太极计划中的星间测距地面电子学验证 -

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太极计划中的星间测距地面电子学验证

doi:10.37188/CO.2022-0041

邓汝杰^{1, 2, 3,},
张艺斌^{1, 2, 3,},
刘河山^3,,
罗子人^{1, 3,,}

1.
国科大杭州高等研究院, 浙江杭州 310024
2.
中国科学院大学, 北京 100049
3.
中国科学院力学研究所, 北京 100190

基金项目:国家重点研发计划资助：“引力波探测”重点专项（No. 2020YFC2200104）

详细信息

作者简介:
邓汝杰（1998—），男，广东东莞人，硕士研究生，现就读于国科大杭州高等研究院，主要从事引力波探测星间测距方面的研究。E-mail:dengrujie20@mails.ucas.ac.cn
张艺斌（2000—）,男，甘肃天水人，硕士研究生，现就读于国科大杭州高等研究院，主要从事引力波探测星间通信方面的研究。E-mail：zhangyibin201@mails.ucas.ac.cn
刘河山（1988—），男，安徽阜阳人，博士，副研究员，2015年于中国科学院大学获得博士学位，现为中国科学院力学研究所副研究员。研究领域涉及干涉测距、高精度相位测量、精密指向控制、锁相等。E-mail：liuheshan@imech.ac.cn
罗子人（1980—），男，湖南长沙人，博士，研究员，2010年于中国科学院数学与系统科学研究院获得理学博士学位，现为中国科学院力学研究所研究员。太极计划首席科学家助理，主要从事引力波探测的空间干涉测距技术的理论分析和方案设计方面的研究。E-mail：luoziren@imech.ac.cn

中图分类号:P228.5
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出版历程
- 收稿日期:2022-03-10
- 修回日期:2022-04-06
- 网络出版日期:2022-06-20

Ground electronics verification of inter-satellites laser ranging in the Taiji program

DENG Ru-jie^{1, 2, 3,},
ZHANG Yi-bin^{1, 2, 3,},
LIU He-shan^3,,
LUO Zi-ren^{1, 3,,}

1.
Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Funds:Supported by the National Key Research and Development Program (No. 2020YFC2200104)

More Information

Corresponding author:luoziren@imech.ac.cn

摘要

摘要:
在空间引力波探测太极计划中，干涉测距系统是获取引力波信号的直接手段，为了消除频率不稳定性对其的影响，需利用时间延迟干涉技术降低噪声的干扰。时间延迟干涉是一种数据后处理方法，要实现该技术的数据构型，需对卫星臂长实现精确的绝对距离测量。本文从太极计划的需求分析出发，分别从信源编码设计、延迟环设计以及数据处理算法等方面介绍测距系统的设计方案。在信源编码中，文章通过分析m序列、gold序列、Weil码三种伪随机码的自、互相关性优劣以及长度选取上的灵活性，最终选择了Weil码并筛选出其自相关性最优的移位-截取组合，将其作为测距系统所用的伪随机码。同时，基于该测距系统，搭建了一套地面电子学验证实验装置，以模拟信号传输的物理过程并验证系统性能。实验主体装置采用一块基于Xilinx公司K7芯片的自研FPGA板卡用以模拟卫星通信测距过程以及实现锁相环、延迟环等功能。实验将24.4 kbps的16位信息码与1.5625 Mbps的1024位Weil码进行BPSK调制，采样频率为50 MHz，通过10~60 m的射频同轴电缆进行传输后，使用质心法对采集数据进行优化，随后测定该距离。实验结果表明：在60 m范围内，测距精度优于1.6 m。实验证明了测距系统原理及设计的可行性，为下一步的光学系统验证奠定了技术基础。
- 空间引力波探测/
- 绝对距离测量/
- 伪随机码调制
Abstract:
In the Taiji program, laser interferometry is utilized to detect the tiny displacement produced by the gravitational wave signals. Due to the large-scale unequal arm, the laser frequency noise is the largest noise budget in the space interferometer system. To reduce the influence of laser frequency noise, a technology called the Time Delay Interferometry (TDI) is utilized to deal with it. The TDI is a kind of data post-processing method, which forms the new data stream by the method of the time delay to initial data. But the premise of TDI needs to obtain accurate absolute arm length between satellites. Thus, for that requirement, we discuss the ranging system scheme and implement a ground electronics verification experiment. The ranging system is based on Direct Sequence Spread Spectrum (DS/SS) modulation, and it mainly includes three parts, which are the signal structure, a Delay Locked Loop (DLL), and a data processing algorithm. In DS/SS modulation, types of pseudo-random code can make a difference to the quality of correlation and the ranging accuracy. Therefore, to design the optimal pseudo-random code, we compare the correlation and flexibility in choosing lengths of the m sequence, gold sequence, and Weil code. Weil code that has a shift-cutoff combination with the best autocorrelation is chosen as the ranging code. The ground electronics verification experiment is set up for simulating the physical process of signal transmission and verifying system performance. The main device of the experiment is a FPGA card based on the K7 chip from Xilinx, which is used to simulate the function of communication and ranging between satellites. Meanwhile, we change the length of the Radio Frequency (RF) coaxial cable to correspond to different ranges. The experimental process can be summarized as follows. Firstly, 16-bit data at 24.4 kbps and 1024-bit Weil code at 1.5625 Mbps are modulated with Binary Phase Shift Keying (BPSK) in the 50 MHz sampling frequency. Then the signal is transmitted through RF coaxial cables of 10 to 60 m in length. In receiving end, the signal is consolidated by DLL and the ranging information is collected. To measure the range accurately, we use a centroid method to optimize the collected data. The results show that the ranging accuracy is better than 1.6 m within 60 m. In conclusion, this experiment proves the principle of the scheme and its feasibility, laying a technical foundation for optical system verification in the future.
- space gravitational wave detection/
- absolute ranging measurement/
- pseudorandom modulation

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图 1星间绝对距离测量与通信原理图

Figure 1.Principle diagram of the inter-satellites absolute ranging and laser communication system

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图 2测距通信系统结构示意图

Figure 2.Schematic diagram of the ranging and communication system

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图 3信号结构设计

Figure 3.Design of the signal structure

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图 4最优移位-截取点的Weil码自相关图像

Figure 4.The autocorrelation figure of Weil codes in the optimal shift-cutoff combination

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图 5捕获结构示意图

Figure 5.Schematic diagram of the acquisition structure

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图 6跟踪结构示意图

Figure 6.Schematic diagram of the tracking structure

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图 7延迟、超前路的相关值对比

Figure 7.The comparison of the correlation value between delay and ahead signals

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图 8不完全对称的相关峰

Figure 8.Asymmetric correlation peak

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图 9实验流程

Figure 9.Experiment flow chat

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图 10实验装置

Figure 10.Experimental equipment

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图 11不同长度射频线的实验结果。（a）10 m；（b）12 m；（c）20 m；（d）30 m；（e）50 m；（f）60 m

Figure 11.Experiment results with different length cables. (a) 10 m; (b) 12 m; (c) 20 m; (d) 30 m; (e) 50 m; (f) 60 m

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表 1伪随机码自相关性对比

Table 1.Autocorrelation comparison of pseudorandom codes

伪随机码	处理（取最优）	码长	最大自相关旁瓣绝对值	dB值
m序列（本原多项式系数2011）	无	1023	0.000977	−120.39
m序列（本原多项式系数2011）	遍历插1或0	1024	0.0469	−86.782
gold序列（本原多项式系数2011、 2157）	无	1023	0.06354	−84.136
	遍历插1	1024	0.082	−81.929
	遍历插0	1024	0.0859	−81.526
Weil码	无	1031	0.0611	−84.544
Weil码	遍历截取7位	1024	0.0625	−84.288

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表 2实验结果附表

Table 2.Attached table of experimental results

真实值/m	实验平均值/m	均方差（测距精度）/m
10	9.03	0.86
12	11.13	1.21
20	19.24	1.24
30	30.18	1.59
50	50.14	1.35
60	61.23	1.26

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表 3相关峰移动点数在50 MHz采样频率下对应的距离

Table 3.Distances corresponding to the number of shifts of the correlation peak at the 50 MHz sampling frequency

相关峰移动点数	光速时对应距离/m	70%光速对应距离/m
1	6	4.2
2	12	8.4
3	18	12.6
4	24	16.8
5	30	21.0
6	36	25.2
7	42	29.4
…	…	…
12	72	50.4
14	84	58.8

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