Jinsheng Zhang

Owing to the integration of numerous electronic devices into flight platforms, the resulting complex magnetic interference environment significantly impacts geomagnetic field measurement accuracy. To improve the compensation accuracy of traditional models and enhance their ability to characterize non-maneuvering interference, this study proposes a dual-channel hybrid-driven aeromagnetic compensation method incorporating time–frequency features. First, a model-data hybrid-driven approach is introduced to model different types of magnetic interference based on the classification of aeromagnetic interference. Additionally, the V-Coherence method is employed to select current signals from onboard equipment that are highly correlated with magnetic interference. Second, to further enrich feature representation, wavelet packet decomposition is introduced to expand the time–frequency characteristics of network inputs, and a dual-channel network is constructed to achieve effective compensation for complex magnetic interference from the aircraft platform. Finally, based on the proposed model, a cross-training strategy for calibrated flight data is explored. The proposed method is validated using field magnetic survey data in a public dataset. The results show that the proposed method achieves superior performance across all test regions compared to traditional approaches, effectively improves the accuracy of geomagnetic field measurements.

In enhanced Loran (eLoran) receiving systems, reliable signal acquisition is a prerequisite for subsequent tracking, timing, and positioning, and significantly affects receiver sensitivity and the effective acquisition range for weak and distant transmitter signals. This paper proposes a high-sensitivity, interference-resilient acquisition method based on band-summed short-time Fourier transform (BS-STFT). The method combines the time-domain pulse structure and frequency-domain energy concentration of eLoran signals to perform time—frequency energy accumulation within selected bands, thereby significantly enhancing the prominence and stability of acquisition peaks in weak signal and interference dominated environments. Simulations show that BS-STFT maintains over 80% acquisition probability at an SNR of − 24 dB and achieves a mean probability of 43% in the SNR range from − 30 dB to − 25 dB. It also shows robustness to in-band continuous wave interference with an SIR as low as − 15 dB at an SNR of − 20 dB, and maintains stable acquisition performance under sky-ground wave coexistence. Field experiments using real eLoran signals from inland and offshore test sites validate the proposed method. BS-STFT successfully acquired all eLoran transmitters deployed in China at both test sites, where the minimum SNR and electric field strength were − 22.46 dB and 26.38 dB μ V m − 1 , respectively, and the signal dynamic range between the two sites reached 65.93 dB. These results indicate that the BS-STFT significantly improves acquisition sensitivity and interference resistance, providing strong support for eLoran systems operating in complex environments.

Receiver system delay is embedded in additional secondary factor (ASF) observations and coupled with the propagation term at the observation level, which is a key factor limiting high-accuracy ASF measurement in enhanced Loran (eLoran) systems. Existing system delay calibration methods either can only calibrate the internal delay of the receiver and therefore cannot cover the complete delay chain involved in field measurements, or rely on single-point theoretical compensation, making the estimated system delay susceptible to errors in theoretical ASF values. To address this issue, this paper proposes a system delay calibration method based on multipoint ASF measurements for eLoran receivers. By exploiting the structural characteristic that the system delay acts as a shared constant bias in multipoint ASF observations, whereas the ASF spatial component varies with the propagation path, a joint inversion model of system delay and equivalent ground conductivity is constructed to separate the two in the absence of true ASF values. On this basis, a rapid calibration procedure is further established, including calibration area selection, reference receiver calibration, determination of the ASF spatial reference value at a fixed calibration site, and rapid calibration of other receivers. Experimental results in the Xi’an and Zhoukou test areas show that the optimal estimates of the reference receiver system delay are 79.046 μs and 79.048 μs, respectively, with a difference of only 2 ns. After correction for system delay and conductivity, the mean absolute error (MAE) and root mean square error (RMSE) between the ASF spatial component at the validation points and the theoretical ASF are 0.039 μs and 0.045 μs, respectively, in the Xi’an test area, and 0.076 μs and 0.091 μs, respectively, in the Zhoukou test area. Furthermore, the rapid calibration method is validated in the Zhoukou area. For two ASF measurement systems, one using the reference receiver calibrated through joint inversion and the other using a receiver rapidly calibrated at a fixed calibration site, the mean bias, MAE, and RMSE at the same measurement points are reduced by 98.9%, 85.9%, and 84.4%, respectively, compared with the corresponding values before calibration. The results demonstrate that the proposed method can provide relatively consistent system delay estimates under different propagation conditions and improve the consistency of ASF measurements obtained by different receivers.

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.

The Stochastic Finite-Difference Time-Domain (SFDTD) method based on Taylor expansion is an effective numerical method for quantifying uncertain parameters in electromagnetic models, but its accuracy is limited by the prediction of correlation coefficients between the electrical properties and fields. In the application of electromagnetic models, the Monte Carlo Correlation Coefficient (MC-CC) method for estimating the correlation coefficient requires approximately 1% of the running times of the Monte Carlo method. Meanwhile, when the S-FDTD method is used for transient field simulation, the MC-CC method has difficulty in estimating the correlation coefficients of the S-FDTD method. In this letter, based on the Non-Intrusive Polynomial Chaos (NIPC) method, the correlation coefficients in the S-FDTD method are estimated, enabling the S-FDTD method to be applied to high-precision simulation of the random properties of transient fields. Two different random ionosphere models were used to simulate the propagation process of electromagnetic waves and obtain the correlation coefficients of the S-FDTD method. The effectiveness of the proposed method was verified by comparing it with the Monte Carlo and MC-CC methods.