多维InSAR复协方差矩阵估计研究

Multivariate covariance matrix is fundamental for the full exploitation of InSAR capabilities and widely applied in data processing. However, the present studies focus more on parameter estimation of the single element in covariance matrix without consideration of complex statistical inference. Conversely, these methods try to mitigate the source of errors at the cost of the increase of constraints. As a result, it is usually difficult to achieve the satisfied results in the real world when the assumptions are broken. .To solve the problem aforementioned, this project dedicates to multivariate covariance matrix estimation in the field of complex numbers under MT-InSAR framework. Instead of parameter estimation for any element in covariance matrix, we implement statistical inference to sample covariance matrix according to the full properties of complex vector. More concretely, under a multi-dimensional zero mean complex (circular) Gaussian population, the intensity observable is first refined by the locally linear minimum mean-squared error estimator, and then the sample coherence is estimated from (complex) Jacknife statistics and second kind statistics respectively, according to the scenes applied. Finally, the interferometric phase is optimized under complex Wishart distribution by maximizing the likelihood function. All estimators mentioned above are based on i.i.d. complex sample which will be obtained by statistically homogeneous pixel selection algorithm proposed in this study..The methodology developed in the project will significantly improve the accuracy of InSAR parameter estimation and simultaneously preserving the resolution of the image particularly over rich texture areas. Moreover, less computational burden can be expected compared with the existing methods. .The technology to be developed will be very useful to monitor natural hazards over complicated scenes with larger extent where the region of interest is woven into an intricate tapestry. The research proposed in the project is therefore of both significant scientific and practical values.

多维复协方差矩阵是时序InSAR技术的基本观测量，广泛应用于InSAR数据处理。现有研究工作大多从实数域的观点出发对矩阵中某一类参数进行估计，没有顾及复数的统计性质，而是以增加约束条件为代价抑制观测误差。上述现象在目前流行的算法和软件中普遍存在，使得对于用户指定的问题，算法可执行性参差不齐，往往难以得到有益的监测结果。为解决这些问题，本课题创新性地将现代统计学方法与InSAR数据特点相结合，在时序InSAR技术框架下，研究一整套多维复协方差矩阵估计理论与优化方法。该方法不以矩阵中某一类参数为研究对象，取而代之地估计样本复协方差矩阵，即根据样本复协方差的统计属性发展估计量、构建统计模型，并顾及复数数据的内在联系，进而达到矩阵全信息量、全参数优化的目的。研发的算法将兼顾运算效率和估计精度，因而适合大范围复杂场景的对地观测，为准确的分析与反演地表变化背后的潜在机理提供有力的科学依据。

多维复协方差矩阵是时序InSAR技术的基本观测量，广泛应用于InSAR数据处理。现有研究工作大多从实数域的观点出发对矩阵中某一类参数进行估计，没有顾及复数的统计性质，而是以增加约束条件为代价抑制观测误差。上述现象在目前流行的算法和软件中普遍存在，使得对于用户指定的问题，算法可执行性参差不齐，往往难以得到有益的监测结果。为解决这些问题，该项目主要利用数理统计中的判决理论和估计理论，削弱统计样本异质性对时序InSAR复协方差矩阵估计的影响，通过快速选择独立同分布样本改善复协方差矩阵的估计精度并兼顾InSAR观测量（包括强度、相干性和相位）的空间分辨率。运用项目研发的理论方法对场景分类和形变监测两个专题开展了测试，论证了InSAR\SAR技术的应用依赖多维复协方差估计的可靠性。.围绕这些研究，培养该方向研究生5名，完成高水平学术论文16篇，申请专利10项，其中授权3项。项目负责人将多维InSAR复协方差估计的理论、方法和模型进行总结，向全球发布了DSIpro开源软件，并公布了源代码，供国内外学界评判，也为地学科研人员提供高质量InSAR数据源，这对于应用大地测量前沿的SAR/InSAR技术对全球进行高精度测图具有现实意义。