低频多跳天波时延估计算法比较

穆中林; 王桥桥; 周丽丽; 胡欣悦; 何立风

doi:10.12265/j.cjors.2021262

低频多跳天波时延估计算法比较

doi: 10.12265/j.cjors.2021262

穆中林¹,
王桥桥²,
周丽丽^{2, 3, ,},
胡欣悦³,
何立风³

1.
空军工程大学航空工程学院, 西安 710038
2.
陕西科技大学电气与控制工程学院, 西安 710021
3.
陕西科技大学电子信息与人工智能学院, 西安 710021

基金项目: 国家自然科学基金(62171265)

详细信息

作者简介:
穆中林：(1981—)，男，江苏人，空军工程大学航空工程学院讲师，博士，研究方向为航空火力指挥与控制、作战效能评估

王桥桥：(1995—)，女，陕西人，陕西科技大学电气与控制工程学院硕士研究生，研究方向为控制工程

周丽丽：(1981—)，女，江苏人，陕西科技大学电子信息与人工智能学院副教授，博士，研究方向为电波传播理论、电磁场数值计算

通讯作者:
周丽丽 E-mail: zhoulili@sust.edu.cn

中图分类号: TN957
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-22
- 录用日期: 2022-01-05
- 网络出版日期: 2022-01-05

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

1.
Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China
2.
School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China
3.
School of Electronic Information and Artificial Intelligence, Shaanxi University of Science & Technology, Xi’an 710021, China

摘要

摘要: 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.
- 低频天波 /
- FDTD /
- 时延估计 /
- FFT/IFFT频谱相除算法 /
- MUSIC算法 /
- ESPRIT算法
Abstract: 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.
- low-frequency sky wave /
- FDTD /
- time delay estimation /
- FFT/IFFT spectrum division algorithm /
- MUSIC algorithm /
- ESPRIT algorithm

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图 1 距发射台400 km处三种传输信道中接收到的耦合电场脉冲

Fig. 1 Coupled electric field pulses received in different transmission channels 400 km from the transmitter

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图 2 基于FFT/IFFT频谱相除算法对三种传输信道中不同模式波的时延估计（无噪声）

Fig. 2 Time delay estimation of different mode waves in different transmission channels based on FFT/IFFT spectral division algorithm (noiseless)

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图 3 基于FFT/IFFT频谱相除算法对三种传输信道中不同模式波的时延估计（SNR= −10 dB）

Fig. 3 Time delay estimation of different mode waves in different transmission channels based on FFT/IFFT spectral division algorithm (SNR= −10 dB)

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图 4 基于MUSIC算法对三种传输信道中不同模式波的时延估计（无噪声）

Fig. 4 Time delay estimation of different mode waves in different transmission channels based on MUSIC algorithm (noiseless)

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图 5 基于MUSIC算法对三种传输信道中不同模式波的时延估计（SNR= −10 dB）

Fig. 5 Time delay estimation of different mode waves in different transmission channels based on MUSIC algorithm (SNR= −10 dB)

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表 1 不同加噪条件下基于三种算法估计得到的多跳天波时延结果

Tab. 1 Time delay results of multi-hop sky waves estimated by three algorithms under different noise conditions

模型	信道类型	算法	$ {\tau _1} $/μs	$ \Delta {\tau _1} $/μs	$ {\tau _2} $/μs	$ \Delta {\tau _2} $/μs	$ {\tau _3} $/μs	$ \Delta {\tau _3} $/μs	$ {\tau _4} $/μs	$ \Delta {\tau _4} $/μs
1	无噪声	FFT/IFFT	1392.476	0.000	1555.391	0.000	1794.323	0.000	2083.150	0.000
		MUSIC	1397.400	4.924	1555.200	−0.191	1793.900	−0.423	2082.500	−0.650
		ESPRIT	1393.904	1.428	1555.676	0.285	1790.767	−3.556	2087.914	4.764
	SNR=0 dB	FFT/IFFT	1392.476	0.000	1555.391	0.000	1794.386	0.063	2082.838	−0.312
		MUSIC	1398.100	5.624	1554.600	−0.791	1792.600	−1.723	2078.500	−4.650
		ESPRIT	1392.500	0.024	1555.234	−0.157	1791.910	−2.413	2088.500	5.350
	SNR= −5 dB	FFT/IFFT	1392.476	0.000	1545.451	−9.940	1794.261	−0.062	2092.822	9.672
		MUSIC	1395.700	3.224	1553.200	−2.191	1792.600	−1.723	2084.200	1.050
		ESPRIT	1394.408	1.932	1553.298	−2.093	1793.900	−0.423	2087.543	4.393
	SNR= −10 dB	FFT/IFFT	1392.602	0.126	1564.830	9.439	1804.576	10.253	-	-
		MUSIC	1394.400	1.924	1565.000	9.609	1790.800	−3.523	-	-
		ESPRIT	1393.954	1.478	1555.496	0.105	1790.797	−3.526	-	-
2	无噪声	FFT/IFFT	1394.103	0.000	1557.079	0.000	-	-	-	-
		MUSIC	1394.000	−0.103	-	-	-	-	-	-
		ESPRIT	1393.724	−0.379	-	-	-	-	-	-
	SNR=0 dB	FFT/IFFT	1388.225	−5.878	-	-	-	-	-	-
		MUSIC	1393.700	−0.403	-	-	-	-	-	-
		ESPRIT	1394.002	−0.101	-	-	-	-	-	-
	SNR= −5 dB	FFT/IFFT	1398.103	4.000	-	-	-	-	-	-
		MUSIC	1395.300	1.197	-	-	-	-	-	-
		ESPRIT	1396.467	2.364	-	-	-	-	-	-
	SNR= −10 dB	FFT/IFFT	1398.352	4.249	-	-	-	-	-	-
		MUSIC	1392.900	−1.203	-	-	-	-	-	-
		ESPRIT	1394.334	0.231	-	-	-	-	-	-
3	无噪声	FFT/IFFT	1389.726	0.000	1545.201	0.000	1774.631	0.000	2053.074	0.000
		MUSIC	1394.700	4.974	1545.200	−0.001	1775.200	0.569	2051.200	−1.874
		ESPRIT	1393.904	4.178	1545.618	0.417	1774.732	0.101	2052.902	−0.172
	SNR=0 dB	FFT/IFFT	1389.663	−0.063	1545.138	−0.063	1774.631	0.000	2053.448	0.374
		MUSIC	1395.500	5.774	1545.500	0.299	1774.300	−0.331	2048.700	−4.374
		ESPRIT	1392.125	2.399	1545.421	0.220	1773.603	−1.028	2051.078	−1.996
	SNR= −5 dB	FFT/IFFT	1389.663	−0.063	1545.263	0.062	1774.691	0.060	2062.808	9.734
		MUSIC	1392.300	2.574	1544.900	−0.301	1775.200	0.569	2063.300	10.226
		ESPRIT	1394.705	4.979	1546.001	0.800	1774.622	−0.009	2055.072	1.998
	SNR= −10 dB	FFT/IFFT	1389.601	−0.125	1544.888	−0.313	1784.508	9.877	2034.167	−19.907
		MUSIC	1388.000	−1.726	1540.200	−5.001	1778.000	3.369	-	-
		ESPRIT	1393.726	4.000	1540.201	−5.000	1776.632	2.001	-	-

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