摘要
针对总体最小二乘估计准则在直线拟合应用中存在的问题,该文在分析当前多种直线拟合模型及相应总体最小二乘估计方法的基础上,提出了附约束的N维直线概括模型及其总体最小二乘分步解法。首先利用间接平差方法通过迭代计算求出总体残差,然后通过条件平差分配残差到各观测量。仿真计算结果验证了该模型及方法的正确性和有效性。
Aiming at application issue of total least squares（TLS）estimation criteria and methods in straight line fittings,on the basis of multiple straight line fitting models and corresponding TLS estimation methods,ageneral model of multidimensional straight line with constraints was proposed in this paper.Based on the general model and classical TLS method,the estimation of parameters and the corresponding covariance matrix was given.First,the total residual error of observations in the coefficient matrix was estimated using classical adjustment method of indirect observations.Then,the total residual error was distributed to each observation applying classical adjustment with conditions.The simulation results of planar straight line testified the validity and effeteness of the general straight line model and estimation method.
出处
《测绘科学》
CSCD
北大核心
2015年第12期55-58,共4页
Science of Surveying and Mapping
基金
国家自然科学基金青年项目(41204011)
大地测量与地球动力学国家重点实验室开放基金项目(SKLGED2014-3-2-E)
关键词
总体最小二乘
N维直线拟合
概括模型
约束条件
total least squares
multidimensional straight line fitting
general model
constraints
