Unbiased Estimation of Unit Weight Variance by TSVD Regularization

JI Kunpu; SHEN Yunzhong

doi:10.13203/j.whugis20180270

Volume 45 Issue 4

Apr. 2020

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Geomatics and Information Science of Wuhan University > 2020 > 45(4): 626-632. > DOI: 10.13203/j.whugis20180270

JI Kunpu, SHEN Yunzhong. Unbiased Estimation of Unit Weight Variance by TSVD Regularization[J]. Geomatics and Information Science of Wuhan University, 2020, 45(4): 626-632. DOI: 10.13203/j.whugis20180270

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Unbiased Estimation of Unit Weight Variance by TSVD Regularization

JI Kunpu,
SHEN Yunzhong^,

1.
College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China

Funds:

The National Natural Science Foundation of China 41731069

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Author Bio:
JI Kunpu, postgraduate, specializes in geodetic data processing.1575540259@qq.com
Corresponding author:
SHEN Yunzhong, PhD, professor.yzshen@tongji.edu.cn
Received Date: January 12, 2019
Published Date: April 04, 2020

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Abstract

Abstract

The truncated singular value method (TSVD) improves the morbidity of model by truncating small singular values of the ill-posed observational equation matrix and increases the stability and accuracy of the parameter estimation. However, the structure of observation equation has been changed after truncating small singular value, which makes parameter valuation and residual biased, the unit weight variance cannot be calculated by using traditional estimation formula. This paper derives the unbiased formula of unit weight variance for TSVD regularization, and uses the first Fredholm integral equation and ill-posed trilateration network as examples to verify the correctness of the formula.
- ill-conditioned equation,
- truncated singular value decomposition,
- unit weight variance,
- TSVD regularization,
- unbiased estimation

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References

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