基于等价观测站的稳健估计研究毕业设计论文.doc

重庆大学本科学生毕业设计（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 Graduation Design (Thesis) of Robust estimation research based on equivalent observations Undergraduate: Supervisor: Major: June 2014  摘 要 测量数据存在着粗差，而经典最小二乘平差对粗差稳健独立同分布（iid）然而测量中的各个观测值。目前的是基于等价方差-协方差阵的仍在一定程度上有缺陷。本文提出了等价观测值，调整平差模型，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性和可行性。 方差- ABSTRACT As we know, measured data necessarily has error, but the classical least squares theory has’t resistant to it. Thus, many academics proposed a series of robust estim- ation methods based on the theory of robust estimation in Statistics 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 samples 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 calls 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：robust estimation, equivalent weight, equivalent variance-covariance, equivalent observation 目 录 摘 要 3 ABSTRACT 4 1绪论 7 1.1课题产生背景 7 1.2课题主要内容 7 1.3实现途径 8 2稳健估计