摘要
针对测量数据处理中存在的病态问题,该文提出采用共轭梯度方法求解病态总体最小二乘问题。利用Tikhonov正则化的思想构造目标函数,将总体最小二乘问题转化为无约束最优化问题,然后利用共轭梯度法进行求解,避免了过程中的矩阵求逆运算。通过模拟数值算例表明了该方法在解决病态总体最小二乘问题中的有效性,并分析比较了该方法同正则化总体最小二乘方法之间的差异。
To solve the ill-posed problem in surveying data processing,the conjunction gradient method（CGM）was proposed in this paper.In the ill-conditioned situation,the objective function was structured by Tikhonov regularization;the total least squares（TLS）problem was solved as unconstrained optimization problem in the field of numerical analysis.Then,the conjunction gradient method was used to estimate the parameters and the matrix inversion was avoided.Finally,the effectiveness of the proposed method was testified and the differences comparing with the regularized TLS were demonstrated by the numerical examples.
出处
《测绘科学》
CSCD
北大核心
2018年第2期95-100,113,共7页
Science of Surveying and Mapping
基金
国家自然科学基金项目(41664001
41204003)
江西省杰出青年人才资助计划项目(20162BCB23050)
测绘地理信息公益性行业科研专项(201512026)
国家重点研发计划项目(2016YFB0501405)
江西省教育厅科技项目(GJJ150595)
