Xinyue Hu

The working accuracy of the eLoran system is susceptible to the interference sky–ground wave multipath aliasing. Therefore, the accurate estimation of the sky–ground wave relative delay plays an important role in suppressing skywave interference. To address the performance degradation of existing methods under low‐SNR or small‐delay‐interval conditions, this paper constructs a delay estimation method that combines IFFT preprocessing with two‐stage MS‐CNN. The IFFT preprocessing is used to enhance the time‐domain features related to delay. The two‐stage MS‐CNN achieves accurate estimation of the groundwave, skywave and their relative delay through multi‐scale convolution, channel attention and local residual correction. Simulation results show that the proposed algorithm can accurately estimate the delay over an SNR range of −5 to 20 dB, and the estimation error can be reduced to as low as 0.021 under high‐SNR conditions. The results of multiple comparative experiments show that the proposed method maintains high delay estimation accuracy under different SNR conditions, and exhibits better stability especially in low‐SNR and small‐delay‐interval scenarios, further verifying its applicability and robustness under complex conditions.

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.

The study of low-frequency (LF) radio-wave propagation phase in the Earth-ionosphere waveguide is of great significance for the accuracy enhancement of related systems such as ionospheric sounding, time service, and lightning location. In this article, the stochastic finite-difference time-domain (S-FDTD) algorithm based on the Taylor series expansion idea is used to propose a new method for measuring the uncertainty of LF radio-wave propagation phase in the random media. We study how to obtain the mean value and standard deviation of the propagation phase of the Loran-C one-hop sky waves when the ionosphere is considered to be the random medium. At the same time, the effects of different ionospheric parameters with random characteristics on the propagation phases of sky waves are analyzed. The results of the wave-hop theory are used for validation. The numerical experimental results show that the method can obtain the statistical characteristics of LF radio-wave propagation phase only by a single FDTD simulation. The method can be further extended to obtain the stochastic characteristics of LF radio-wave propagation phases in the complex Earth-random ionosphere waveguide.

The analysis of propagation characteristics of low-frequency(LF) radio waves in the Earth-ionosphere waveguide is of great significance for timing, navigation and many other fields. Because the ionosphere changes with different time and geographical location, there are random changes besides regular time-varying effects, which limits the application of traditional finite-difference time-domain (FDTD) model. In this letter, the polynomial chaos expansion FDTD (PCE-FDTD) method based on cylindrical coordinates is used to predict the statistical characteristics of LF radio-wave propagation in isotropic stochastic ionosphere environment with dielectric constant and conductivity as random variables. Compared with Monte Carlo FDTD (MC-FDTD) method and wave-hop theory, the accuracy and efficiency of PCE-FDTD method are verified. And the influence of different distributions and amplitude fluctuations of random electromagnetic parameters in the ionosphere and irregular terrain on the variance field of LF sky-wave signals is further analyzed. It provides some reference for ionospheric detection and research on propagation characteristics of LF radio waves.