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| 引用本文： | 王乐洋.������С���˽������о�[J].大地测量与地球动力学,2012,32(5):48-52. |
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| 作者姓名： | 王乐洋 |
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| 作者单位： | 东华理工大学测绘工程学院,南昌330013;江西省数字国土重点实验室,抚州344000 |
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| 基金项目： | 国家自然科学基金(41204003);东华理工大学博士科研启动基金(DHBK201113);江西省数字国土重点实验室开放研究基金(DLLJ201207) |
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| 摘 要： | ??????????,??????????С?????????С??????????任???????????????????С?????????????????????С???????????????????С??????????????????С????????????????????С???????????????????????????????????????????????С????????С????????в??λ??????????????????
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| 关 键 词： | ??????С???? ??С???? ???????? ?в? ??λ????? |
RESEARCH ON PROPERTIES OF TOTAL LEAST SQUARES ESTIMATION |
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| Wang Leyang.RESEARCH ON PROPERTIES OF TOTAL LEAST SQUARES ESTIMATION[J].Journal of Geodesy and Geodynamics,2012,32(5):48-52. |
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| Authors: | Wang Leyang |
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| Institution: | Wang Leyang1,2) 1)Faculty of Geomatics,East China Institute of Technology,Nanchang 3300132)Jiangxi Province Key Laboratory for Digital Land,Fuzhou 344000 |
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| Abstract: | Through theory derivation and proof, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation. When the coefficient matrix contains error,the least squares is biased.The total least squares estimation is unbiased. The condition number of the total least squares estimation is bigger than that of the least squares estimation, so the total least squares estimation is more easier to be affected by the data error than the least squares estimation. Through further derivation, the relation of solutions, residuals, unit weight variance estimations between the total least squares and the least squares are given. |
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| Keywords: | total least squares (TLS) least squares (LS) singular value decomposition (SVD) residual unit weight variance |
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