring is performed through a global chi-square consistency test combined with a solution separation strategy for fault identification and exclusion. Horizontal Protection Level (HPL) is derived from the covariance of the estimation process to ensure bounded positioning error under nominal and fault conditions. Unlike conventional GNSS-only RAIM, the proposed framework enables improved redundancy and fault observability in satellite-deficient scenarios by incorporating heterogeneous terrestrial measurements. Simulation experiments consider satellite faults, eLoran measurement disturbances, and inter-system clock bias effects. Results demonstrate that the proposed method maintains reliable fault detection capability and ensures that positioning errors remain consistently bounded by the protection level under all tested scenarios.