1、 1 本科学生毕业设计（论文） 基于等价观测值的稳健估计研究 学 生： 学 号： 指导教师： 专 业： 大学学院 二 O 一四年六月 2 Graduation Design (Thesis) of Robust estimation research based on equivalent observations Undergraduate: Supervisor: Major: June 2014 3 摘 要 测量数据可能存在着粗差，而经典最小二乘平差方法对粗差敏感，为了减弱 粗差的影响，许多学者基于统计学中稳健估计的理论，提出了各种稳健估计方法。 注意到，经典的稳健估计理论是基于独立同分
2、布（iid）样本，然而测量中的各个 观测值常常是相关的。适用于独立样本的理论和方法，推广到相关观测，不可避 免会遇到困难。目前流行的是基于等价权的方法和基于等价方差-协方差阵的稳健 估计方法。但这些方法仍在一定程度上有缺陷。 本文提出了等价观测值的概念，基于经典的稳健估计理论，通过严密的数学 变换，调整相关观测条件下的平差模型，建立了一种全新的稳健最小二乘估计理 论，使不等价权函数最终在形式上又回归到等价权函数的严密数学运算中，避免 了测量界与数学界间的不一致性。并且，这一理论还将通过具体算例，与基于等 价方差-协方差阵的稳健最小二乘估计理论在思想、模型和精度方面进行比较，从 而严格证明其正确
3、性和可行性。 关键词：稳健最小二乘估计，等价权，等价方差-协方差，等价观测值 重庆大学本科学生毕业设计（论文） 英文摘要 4 ABSTRACT As we know, measured data necessarily has error, but the classical least squares theory hast resistant to it. Thus, many academics proposed a series of robust estim- ation methods based on the theory of robust estimation in Stat
4、istics to weaken the influence of gross error. Attention, classical robust estimation theory based on inde- pendent identical distribution, but the observations are not completely independent of each other and often have some correlation. So, the theory and method being suitable for independent samp
5、les will inevitably encounter difficulties to extend to correlated observations. Currently, robust estimation based on equivalent weight and robust estimation based on equivalent variance- covariance matrix is popular. However, they still have some defect. This thesis proposes a new theory which cal
6、ls equivalent observation. We adjust the classical adjustment models to structure a new robust estimation based on classical robust estimation theory by strict mathematical transform, which avoids inconsistency between math and survey. Besides, the theory will be compared with the robust estimation based on variance-covariance by concrete example in theory, model and accuracy to strictly prove its rightness and feasibility. Key words：ro
