Jiaju Zhou

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.

This paper investigates the effects of frequency, polarization, and incidence angle on very low frequency (VLF) reflection and transmission in an anisotropic ionosphere. By deriving the refractive indices and altitude evolution of the propagation direction of the ordinary (O) and extraordinary (E) modes, we show that, unlike the O mode whose wave normal bends toward the horizontal and approaches an effective turning condition with increasing altitude, the E-mode wave-normal direction progressively turns toward the vertical and is governed by the coupling among the pseudo-Brewster effect (PBE), magnetic guidance, and ionospheric parameter gradients. Accordingly, a dynamic pseudo-Brewster angle (PBA) matching window is proposed to quantify the matching relationship between the E-mode propagation angle and the local PBA condition. Simulations show that this window has a strong frequency dependence: as the frequency increases, the window shifts upward and broadens; under oblique incidence, the local overlap between the window and the upward E-mode flux profile becomes more evident. Further energy-flux analysis indicates that the overall upward E-mode flux transmission in the lower-ionospheric entrance region and the PBA-window flux-overlap ratio do not reach their peaks at the same incidence angle. This suggests that the upward energy transfer of VLF waves into the lower ionosphere is influenced by the combined effects of propagation path length, collisional absorption, and PBE-related local coupling. These results provide a theoretical reference for understanding the local incidence mechanism of VLF waves entering the lower ionosphere, and for developing future ground-to-satellite VLF propagation models that incorporate source angular spectra, lower-ionospheric entrance coupling, and in-orbit receiving geometry.

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.