Deterministic Maximum Likelihood Algorithm for Sky-Ground Waves Recognition in ELoran Systems

It is crucial to recognize the sky and ground waves, i.e., to determine the delays of the waves, in enhanced long-range navigation (eLoran) systems. However, the performance of most existing algorithms sharply decreases when the delay differences <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \tau$</tex-math></inline-formula> between the sky and ground waves are small or the signal-to-noise ratios (SNRs) are low. In this paper, after transforming the originally time-domain sky-ground waves recognition problem to the frequency domain, we interestingly find that it can be effectively addressed by the deterministic maximum likelihood (DML). Thus, we design a DML-based sky-ground waves recognition algorithm. The verification results based on both the simulated and the realistic data show that the DML outperforms the four representative algorithms, including the IFFT, the FOC-MUSIC, the WRELAX, and the LM, in terms of the success rate in recognizing the groundwave, particularly in situations with small <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \tau$</tex-math></inline-formula> or low SNRs. Numerically, compared to the IFFT, the LM, and the FOC-MUSIC, the success rate achieved by the DML is improved by 67.11%, 66.67%, and 64.19% respectively, and the WRELAX fails to work, in a challenging situation of SNR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$=0$</tex-math></inline-formula> dB and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \tau =37\ \mu s$</tex-math></inline-formula>.