复数域最小二乘平差模型的理论与方法研究

The traditional survey observations are real numbers,so adjustments are mainly dealt in the real space. However, recently more and more observations expressed in complex form appear, such as correlation parameters from PolInSAR, complex data transformed from real number domain in image edge detection, observations in seismic signal processing and so on. Obviously, the classical survey adjustment theories do not involve such problems which are usually solved by means of some non-adjustment or geometric methods or converted into the real number domain. The disadvantage of such approaches is that we cannot choose an optimal solution under some rule and assess the accuracy of the solution.This project will take the PolSAR data processing of random volume over ground (RVOG) model as an example. The main objective of this project is to investigate: the establishment of complex least squares observation equation（adjustment model）; the selection of the adjustment norm and adjustment parameters with their physical interpretation; the calculation method of the adjustment model and utilization of prior information; the probability distribution and statistical properties of complex random noise; the accuracy assessment of adjustment model; the establishment of a complete set of adjustment model parameter estimation and accuracy assessment system in the complex number domain. Finally, these new algorithms are applied to other fields of geodesy to verify their scientific significance and practical value.

传统的测量观测值都是实数，因此测量平差都是在实数域空间中进行的。而现代测绘领域中出现了一些用复数表示的观测数据，如极化干涉合成孔径雷达观测地表时的复相干系数、图像边缘检测时将实数观测变换到复数域后进行处理的数据、地震信号处理中的观测等。由于经典的测量平差理论没有涉及此类问题，上述复数观测一般是用几何方法或其他一些非平差方法或转换到实数域进行处理，这些处理方法的缺陷就是不能按某种标准选择最优解，并且评价解的质量。本项目将以极化SAR随机体散射模型（RVOG）数据处理为实例，研究复数域观测方程（平差模型）的建立、平差准则和参数的选取及物理解释、平差模型的计算、复数域先验信息的利用及复数随机噪声的概率分布和统计性质、平差模型的精度评定等，建立起一套完整的复数域平差模型的参数估计与精度评价体系，并将其运用到大地测量的其他领域，验证该理论的科学意义和理论价值。

经典测量平差都是在实数域空间中进行的，而现行的很多观测数据都是用复数来表达。但是目前尚缺少完善的复数平差理论。鉴于此，本项目首先系统研究了复数最小二乘平差准则，根据复数观测量特点，提出实部、虚部联合平差及幅度、相位联合平差两种准则。在此基础之上，建立了基于先验信息及后验信息的随机模型。之后，根据平差模型的特点提出了附有自适应限制条件的复数非线性方程解法、线性化法两种方程解算方案，并针对线性化方法中病态问题提出TSVD方法。项目以极化干涉SAR植被参数反演为应用对象，建立了RVoG散射模型的测量平差表达，并成功用于植被参数反演。与传统三阶段方法相比，复数平差法不仅能获取高精度参数估值，且观测估值对观测误差具有更强抵御性。