Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (4): 115-125.doi: 10.16088/j.issn.1001-6600.2021091402

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Principal Component Liu Estimation Method of the Equation    Constrained Ⅲ-Conditioned Least Squares

WENG Ye1, SHAO Desheng1,2*, GAN Shu1,3   

  1. 1. Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming Yunnan 650093, China;
    2. Yunnan Earthquake Agency, Kunming Yunnan 650041, China;
    3. Plateau Mountain Spatial Information SurveyTechnique Application Engineering Research Center at Yunnan Province’s University, Kunming Yunnan 650093, China
  • Published:2022-08-05

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Abstract: For the parameter estimation of the Ⅲ-conditioned adjustment problem, reasonable equality prior information among parameters helps to improve the accuracy of the model solution. The joint calculation is carried out under the sample information and the prior information of the equation. Based on the morbid least squares adjustment criterion, a new biased estimation algorithm, principal component Liu estimation, is constructed through the principal component estimation and Liu estimation. The parameter solution of theprincipal component Liu estimation with equality constrained least squares is derived, and the formula of correction factor is derived by using the principle of mean square error minimization. The effectiveness and reliability of the proposed method are verified by an example, which can be applied to the problem of solving Ⅲ-conditioned least squares parameters with equality constraints.

Key words: equation prior information, principal component estimation, Liu estimation, principal component Liu estimate, correction factor

CLC Number: 

  • O212
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