乘性随机误差模型的粗差剔除，稳健与附有约束的估计理论研究

GNSS/EDM/VLBI baselines, LiDAR and InSAR have clearly shown, both theoretically and practically, that modern geodetic measurements of these types contain both additive and multiplicative random errors. Conventional adjustment theory and methods have been developed under the assumption that random errors are added to the functional mathematical models of measurements. From this point of view, the conventional adjustment theory and methods can no longer be able to meet the theoretical and practical need of processing geodetic measurements that are of multiplicative error nature. Recognizing the fact that almost nothing has ever been done in the geodetic community worldwide, except for some works by this investigator and her collaborators, a lot of work remains to be done in order to further systematically develop adjustment theory and methods for mixed additive and multiplicative random error models. The major purposes of this research project are threefold: (1) We will investigate the effect of outliers on the quantities of geodetic interest in mixed additive and multiplicative error models, analyze the sensitivity of these quantities to potential outliers and construct appropriate statistics to detect and identify outliers; (2) We will design robust estimators for mixed additive and multiplicative error models. More specifically, we will design appropriate reweighting functions to reduce and/or remove the effect of outliers on parameter estimation. We will investigate the applicability of L1 norm to measurements with multiplicative errors and develop solution algorithms to find the L1 norm solution numerically. Robust estimators with a high breakdown point will also be explored. Accuracy formulae up to linear approximation will be derived; and finally, (3) We will investigate (equality- and inequality-)constrained parameter estimation for mixed additive and multiplicative error models, construct the corresponding numerical algorithms to find the optimal solution and derive the accuracy formulae for error analysis.

理论与实践已经表明，以电磁波为载体的观测量具有乘性或者加乘性混合随机误差的特征，传统的测量平差理论与方法已经无法满足乘性或者加乘性混合误差数据处理的需要。本项目针对乘性以及加乘性混合误差模型，进一步深入系统地开展相应的平差理论与方法的研究。重点研究加乘性混合误差模型的粗差处理问题，分析观测值粗差对各有关估计量的影响，推导相应的统计检验量，建立适用于加乘性混合误差观测值的粗差剔除准则。开展大地测量中加乘性混合误差模型的稳健估计理论与方法研究，集中研究以迭代权为基础的偏差改正加权最小二乘稳健估计以及L1范数估计，提出适用于大地测量加乘性混合误差数据处理的稳健估计方法。发展附有等式约束与不等式约束的加乘性混合误差大地测量平差理论与方法，假定大地测量中的观测值服从正态分布，推导不等式约束解的精度评定公式。

基于乘性以及加乘性混合误差模型，开展了大地测量乘性误差模型的新平差理论与方法的研究，系统分析了著名的Tienstra方法的计算复杂性，开展了一些模型中方差分量的极大似然估计不存在问题的研究，集中研究以迭代权为基础的偏差改正加权最小二乘稳健估计以及L1范数估计，提出了一种改进的EIV模型中参数的加权最小二乘估计算法，研究了极高频率（50 Hz）的GNSS单点定位并取得自1923年以来速度和加速度的成功重构，取得突破性成果，提出了一种用于HSI分类的新型不对称卷积转移学习模型，并基于InSAR技术利用多源数据在环境遥感与防灾减灾方面的应用研究开展了深入研究，这些研究取得了一批创新性理论成果，为大地测量乘性误差领域提供了新的理论与方法，在国家重要工程项目中得到应用，为我国环境遥感与防灾减灾领域的应用研究提供了强有力的科学支撑。