Lili Zhou

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.

Studying the impact of terrain undulation on low frequency (LF) sky-wave propagation delay is of great signifi-cance for exploring the potential applications in low-ionospheric detection, remote navigation, and timing service. This letter combines gradient ionospheric parameters and uses the finite-difference time-domain (FDTD) method to calculate the reflected signal of LF radio waves from the ionosphere. Using the sky- and ground-wave separation technology in time domain, the variation law of LF sky-wave propagation delay with terrain changes is given in both daytime and nighttime models. At the same time, this letter also analyze the influence of different ionospheres (in the presence or absence of natural magnetic field) on LF one-hop sky-wave propagation delay, providing some reference significance for studying the propagation characteristics of LF sky waves.

The far-field calculation of arbitrarily oriented electric dipole in a stratified confined space is of great significance in analyzing electromagnetic properties in the lightning return stroke, submarine communication, over-the-horizon ground-wave radar, etc. Based on the mirror image method and the far-field approximation of an electric dipole in free space, a three-layer horizontal confined space model with an arbitrarily oriented dipole is established in this work. Through novel vector operations, the expression of the far field generated by an arbitrarily oriented electric dipole in the confined space model is derived, where the direct wave from the source point to the observation point and the waves reflected by the upper boundary and the lower boundary are all comprehensively considered. On this basis, the radiation characteristics of the electric dipole with frequencies of 100 kHz, 6 MHz and 10 MHz at different positions in the Earth-ionosphere waveguide are compared and analyzed, which are taken for example. Three different orientations of electric dipoles,i.e. vertical direction, horizontal direction, and 45º tilt are taken into account and the corresponding radiation patterns are presented. The results show that the radiation characteristics of electric dipoles in the Earth-ionosphere waveguide will change greatly with their frequencies, orientations and positions. For the electric dipole source at the same location, the higher the frequency, the more the number of radiation lobes is. In addition, when the source frequency keeps unchanged, the farther the dipole source is from the bottom boundary, the more the radiated lobes are. The proposed expression can conveniently and accurately consider the direct wave of a dipole source and its primary reflection from the upper interface and the lower interface in a confined space, and can also be further extended to solving the contribution of multiple reflections from the interfaces.

To expand the space applications of low-frequency sky-wave signals, Loran-C electromagnetic fields at low and high altitudes in the earth–ionosphere waveguide are studied in this letter. In order to consider the influence of the earth's surface on one-hop sky-wave fields at different altitudes, the wave-hop theory that used for field predictions on the ground is improved, and the wave-hop equation based on the frequency domain is further transformed into the time domain. Then, the proposed approach is applied to calculate the sky-wave fields at the altitudes 0–50 km under given earth–ionosphere models. The accuracy and efficiency of the method are verified by comparison to the finite-difference time-domain method.