An Efficient Algorithm for Weighted Total Least Squares Method
CSTR:
Author:
Affiliation:

1.College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024;2.State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China;3.Aerial Photogrammetry and Remote Sensing Research Institute Co., Ltd. , Xi’an 710100, China

Clc Number:

P207

Fund Project:

  • Article
  • |
  • Figures
  • |
  • Metrics
  • |
  • Reference
  • |
  • Related
  • |
  • Cited by
  • |
  • Materials
  • |
  • Comments
    Abstract:

    The weighted total least-squares (WTLS) adjustment is a rigorous method for estimating parameters in the errors-in-variables (EIV) model. However, the WTLS are not proper for larger data problem in terms of computational efficiency. Aimed at the structural characteristics of the design matrix in the EIV model,a partially weighted total least-squares (PWTLS) algorithm is proposed based on weighted least-squares (WLS) adjustment by weighting the random column of the design matrix. The PWTLS can obtain an exact solution of the EIV model without applying Lagrange multipliers in a straightforward manner. In addition, the PWTLS reduces the dimensions of the cofactor matrix and does not estimate the random error of the design matrix, as this would greatly improve the computational efficiency. Finally, real and simulated examples are used to demonstrate the accuracy and computational performance of the proposed algorithms . The results show that the PWTLS can obtain the same accuracy as the existing seven improved algorithms, but the computational efficiency is significantly improved .

    Reference
    Related
    Cited by
Get Citation

WANG Jianmin, NI Fuze, ZHAO Jianjun. An Efficient Algorithm for Weighted Total Least Squares Method[J].同济大学学报(自然科学版),2021,49(5):737~744

Copy
Share
Article Metrics
  • Abstract:
  • PDF:
  • HTML:
  • Cited by:
History
  • Received:June 23,2020
  • Revised:
  • Adopted:
  • Online: May 24,2021
  • Published:
Article QR Code