数据采集与处理Issue(4)：802-809,8.DOI:10.16337/j.1004-9037.2015.04.011
混合总体最小二乘的迭代解算算法
Iterative Algorithm for Mixed LS-TLS Estimation
摘要
Abstract
The total least squares (TLS) approximation estimates a parameter matrix from a linear model considering errors in both the observation vector L and the data matrix A .The TLS theory is more rigor‐ous than the standard least squares .If some columns of A can be known exactly ,the problem is defined as the mixed least squares—TLS problem .An iterative algorithm is derived to solve the LS‐TLS problem by using the principle of indirect adjustment .Compared with the method based on singular‐value decom‐position(SVD) QR decompositon ,the iterative algorithm coincides with the SVD algorithm .The calcu‐lated example proves that the iterative algorithm is valid and rational .关键词
混合总体最小二乘/奇异值分解/迭代算法/测量平差Key words
LS-TLS/singular-value decomposition (SVD)/iterative algorithm/surveying adjustment分类
天文与地球科学引用本文复制引用
鲁铁定,周世健,王乐洋..混合总体最小二乘的迭代解算算法[J].数据采集与处理,2015,(4):802-809,8.基金项目
国家自然科学基金（41464001，41204003，41374007，41161069）资助项目；江西省自然科学基金（20132BAB216004）资助项目；地球空间环境与大地测量教育部重点实验室开放基金（100106）资助项目；江西省教育厅科研规划重点（GJJ10022）资助项目；江西省科技落地计划（KJLD12077）资助项目；江西省教育厅科技（GJJ13457，GJJ13456）资助项目；中国博士后基金（94773）资助项目；江西省中青年教师发展计划访问学者专项（赣财指2012－132）资助项目；江西科协远航工程资助项目。 （）
