互质层析SAR最少航过数量估计方法

于龙龙; 冯东; 王建; 黄晓涛

doi:10.12000/JR22047

互质层析SAR最少航过数量估计方法

DOI: 10.12000/JR22047

国防科技大学电子科学学院长沙 410073

基金项目: 国家自然科学基金(62101562)

详细信息

作者简介:
于龙龙(1988-)，男，宁夏固原人，国防科技大学电子科学学院博士生，研究方向为层析SAR三维成像技术

冯　东(1991-)，男，重庆涪陵人，国防科技大学电子科学学院讲师，主要研究方向为机载SAR三维成像技术

王　建(1981–)，男，湖北宜城人，国防科技大学电子科学学院讲师、博士，主要研究方向为宽带雷达系统与智能信息处理技术

黄晓涛(1972-)，男，湖北武汉人，国防科技大学电子科学学院教授、博士生导师，主要研究方向为雷达成像技术、超宽带雷达成像技术以及阵列信号处理技术等

通讯作者:
黄晓涛 xthuang@nudt.edu.cn

责任主编：仇晓兰 Corresponding Editor: QIU Xiaolan
中图分类号: TN957.52
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出版历程
- 收稿日期: 2022-03-15
- 修回日期: 2022-05-12
- 网络出版日期: 2022-05-29
- 刊出日期: 2022-08-28

Estimation of the Minimum Number of Acquisitions for Coprime Tomographic Synthetic Aperture Radar

College of Electronic Science, National University of Defense Technology, Changsha 410073, China

Funds: The National Natural Science Foundation of China (62101562)

More Information

Corresponding author: HUANG Xiaotao, xthuang@nudt.edu.cn

摘要

摘要: 在层析SAR技术的实际应用中，航过数量通常受高昂成本等因素的限制。互质层析SAR技术通过稀疏分布航过位置、延长基线孔径长度，可以降低所需的航过数量。当采用子空间方法开展互质层析SAR重构处理时，为了获得可靠的层析图，研究最少航过数量估计问题。考虑到子空间方法的重构性能受多个参数的影响，因此航过数量的选择必须综合考虑所有相关参数对重构结果的影响。为此，通过样本特征值分析方式建立子空间方法的可靠性保证条件。根据这个可靠性保证条件，提出了一种估计最少航过数量的方法。与传统的最少航过数量估计方法相比，所提方法的优势在于：同时考虑所有的相关参数，且具有解析的数学描述式。最后，仿真实验证实由所提方法估算的航过数量确实接近最小，且能够保证重构结果可靠。
- 层析合成孔径雷达 /
- 互质阵列 /
- 最少航过数量 /
- 样本协方差矩阵的特征值 /
- 散射点数量估计
Abstract: In the practical application of Tomographic Synthetic Aperture Radar (TomoSAR), the number of acquisitions is usually restricted due to their expensive cost. A coprime TomoSAR technique was proposed to reduce the required number of acquisitions by sparsely distributing acquisitions and elongating baseline aperture. To guarantee a reliable tomogram, this study aims to determine the minimum number of acquisitions for the coprime TomoSAR when adopting a subspace method for performing the tomographic reconstruction. However, the performance of the subspace method depends on multiple parameters. In light of this, the selection of acquisition times has to comprehensively weigh the effects of all these parameters on the reconstruction performance. To this end, a prerequisite for reliable reconstruction is established by quantifying the relationship between the sample eigenvalues and all related parameters. Compared with conventional estimation approaches for the minimum number of acquisitions, the proposed approach has twofold advantages of containing all related parameters and of having a closed-form expression. Finally, the simulation experiments verify that the number of acquisitions estimated by our approach is close to the minimum and can guarantee reconstruction reliability.
- Tomographic Synthetic Aperture Radar (TomoSAR) /
- Coprime array /
- Minimum number of acquisitions /
- Eigenvalues of the sample covariance matrix /
- Scatterer detection

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图 1 互质层析SAR的数据获取几何

Figure 1. The acquisition geometry of the coprime TomoSAR

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图 2 本文提出的最少航过数量估计方法的流程图

Figure 2. The flow chart for the propose approach to estimate the minimum number of acquisitions

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图 3 基于样本特征值检测方法的正确检测概率随航过数量的变化曲线(K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

Figure 3. Successful detection rate varies with the number of acquisitions (K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

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图 4 高度估计的RMSE随航过数量的变化(K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

Figure 4. The RMSE of the height estimation varies with the number of acquisitions (K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

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图 5 基于样本特征值的信号检测方法的正确检测概率随高度间隔的变化曲线(K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

Figure 5. Successful detection rate varies with the height separation (K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

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图 6 高度估计的RMSE随高度间隔的变化曲线(K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

Figure 6. The RMSE of the height estimation varies with the height separation (K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

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图 7 基于样本特征值检测方法的正确检测概率随航过数量的变化曲线(Δh=1 m; L=20；所有散射点信噪比均等于0 dB)

Figure 7. Successful detection rate varies with the number of acquisitions (Δh=1 m; L=20; all the SNRs=0 dB)

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图 8 高度估计的RMSE随航过数量的变化曲线(Δh=1 m; L=20；所有散射点信噪比均等于0 dB)

Figure 8. The RMSE of the height estimation varies with the number of acquisitions (Δh=1 m; L=20; all the SNRs=0 dB)

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图 9 基于样本特征值检测方法的正确检测概率随高度间隔的变化曲线(L=20；所有散射点信噪比均等于0 dB；ρ_h=1 m)

Figure 9. Successful detection rate varies with the height separation (L=20; all the SNRs=0 dB; ρ_h=1 m)

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图 10 高度估计的RMSE随高度间隔的变化曲线(L=20；所有散射点信噪比均等于0 dB；ρ_h=1 m)

Figure 10. The RMSE of the height estimation varies with the height separation (L=20; all the SNRs=0 dB; ρ_h=1 m)

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图 11 最少航过数量与信噪比之间的约束关系(K=2; Δh=1 m; L=10)

Figure 11. The constraint relationship between the minimum number of acquisitions and the SNR (K=2; Δh=1 m; L=10)

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图 12 |<a₁, a₂>|/M随航过数量的变化(d=7.5 m; K=2; Δh=1 m)

Figure 12. |<a₁, a₂>|/M varies with the number of acquisitions (d=7.5 m; K=2; Δh=1 m)

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图 13 高度估计RMSE随航过数量和信噪比的相变图(K=2; Δh=1 m; L=10)

Figure 13. The phase transition of the RMSE as a function of the number of acquisitions and the SNR (K=2; Δh=1 m; L=10)

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图 14 由文献[9]方法设计的均匀层析SAR和互质层析SAR的重构结果[均匀层析SAR (M=16; d=7.5 m; B=112 m)；互质层析SAR (M₁=9, M₂=8; d=1.8 m; B=112 m)]

Figure 14. The reconstruction results from the uniform TomoSAR and the coprime TomoSAR which are designed by Ref. [9] vary with the SNR [the uniform TomoSAR (M=16; d=7.5 m; B=112 m); the coprime TomoSAR (M₁=9, M₂=8; d=1.8 m; B=112 m)]

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图 15 存在基线偏差情况下和理想情况下的正确检测概率(K=2；所有散射点的信噪比均等于0 dB；L=20；ρ_h=1 m)

Figure 15. Successful detection rate calculated from the deviated tracks and the nominal tracks (K=2; all the SNRs=0 dB; L=20; ρ_h=1 m)

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图 16 存在基线偏差情况下和理想情况下的高度估计的RMSE(实验参数的设置与图 15中的参数相等)

Figure 16. RMSE of the height estimation calculated from the deviated tracks and the nominal tracks (the simulation parmeters are seted as the same as in Fig. 15)

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表 1 由本文方法计算得到的最少航过数量和最小航过间隔(K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

Table 1. The minimum number of acquisitions and the minimum inter-acquisition spacing calculated by the proposed approach (K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

视数	均匀层析SAR	互质层析SAR
L=10	M_min=20; d_M=7.0 m	M_min=13;d_M=4.6 m
L=20	M_min=15; d_M=7.3 m	M_min=9; d_M=7.3 m
L=50	M_min=12; d_M=7.0 m	M_min=8; d_M=5.5 m

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表 2 基于样本特征值检测方法所需的最少航过数量的理论估计值和实测估计值(K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

Table 2. The theoretical estimate and the measured estimate of the minimum number of acquisitions in the sense of the sample-eigenvalue-based detection (K=2; SNR₁=0 dB, SNR₂=10 dB; Δh=1 m)

视数	均匀层析SAR		互质层析SAR
视数	理论值	实测值	理论值	实测值
L=10	20	16	13	11
L=20	15	13	9	8
L=50	12	10	8	7

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表 3 基于样本特征值检测方法的实测分辨率(K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

Table 3. The measured tomographic resolution of the sample-eigenvalue-based detection (K=2; SNR₁=0 dB, SNR₂=10 dB; ρ_h=1 m)

实验参数	分辨的实测值(m)	瑞利分辨率(m)
L=10；均匀层析SAR (M_min=20, d_M=7.0 m)	0.73	1.69
L=10；互质层析SAR (M_min=13; d_M=4.6 m)	0.64	1.22
L=20；均匀层析SAR (M_min=15; d_M=7.3 m)	0.73	2.19
L=20；互质层析SAR (M_min=9; d_M=7.3 m)	0.69	1.71
L=50；均匀层析SAR (M_min=12; d_M=7.0 m)	0.70	2.91
L=50；互质层析SAR (M_min=8; d_M=5.5 m)	0.69	2.55

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表 4 本文方法计算所得的最少航过数量和最小航过间隔(Δh=1 m; L=20；所有散射点信噪比均等于0 dB)

Table 4. The minimum number of acquisitions and the minimum inter-acquisition spacing calculated by the proposed approach (Δh=1 m; L=20; all the SNRs=0 dB)

散射点数量	均匀层析SAR	互质层析SAR
K=2	M_min=18; d_M=7.4 m	M_min=10; d_M=6.1 m
K=3	M_min=23; d_M=7.2 m	M_min=10; d_M=7.1 m

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表 5 基于样本特征值检测方法所需的最少航过数量的理论估计值和实测估计值(Δh=1 m; L=20；所有散射点信噪比均等于0 dB)

Table 5. The theoretical estimate and the measured estimate of the minimum number of acquisitions in the sense of the sample-eigenvalue-based detection (Δh=1 m; L=20; all the SNRs=0 dB)

视数	均匀层析SAR		互质层析SAR
视数	理论值	实测值	理论值	实测值
K=2	18	15	10	10
K=3	23	21	10	10

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表 6 基于样本特征值检测方法的实测分辨率(L=20；所有散射点信噪比均等于0 dB；ρ_h=1 m)

Table 6. The measured tomographic resolution of the sample-eigenvalue-based detection (L=20; all the SNRs=0 dB; ρ_h=1 m)

实验参数	分辨的实测值(m)	瑞利分辨率(m)
K=2；均匀层析SAR (M_min=18;d_M=7.4 m)	0.75	1.78
K=2；互质层析SAR (M_min=10; d_M=6.1 m)	0.72	1.47
K=3；均匀层析SAR (M_min=23; d_M=7.2 m)	0.90	1.42
K=3；互质层析SAR (M_min=10; d_M=7.1 m)	0.88	1.26

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