An envelope extraction method for eLoran signals based on convolutional neural networks

As a reliable backup to the GNSS, the Enhanced Long-Range Navigation (eLoran) system delivers credible positioning, navigation, and timing (PNT) information in GNSS-denied or severely interfered scenarios. To address the envelope distortion issue in eLoran signal extraction, a convolutional neural network (CNN)-based method was developed to improve extraction robustness under low signal-to-noise ratio (SNR) conditions. Simulated datasets were employed to generate eLoran signals and their corresponding ideal envelopes. A deep CNN model, integrated with large-scale one-dimensional convolutional kernels, batch normalization, max pooling, and transposed convolution, was constructed to directly extract envelope information from input noisy signals. Statistical results show that, within the SNR range of –10 dB to 0 dB, both the root mean square error (RMSE) and correlation coefficient of the proposed method are significantly superior to those of the band-pass filtering combined with Hilbert transform method and the quadrature demodulation low-pass filtering method. At an SNR of –10 dB, the RMSE of the proposed method remains at 0.098 2, and the correlation coefficient reaches 0.926 3. Furthermore, for any fixed SNR value, the error bars of both evaluation metrics are minimized. These findings demonstrate that the proposed method offers substantial advantages in extraction accuracy and anti-noise performance, providing a robust waveform foundation for high-precision time delay measurement in eLoran systems.