Journal of Geodesy

, Volume 93, Issue 6, pp 911–925 | Cite as

M-estimation using unbiased median variance estimate

  • Ling Yang
  • Yunzhong ShenEmail author
  • Bofeng Li
Original Article


This paper first proves that the traditional median variance estimate is biased when the sample number is small and then proposes an unbiased median variance estimate to calibrate for the bias of the variance estimate. The scaled median variance estimate is firstly derived, and the unbiased median variance estimate is formed with independent residuals in an adjustment model no matter whether the measurements are contaminated by outliers or not. Using the unbiased median variance estimate, the M-estimate is constructed to mitigate for the biases caused by the variance estimate. The IGGIII reduction factor is used to verify the proposed algorithms by a levelling network example. Numerical analysis confirms that the proposed median variance estimate can achieve better unbiasedness for contaminated measurement set, but the dispersion of our estimate is unfortunately larger than that for the least-squares estimate.


M-estimation Unbiased median variance estimate Finite sample size IGGIII 



The authors are grateful to Prof. Chris Rizos for his very helpful revision on the draft of this paper. This work is sponsored by the National Key R&D Program of China (2017YFA0603103) and National Natural Science Foundation of China (41731069, 41504022).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Surveying and Geo-informaticsTongji UniversityShanghaiChina

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