基于GCV的迭代Tikhonov正则化在测绘中的应用  

Application of Iterative Tikhonov Regularization Based on GCV in Surveying and Mapping

作　　者：邓伟 宋迎春[1] 谢雪梅 DENG Wei;SONG Yingchun;XIE Xuemei(School of Geosciences and Info-Physics,Central South University,932 South-Lushan Road,Changsha 410083,China;School of Civil Engineering,Central South University of Forestry and Technology,498 South-Shaoshan Road,Changsha 410004,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙市410083 [2]中南林业科技大学土木工程学院,长沙市410004

出　　处：《大地测量与地球动力学》2023年第6期587-592,共6页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41674009,41574005)。

摘　　要：由于Tikhonov正则化(Tikhonov regularization,TR)法求解大地测量领域中的病态问题时,其求解质量过于依赖正则化参数的确定,且稳定性较差,因此提出改进的迭代Tikhonov正则化(iterated Tikhonov regularization,ITR)法,结合广义交叉验证法(generalized cross-validation,GCV),可以有效克服上述缺点。算例结果表明,ITR-GCV法在解算精度、稳定性以及抗干扰性方面表现良好。Since the quality of the solution of the Tikhonov regularization(TR)method is too dependent on the determination of the regularization parameters and less stable when solving ill-conditioned problems in the field of geodesy by TR method,an improved iterated Tikhonov regularization(ITR),combined with generalized cross-validation(GCV),can effectively overcome the above shortcomings.The calculation example results show that the ITR-GCV method is better in terms of solution accuracy,stability,and anti-interference.

关 键 词：病态问题 TIKHONOV正则化 迭代Tikhonov正则化 广义交叉准则 

分 类 号：P207[天文地球—测绘科学与技术]