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《Science of Surveying and Mapping》 2008-03

## An algorithm for least-square collocation by singular value decomposition

LU Tie-ding①②,NING Jin-sheng①,ZHOU Shi-jian②③,ZANG De-yan②(①School of Geodesy and Geomatics,Wuhan university,Wuhan 430079,China;②School of Geological Science and Surveying Engineering,East China Institute of Technology,Fuzhou 344000,China;3Jiangxi Academy of Sciences,Nanchang 330029,China)
Least Square Collocation is the mathematics method that is initially used to study the earth shape and gravity field together with the various gravity data.At present,Least Square Collocation has been widely applied in surveying data processing.Based on the analysis of the algorithm of least square collocation and discussion of the matrix singular value decomposition(SVD),the relationshi Pbetween SVD decomposition and Moore-Penrose generalized inverse is deduced.Then the calculation formulaes of Least Square Collocation and Moore-Penrose generalized inverse based on SVD decomposition are provided.Finally practical computations of the gravity anomaly have shown that the SVD method is correct and validity in Least-Square collocation calculation.From this new collocation algorithm in this paper,the special function of matrix decomposition in surveying data processing,as well as the relationshi Pbetween matrix decomposition and adjustment,are found out.
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