SHI Yun. Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1033-1037. DOI: 10.13203/j.whugis20130355
Citation:
SHI Yun. Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1033-1037. DOI: 10.13203/j.whugis20130355
SHI Yun. Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1033-1037. DOI: 10.13203/j.whugis20130355
Citation:
SHI Yun. Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1033-1037. DOI: 10.13203/j.whugis20130355
1School of Geomatics,Xi’an University of Science and Technology,Xi’an 710054,China
Funds: The National Naturel Science Foundation of China,No.41204006;the Special Foundation of Education Departmentof Shanxi Provincial Government,China,No.2013JK0960.
Objective Adjustment methods for parameter estionation were basically developed on the basis of addi-tive random error models.With advances in the technology for modern geodetic observation,measure-ment errors can change with functional models such as EDM,GPS and VLBI baselines.Thus,ran-dom errors in measurements are proportional to the true values of the measurements themselves.Ob-servational models of this type are called multiplicative error models.The purpose of this paper is tocomplement or extend the work of Xu and Shimada(2000)to mixed additive and multiplicative errormodels.We briefly discuss three least squares(LS)adjustment methods for parameter estimation inmixed additive and multiplicative error models.In case of the weighted LS adjustment,we explicitlydescribe the biases in the adjusted parameters.Then,we construct a bias-corrected weighted leastsquares estimator.Finally,we demonstrate that the bias-corrected weighted LS method is optimal andunbiased using a simulated example.
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