Zhenzhu Zhao

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.

Accurate estimation of sky‐ground wave delays and intervals is critical to Time of Arrival (TOA) measurements for timing and positioning in enhanced long‐range navigation (eLoran) systems. To overcome the performance limitations of conventional methods, this paper proposes a Multiple Signal Classification algorithm based on Forward‐Backward Spatial Smoothing and Toeplitz Reconstruction (FBSS‐TMUSIC) algorithm. By constructing a virtual frequency‐domain subarray model, the method incorporates FBSS combined with Toeplitz matrix reconstruction, ultimately utilising the MUSIC algorithm to estimate the delays. Simulation results and field tests from two receiver sites at different distances confirm its superiority over six representative sky‐ground wave delay estimation methods. Quantitatively, FBSS‐TMUSIC achieves an signal‐to‐noise ratio (SNR) gain of 4–8 dB for small delay intervals as narrow as 33 µs and extends the tolerance threshold for strong noise to dB, corresponding to an improvement of 6–12 dB over comparative algorithms. When SNR dB, the root mean square error of the single component remains consistently below 5 µs. In addition, the method exhibits the minimum standard deviation in pure groundwave field tests; under severe sky‐ground wave aliasing, it enhances estimation stability by a factor of approximately two relative to other algorithms.

A model based on the wave-hop method for low-frequency (LF) sky-wave prediction considering the effect of the geomagnetic field is studied in this letter. The Hybrid Matrix Method (HMM) is chosen to calculate the reflection coefficient of the anisotropic ionosphere, which can take the inhomogeneity of the ionosphere and the influence of geomagnetism into account. Then the one-hop sky-wave field strength at different simulation conditions is analyzed by the proposed model. To obtain sky-wave, a Low-Frequency Signal Acquisition System is established, which can provide the raw signal to be analyzed. By comparing with the measured data, the accuracy of the proposed model is higher than that of previous algorithms.

In this study, the effect of random characteristics of the ionosphere on the enhanced Loran (eLoran) sky-wave signal was analyzed. First, the bilinear transform stochastic finite-difference time-domain (S-BT-FDTD) method in layered half-space isotropic plasma is derived, and the correctness of the calculation of the mean value and standard deviation of the field components of the eLoran sky-wave signal is verified. Second, the mean value and standard deviation of the amplitude and time delay of the eLoran sky-wave signal were analyzed by combining the International Reference Ionosphere, pseudo-1-D BT-FDTD method, and Monte Carlo method. The simulation results show that the mean value of the amplitude of the reflection coefficient amplitude (RA) in the eLoran signal bandwidth remains unchanged. The larger the standard deviation of the electron density, the larger is the standard deviation of RA. The standard deviation of RA during the day is greater than that at night. The mean value of the time delay remains unchanged, and the standard deviation of the time delay is related to the way the electron density varies randomly. When the incident angle increases, the RA increases, the standard deviation of RA decreases, the time delay decreases, the standard deviation of the time delay decreases, and the signal becomes more stable.