测量平差双光滑参数解算半参数模型的研究  

Solution method of semi-parametric model by adding double-smoothing parameters

作　　者：张俊[1,2] 独知行[1] 张显云[2] 

机构地区：[1]山东科技大学测绘科学与工程学院,山东青岛266510 [2]贵州大学矿业学院,贵阳550025

出　　处：《测绘科学》2014年第5期96-98,60,共4页Science of Surveying and Mapping

基　　金：教育部博士点基金项目(20103718110003);国家自然科学基金项目(41274006);贵州省自然科学基金项目(黔科合J字[2009]2264)

摘　　要：半参数模型解算的补偿最小二乘法用于测量平差,是基于残差带权平方和与系统误差补偿项之间的平衡关系而提出的,这种平衡是通过光滑参数来实现的。光滑参数一般利用特定方法在正实数中选取,范围较大。本文尝试在极小化过程中,将残差和补偿项两部分同时赋予光滑参数,给出了此种情况下的半参数模型的解及简单的统计性质。为保证残差和补偿项的平衡关系,解算时,要求两部分光滑参数之和等于1,且光滑参数在不大于1的正数中选取,这样大大缩小了光滑参数的选择范围。模拟算例证明了这种方法的可行性。The penalized least squares method with semi-parametric model using for surveying adjustment is based on the principle of the balance between the weighted sum-squared residual errors and systematic errors,and this balance is achieved by attaching a smoothing parameter to the penalized part,which needs to be selected from the positive real numbers.A method that adds smoothing parameters both to the residual errors and systemic errors at the same time was put forward and the formula and statistical properties of estimates were given in the paper.To ensure the balance of the two parts,the sum of smoothing parameters of two parts were requested to be equal to 1,and the smoothing parameters scale must be restricted to between 0and 1,which would greatly reduce the smoothing parameter selection range.The simulated examples demonstrated the feasibility of the method.

关 键 词：半参数模型 补偿最小二乘 光滑参数 双光滑参数 

分 类 号：P207.2[天文地球—测绘科学与技术]