Wenhe Yan

Positioning, navigation, and timing (PNT) services require stable time transfer, but satellite-based PNT signals are vulnerable to interference, attenuation, and limited availability in constrained environments. Very-low-frequency (VLF) signals propagate over long distances in the Earth–ionosphere waveguide and can serve as a terrestrial complement to satellite-based timing systems. Their timing performance, however, is affected by propagation-delay variation, especially the diurnal component associated with changes in the effective ionospheric reflection height. This study presents a propagation-delay correction method for VLF timing signals based on a phase-variation model. The total delay error is separated into primary path delay, secondary propagation delay, and residual random error. The primary delay is calculated from the transmitter–receiver path, while the periodic secondary delay is corrected using the predicted phase variation. Historical Alpha observations recorded at Chongqing and Guilin were used to evaluate the correction performance. The results show that the corrected standard deviation is reduced to 2.0054–2.2500 μs for the Chongqing paths and 2.7987–4.4792 μs for the Guilin paths. The corrected root mean square error (RMSE) ranges from 2.1316 μs to 4.5641 μs across the six Alpha propagation paths. These results indicate that the proposed method can suppress the main diurnal propagation-delay component in the selected historical Alpha datasets, although further validation with contemporary and multi-season VLF observations is still needed.

As a crucial long-range positioning, navigation, and timing (PNT) system, eLoran will utilize the ninth pulse to broadcast differential data. However, conventional demodulation methods are ill-suited to the unique modulation characteristics of the ninth pulse and suffer from poor noise resistance, necessitating a more efficient demodulation solution. To address this, this paper proposes a lightweight Multilayer Perceptron (MLP)-based demodulation framework designed explicitly for the eLoran ninth pulse. The approach begins with a preprocessing stage that extracts a 1600-point key segment from each received frame, which is then fed into a compact MLP architecture with a 1600-dimensional input layer, a 512-neuron hidden layer, and a 32-class output layer trained using the Adam optimizer. Experimental results demonstrate that the proposed model achieves 99.97% accuracy on the validation set and maintains over 90% demodulation accuracy even at an SNR of −10 dB, whereas the improved EPD algorithm yields only about 70% demodulation accuracy. Notably, although the improved EPD algorithm itself exhibits a clear performance advantage over the basic correlation method and the peak-position detection method—both of which still present non-zero error rates even at an SNR of 20 dB—it remains significantly inferior to the proposed MLP-based scheme in the low-SNR regime. In addition, CNN-based and LSTM-based demodulation models show very poor performance under severe noise conditions, with symbol error rates rising to around 0.8 at −10 dB, despite being able to reach an error-free state when the SNR increases to approximately 2 dB. By adopting an end-to-end learning strategy, the method effectively avoids performance degradation caused by inter-module error propagation, while combining high precision with strong noise immunity. These features meet the requirements for real-time differential data reception and highlight the promising engineering potential of neural-network-based demodulation for high-reliability PNT applications in complex electromagnetic environments.

In integrated PNT systems, due to defects in satellite signals and long-wave signals, VLF signals can be an essential supplement. However, there is currently a lack of VLF timing systems in the world, and it is impossible to evaluate the impact of the propagation delay of these signals. Based on the theory of very-low-frequency propagation, this paper determines the waveguide mode propagation at ultra-long distances as the main research direction, establishes a signal phase change model, gives a theoretical formula for the phase velocity of VLF signals, and analyzes the main factors affecting the phase velocity of VLF signal propagation. Finally, combined with historical observation data, the phase change is predicted, compared, and analyzed. The results show that the theoretical calculation is consistent with the measured data. The average error of the delay prediction is 0.015 microseconds per 100 km, and the maximum error of the delay prediction is 0.152 microseconds per 100 km.

The shortwave time service system is a vital land-based wireless time service solution, serving as a supplement and backup to the global navigation satellite system. It ensures that time users can access reliable timings, especially in extreme situations. However, the current BPM shortwave time service signal in China faces issues such as insufficient anti-interference reception capabilities and poor timing accuracy. This paper capitalizes on the advantages of Chirp signals and explores a new modulation technology for BPM shortwave time signals that is compatible with the existing modulation system. A Dual Chirp Time-Division Combined Modulation (DCTDCM) scheme is proposed for broadcasting two time signals: Coordinated Universal Time (UTC) and Universal Time 1 (UT1). Furthermore, an in-depth study of the receiving method for this scheme is conducted, with detailed design of its parameters. The designed DCTDCM signals offer a spread spectrum gain of 24 dB and a multipath resolution capability of at least 125 μs, significantly enhancing the anti-interference reception and anti-multipath attenuation capabilities of shortwave time signals. As a result, the availability and timing accuracy of shortwave time signals are substantially improved. Finally, extensive comparative experiments on reception performance validate the effectiveness of this approach.

The Alpha navigation system is the only operating radio system based on very-low-frequency (VLF) signals that can be used to research VLF navigation, timing, and ionospheric characteristics. The detection of the Alpha navigation signal is the key step in the Alpha receiver; however, the received Alpha navigation signal is susceptible to noise and mutual interference, which deteriorates signal detection performance. This paper presents a multichannel orthogonal correlation method for Alpha navigation signal detection. Once the three frequency signals of the Alpha navigation system are obtained using a notch filter, station identification is realized using a multichannel orthogonal correlation method and signal format. The selection of key parameters and the detection performance under noise and mutual interference are analyzed. This method’s detection probability exceeds 90% when the signal-to-noise ratio (SNR) is greater than −10 dB. The influence of mutual interference on the signal correlation peak is less than 1% when the signal-to-interference ratio (SIR) of the mutual interference is greater than −28 dB. The proposed method is verified using an actual signal collected using an Alpha receiver. The results show that an Alpha signal can be detected at an extremely low SNR. This method has strong practicability and satisfies the application requirements of an Alpha receiver.

Currently, eLoran is the ideal backup and supplement for global navigation satellite systems. The time synchronization accuracy between stations in the eLoran system has improved, providing conditions for eLoran pseudorange positioning. The pseudorange positioning of eLoran is a nonlinear least-squares problem and the location of the eLoran transmitting stations may cause the above problem to be non-convex. This makes the conventional pseudorange positioning al-gorithm strongly depend on the initial value when solving the eLoran pseudorange positioning. We propose a shrink-branch-bound (SBB) algorithm to solve the eLoran pseudorange positioning initialization problem. The algorithm first uses a shrink method to reduce the search space of the position estimator. Then, optimization is performed using a branch and bound algorithm within the shrunk region, where a trust region reflective algorithm is used for the lower bound process. The algorithm can help the receiver to complete the initial positioning without any initial value information. Simulation experiments verify that the algorithm has a success rate of more than 99.5% in solving the initialization problem of eLoran pseudorange positioning, and can be used as an initialization algorithm for pseudorange positioning problems for eLoran or other long-range terrestrial-based radio navigation system.

The eLoran system is an international standardized positioning, navigation, and timing service system, which can complement global navigation satellite systems to cope with navigation and timing warfare. The eLoran receiver measures time-of-arrival (TOA) through cycle identification, which is key in determining timing and positioning accuracy. However, noise and skywave interference can cause cycle identification errors, resulting in TOA-measurement errors that are integral multiples of 10 μs. Therefore, this article proposes a cycle identification method in the joint time–frequency domain. Based on the spectrum-division method to determine the cycle identification range, the time–domain peak-to-peak ratio and waveform matching are used for accurate cycle identification. The performance of the method is analyzed via simulation. When the signal-to-noise ratio (SNR) ≥ 0 dB and skywave-to-groundwave ratio (SGR) ≤ 23 dB, the success rate of cycle identification is 100%; when SNR ≥ −13 dB and SGR ≤ 23 dB, the success rate exceeds 75%. To verify its practicability, the method was implemented in the eLoran receiver and tested at three test sites within 1000 km using actual signals emitted by an eLoran system. The results show that the method has a high identification probability and can be used in modern eLoran receivers to improve TOA-measurement accuracy.

There are mainly two types of data modulation methods used for enhanced LOng-RAnge Navigation (eLORAN) systems: pulse position modulation (PPM) and supernumerary interpulse modulation (SIM). The typical application for PPM is tri-state PPM (3S-PPM), also known as Eurofix. The typical application for SIM is ninth pulse modulation. Both of these methods are phase modulation methods. Phase modulation coding, a very mature technology, is used at present. To achieve a better demodulation success rate of eLORAN digital modulation signals at longer distances, a method of using the transmitting station duplex mode to transmit a digital modulation pulse group after LORAN-C transmitting a pulse group is proposed to realize modulation pulse on–off modulation. In this method, a broadcasting experiment was performed on the BPL (The call sign of eLORAN time service system in China) broadcaster station. After monitoring, a good receiving demodulation effect was initially obtained.

Loran-C is the most important backup and supplement system for the global navigation satellite system (GNSS). However, existing Loran-C demodulation methods are easily affected by noise and skywave interference (SWI). Therefore, this article proposes a demodulation method based on Loran-C pulse envelope correlation–phase detection (EC–PD), in which EC has two implementation schemes, namely moving average-cross correlation and matched correlation, to reduce the effects of noise and SWI. The mathematical models of the EC, calculation of the signal-to-noise ratio (SNR) gain, and selection of the EC schemes are given. The simulation results show that compared with an existing method, the proposed method has clear advantages: (1) The demodulation SNR threshold under Gaussian channel is only −2 dB, a reduction of 12.5 dB; (2) The probability of the demodulated SNR threshold, being less than zero under the SWI environment, can reach 0.78, a 26-fold increase. The test results show that the average data availability of the proposed method is 3.3 times higher than that of the existing method. Thus, our demodulation method has higher engineering application value. This will improve the performance of the modern Loran-C system, making it a more reliable backup for the GNSS.