分布式散射体相位估计奇异值分解法

doi:10.11947/j.AGCS.2024.20230017

摘要/Abstract

摘要：

常规的分布式散射体（DS）相位估计方法需要生成全组合干涉对以构建样本协方差矩阵（SCM），然后根据SCM的统计特性估计DS相位，这一过程不但计算耗时，而且占据大量存储空间。本文提出了一种基于奇异值分解技术的DS相位快速估计方法（SVDI）。该方法分析的对象是单主影像干涉对组成的干涉相位矩阵而非全组合干涉对组成的SCM，因而可以有效提高计算效率、节省存储空间。并且，理论上证明了在一定条件下SVDI的结果与常规的特征值分解方法（EVD）是一致的。模拟数据和真实SAR数据的结果表明，SVDI算法有更高的计算效率，并且其相位估计精度以及形变解算精度与常规算法是一致的。

关键词: 分布式散射体, 相位估计, 样本协方差矩阵, 特征值分解, 奇异值分解

Abstract:

The covariance matrix is the basis for estimating the phase of distributed scatterer (DS) when using conventional algorithm. Therefore, a full combination of SAR data should be generated firstly to construct the sample covariance matrix (SCM). However, this process is not only computationally expensive but also consumes a large amount of storage space. In this paper, a fast algorithm, referred to as SVDI (SVD to interferometric phase matrix), for estimating the phase of DS based on singular value decomposition is proposed. SVDI estimates the phase of DS from the interferometric phase matrix constructed by single-master interferograms rather than the SCM constructed by multi-master interferograms (i.e., the full combination of SAR data). Therefore, SVDI can effectively improve the computationally efficient and save the storage space. Moreover, it is theoretically proved that the results of SVDI are consistent with the conventional eigenvalue decomposition (EVD) method based on an assumption. The simulated and real SAR data is used to verify the feasibility and reliability of SVDI. The experimental results show that the phase and deformation estimation accuracy of SVDI is consistent with that of the conventional method.

Key words: distributed scatterer, phase estimation, sample covariance matrix, eigen value decomposition, singular value decomposition

中图分类号:

P258

祝传广, 张继贤, 龙四春, 杨容华, 吴文豪, 张立亚. 分布式散射体相位估计奇异值分解法[J]. 测绘学报, 2024, 53(7): 1308-1320.

Chuanguang ZHU, Jixian ZHANG, Sichun LONG, Ronghua YANG, Wenhao WU, Liya ZHANG. Phase estimation of distributed scatterer based on singular value decomposition[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(7): 1308-1320.

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组	γ₀	γ_∞	τ/d
1	0.60	0.00	50
2	0.60	0.20	50
3	0.60	0.05	180

项目	参数
试验区	章丘	休斯敦
数据集	Sentinel-1A	Sentinel-1A
Path	142	143
Subswath	IW3	IW2
日期	2017-07—2022-11	2017-01—2020-12
数据量	157	119
轨道模式	Ascending	Descending
入射角/（°）	43.8	39.2
航向角/（°）	-13.2	-167.3

点名	最大互差/mm	互差绝对值小于2 mm的比例/（%）	标准差/mm
Z1	3.2	99.987	0.5
Z2	2.0	100	0.3
Z3	0.2	100	0.1
Z4	0.3	100	0.1
Z5	2.5	99.994	0.5
H1	0.8	100	0.1
H2	0.1	100	0.0
H3	0.1	100	0.0
H4	0.1	100	0.0
H5	0.9	100	0.2