核函数约束的S模式信号脉冲结构简化及TOA精确度研究

宫峰勋; 刘焘

doi:10.13700/j.bh.1001-5965.2024.0204

核函数约束的S模式信号脉冲结构简化及TOA精确度研究

doi: 10.13700/j.bh.1001-5965.2024.0204

宫峰勋^,,
刘焘

中国民航大学电子信息与自动化学院，天津 300300

基金项目:

国家重点研发计划(2018YFC0809500)

详细信息

通讯作者:
E-mail：fxgong@cauc.edu.cn

中图分类号: V351.3；TN851
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出版历程
- 收稿日期: 2024-04-11
- 录用日期: 2024-07-26
- 网络出版日期: 2024-09-09
- 整期出版日期: 2026-06-30

Simplified S-mode signal pulse structure with kernel function constraints and TOA accuracy study

GONG Fengxun^,,
LIU Tao

School of Electronic Information and Automation，Civil Aviation University of China，Tianjin 300300，China

Funds:

National Key Research and Development Program of China (2018YFC0809500)

More Information

Corresponding author: E-mail：fxgong@cauc.edu.cn

摘要

摘要:
民航S模式应答信号空时结构复杂，易受到传输链路非线性影响和临近电磁干扰，严重影响到达时间(TOA)高精确提取。在民航S模式应答信号空时结构与频谱分析基础上，提出S模式信号脉冲结构简化的准S模式信号模型，根据准S模式信号、弱非线性系统特性反演约束的核函数，构建简化Volterra级数模型。仿真结果表明，基于准S模式信号的简化Volterra级数模型的核函数收益倍数不低于27倍。采用3阶简化Volterra级数模型与高次频点频谱补偿组合方式，对实测信噪比约为13 dB的受干扰S模式信号的准S模式信号进行恢复，实现了用约8.8%的准S模式信号模型的计算量得到约1.54%波形恢复误差，且恢复信号比受干扰信号提取TOA的准确度提升超过73%。基于核函数约束的准S模式信号简化Volterra级数模型，对民航S模式应答信号TOA的准确估计、定位精确度提升具有重要理论价值。
- 核函数 /
- 准S模式信号 /
- 简化Volterra级数 /
- 频谱补偿 /
- 到达时间 /
- 多点定位
Abstract:
The very accurate time-of-arrival (TOA) extraction is significantly impacted by the complicated space-time structure of the civil aviation S-mode transponder signal, which is also vulnerable to neighboring electromagnetic interference and transmission link nonlinearities. Based on the air-time structure and spectral analysis of the civil aviation S-mode transponder signal, a quasi-S-mode signal definition model is proposed to simplify the pulse structure of the S-mode signal, and a simplified Volterra level model is constructed based on the quasi-S-mode signal, the kernel function of the inversion constraints of the weak nonlinear system characteristics. Simulation results show that the kernel function gain multiplier of the simplified Volterra level model based on the quasi-S-mode signal is not less than 27 times. Finally, the quasi-S-mode recovery of an interfered S-mode signal with a measured signal-to-noise ratio of about 13 dB is achieved by using a combination of the 3rd-order simplified Volterra level model and spectral compensation at high sub-frequency points, and the waveform recovery error of about 1.54% is obtained with the computation of about 8.8% of the standard S-mode signal model. Additionally, the accuracy of the recovered signal is improved by more than 73% over the TOA extracted from the disturbed signal. Consequently, the reduced Volterra level model of quasi-S-mode signal based on kernel function constraints has significant theoretical significance for improving localization accuracy and accurately estimating the arrival time of S-mode signals in civil aviation.
- kernel function /
- quasi S-mode signal /
- simplified Volterra series /
- spectrum compensation /
- time-of-arrival /
- multilateration

HTML全文

图 1 S模式基带信号及简化前导脉冲波形结构

Figure 1. S-mode baseband signal and simplified leading pulse waveform structure

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图 2 前导脉冲频谱比较

Figure 2. Leading pulse spectrum comparison

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图 3 准S模式输入的弱非线性系统建模流程

Figure 3. Modeling process for weakly nonlinear systems with quasi-S mode inputs

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图 4 准正弦信号输入时3阶核函数H(n₁,n₂,3)

Figure 4. 3rd order kernel function H(n₁,n₂,3) for quasi-sin signal inputs

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图 5 准S模式信号输入时3阶核函数H(p₁, p₂, 20/7)

Figure 5. 3rd order kernel function H(p₁, p₂, 20/7) for quasi-S-mode signal inputs

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图 6 串联电路的输入与输出信号频谱

Figure 6. Spectrum of input and output signals of series circuits

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图 7 仿真系统输出信号的核收益

Figure 7. Nuclear gain of output signal of simulation system

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图 8 仿真系统各频点输出误差

Figure 8. Output error at each frequency point of simulation system

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图 9 简化Volterra级数误差补偿项长度的影响

Figure 9. Effect of length of simplities Volterra series error compensation term

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图 10 准S模式信号脉冲的输入与输出波形

Figure 10. Input and output waveforms of quasi-S mode signal pulse

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图 11 模型恢复波形与失真前输入信号波形

Figure 11. Model recovery and pre-distortion input signal waveform

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图 12 门限法提取信号TOA原理

Figure 12. Principle of signal TOA extraction by threshold method

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图 13 带噪声模型性能

Figure 13. Model performance with noise

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图 14 带宽和上升沿过渡时间对于恢复波形误差的影响

Figure 14. Influence of bandwidth and rising edge transition time on waveform recovery error

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图 15 实测S模式基带信号波形及处理参数

Figure 15. Measured S-mode baseband signal waveform and processing parameters

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表 1 传统Volterra级数模型所需核函数总数

Table 1. Total number of kernel functions required for traditional Volterra series model

建模参数		输入信号	核函数数目
阶数	带宽/MHz	输入信号	核函数数目
3	10	S模式信号	12340
3	10	准S模式信号	1329
3	20	S模式信号	91800
3	20	准S模式信号	8435
8	10	S模式信号	3.77×10⁸
8	10	准S模式信号	1.56×10⁶
8	20	S模式信号	6.42×10¹⁰
8	20	准S模式信号	1.45×10⁸

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表 2 简化Volterra级数模型所需核函数总数

Table 2. Total number of kernel functions required to simplify Volterra series model

建模参数		输入信号	核函数数目
阶数	带宽/MHz	输入信号	核函数数目
3	10	准正弦信号	56
		准S模式信号	213
		S模式信号	983
3	20	准正弦信号	116
		准S模式信号	498
		S模式信号	5679

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表 3 模型参数

Table 3. Model parameters

模型	阶数	带宽/ MHz	补偿项个数	样本数	运算时间/s	误差率/%
简化Volterra 级数模型	3	10	0	300	0.343	0.31
简化Volterra 级数结合高次频点频谱补偿组合模型	3	10	42	300	0.436	0.15

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表 4 恢复前后波形TOA误差比较

Table 4. Comparison of TOA error in waveforms before and after restoration

波形	ΔT/ns
失真后波形	36
S模式信号	9
准S模式信号	8

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表 5 模型恢复信号的TOA误差比较

Table 5. Comparison of TOA error in model recovery signals

模型	ΔT/ns
模型	10 MHz带宽	无限制带宽
失真后信号	34	42
简化Volterra级数模型恢复信号	3	11
简化Volterra级数结合高次频点频谱补偿组合模型恢复信号	2	10

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