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| 引用本文： | 王乐洋.??????С????????????[J].大地测量与地球动力学,2013,33(1):40-44. |
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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： | ??????????????????????????????????????????????????????????????????????????????????????????????????μ???С???????????С????????????????????????С??????????????????????????????????????????????С???????????????????????????????????С??????????????????С???????????С????????????????????????????
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| 关 键 词： | ??????С???? ??С???? ??????С???? ??????? ?????? |
RESEARCH ON PERTURBATION ANALYSIS OF THE TOTAL LEAST SQUARES |
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| Wang Leyang.RESEARCH ON PERTURBATION ANALYSIS OF THE TOTAL LEAST SQUARES[J].Journal of Geodesy and Geodynamics,2013,33(1):40-44. |
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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: | On the basis of the condition number definition of coefficient matrix and from the viewpoint of numerical analysis, the perturbation analysis equations of least squares (LS) and data least squares (DLS) are deduced, in following cases when the perturbation is only contained in the observation data, the perturbations are contained in the observation data and coefficient matrix, and the perturbation is only contained in the coefficient matrix. On the basis of the closed form expression of the total least squares (TLS) solution and with the tool of the singular value decomposition (SVD), the perturbation analysis equation of TLS is deduced. Through the analysis, the perturbation analysis equation of TLS is the unified form of the perturbation analysis equation of LS and DLS. |
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| Keywords: | total least squares (TLS) least squares (LS) data least squares (DLS) perturbation analysis condition number |
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