低频多跳天波时延估计算法比较

低频天波传播时延的准确预测对其在远程导航授时中的应用潜力挖掘具有重要意义. 为了获得地-电离层波导中低频多跳天波模式的传播时延特性，同时验证典型多径时延估计算法在不同信道环境下的作用性能，文中首先采用时域有限差分(finite-difference time-domain, FDTD)电磁计算方法对不同电离层反射情况下的距发射台400 km处地面接收的低频天地波耦合总场进行正演预测，然后分别基于快速傅里叶变换(fast Fourier transform, FFT)/快速傅里叶逆变换(inverse fast Fourier transform, IFFT)频谱相除、多重信号分类(multiple signal classification, MUSIC)和旋转不变技术信号参数估计(estimating signal parameters via rotational invariance techniques, ESPRIT)三种算法对电磁场数值预测结果进行后处理，解耦得到不同模式（地波、一跳天波、二跳天波、三跳天波及四跳天波）的时延，并在此基础上分析比较了无噪声和信噪比(signal-noise ratio, SNR)为0 dB、?5 dB以及?10 dB情况下三种算法对多跳天波的时延估计结果. 结果表明，波跳次数越高，算法的检测能力越差. 对于文中所模拟的信道条件，在弱噪声（SNR=0 dB）、电离层强反射时，FFT/IFFT算法结果精度最高，时延误差不超过400 ns；而在强噪声（SNR= ?10 dB）、电离层弱反射时，ESPRIT算法稳定性最好，误差范围在5 μs以内.

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.