乘性随机误差模型的最小二乘平差与精度评定

摘要

针对乘性随机误差模型参数估计问题，在现有研究的基础上，应用最小二乘理论，讨论了普通最小二乘、加权最小二乘和偏差改正加权最小二乘3种参数平差方法；导出了这3种基于最小二乘原理的参数平差方法的精度评定公式；给出了观测值平差值与观测值改正数的精度评定公式以及大地测量各有关量间的互协方差矩阵；构造了3种最小二乘平差方法相应的单位权方差估计．数据模拟计算结果表明：偏差改正加权最小二乘适用于乘性误差模型的大地测量数据处理，具有二阶近似无偏性；根据模拟数据计算的3种方法参数估计的单位权中误差分别为1．9648、0．9998和0．9807．%To probe into the parameter estimation in multiplicative error models,three least squares (LS )adjustment methods,i. e. ,the LS method,the weighted LS method and the bias-corrected weighted LS method,in multiplicative error models were discussed based on the existing researches and using the least squares theory. Their accuracy estimation expressions were derived,the parameter estimations and the variance-covariance matrices were obtained,and the variances of unit weight were constructed for the three LS adjustment methods. A simulated example demonstrates that the bias-corrected weighted LS method is optimal and unbiased because in the example the estimations of unit weight variance are respectively 1. 964 8,0. 999 8 and 0. 980 7 to the LS method,the weighted LS method and the bias-corrected weighted LS method.