Studia Geophysica et Geodaetica

, Volume 63, Issue 4, pp 485–508 | Cite as

Variance-covariance component estimation for structured errors-in-variables models with cross-covariances

  • Zhipeng LvEmail author
  • Lifen Sui


In this contribution, an iterative algorithm for variance-covariance component estimation based on the structured errors-in-variables (EIV) model is proposed. We introduce the variable projection principle and derive alternative formulae for the structured EIV model by applying Lagrange multipliers, which take the form of a least-squares solution and are easy to implement. Then, least-squares variance component estimation (LS-VCE) is applied to estimate different (co)variance components in a structured EIV model. The proposed algorithm includes the estimation of covariance components, which is not considered in other recently proposed approaches. Finally, the estimability of the (co)variance components of the EIV stochastic model is discussed in detail. The efficacy of the proposed algorithm is demonstrated through two applications: multiple linear regression and auto-regression, on simulated datasets or on a real dataset with some assumptions.


variable projection principle structured total least-squares STLS covariance component estimability analysis 


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We would like to acknowledge useful comments of the Associate Editor, P.J.G. Teunissen, and the anonymous reviewers that improved the presentation of this paper. This research was supported by the National Natural Science Foundation of PR China (Grant Nos 41674016, 41274016 and 41904039).


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© Inst. Geophys. CAS, Prague 2019

Authors and Affiliations

  1. 1.Institute of Surveying and MappingInformation Engineering UniversityZhengzhouChina

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