Comparison of low frequency multi-hop sky wave delay estimation algorithms

Accurate prediction of low-frequency (LF) sky wave is of great significance for its potential application in long-range navigation time service. In order to obtain the propagation delay characteristics of LF multi-hop sky waves in the earth-ionospheric waveguide and verify the performance of typical multipath time delay estimation methods in different channel environments, firstly, the finite-difference time-domain (FDTD) electromagnetic calculation method is used to predict the total coupling fields of sky and ground waves received on the ground 400 km away from the transmitting station under different ionospheric reflections. Then, the numerical prediction results are post processed based on the fast Fourier transform/inverse fast Fourier transform (FFT/IFFT) spectrum division, multiple signal classification (MUSIC) and estimating signal parameters via ratational invariance techniques (ESPRIT) algorithm respectively, and the time delays of different modes (ground wave, one hop sky wave, two hop sky wave, three hop sky wave and four hop sky wave) are decoupled. Finally, the time delay estimation results of multi-hop sky-wave without noise, SNR= −5 dB and SNR= −10 dB are compared. The results show that the higher the number of wave hops, the worse the detection ability of the three algorithms. In the case of weak noise (SNR=0 dB) and strong ionospheric reflection (channels considered in the study), the result accuracy of FFT/IFFT algorithm is the highest, and the delay error is no more than 400 ns, while in the case of strong noise (SNR= −10 dB) and weak ionospheric reflection, ESPRIT algorithm has the best stability and the error is within 5 μs.