整体最小二乘求解线性模型的改进算法

基金项目: 国家国土资源部国土资源大调查资助项目(1212010914015)

详细信息

An Improved Algorithm of Total Least Squares for Linear Models

¹School of Geodesy and Geomatics,Wuhan University,129 Luyou Road,Wuhan 430079,China;²Hazard Monitoring and Prevention Research Center,Wuhan University,129 Luyou Road,Wuhan 430079,China

Funds: 国家国土资源部国土资源大调查资助项目(1212010914015)

摘要: 针对观测方程中观测向量和数据矩阵均有误差的情况,提出了整体最小二乘的改进算法,利用附有限制条件的平差模型,导出了观测向量和数据矩阵精度不等情况下的计算公式。该算法满足拟合方程应有的条件,提高了整体最小二乘递推算法的逼近精度,为整体最小二乘应用于测量数据处理提供了可行的方法。
- 数据矩阵 /
- 附有限制条件的平差模型 /
- 整体最小二乘递推算法
Abstract: Aiming at the condition that among observation equations there are errors in both observation vector and structure matrix,we propose an improved algorithm of total least squares(TLS).Meanwhile,when observation vector and structure matrix are with unequal precision,we deduce the calculation formula using an adjustment model with constraints.Analysis and calculation show that the algorithm that improves approximation accuracy of recursive TLS effectively,can satisfy the conditions needed by fitting equation.
- structure matrix /
- adjustment model with constraints /
- TLS iterative solution