MAD Estimate of Scale Factor and Its Applications in Measurement Adjustment

GUO Jianfeng

doi:10.13203/j.whugis20190166

Volume 46 Issue 11

Nov. 2021

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Geomatics and Information Science of Wuhan University > 2021 > 46(11): 1636-1640. > DOI: 10.13203/j.whugis20190166

GUO Jianfeng. MAD Estimate of Scale Factor and Its Applications in Measurement Adjustment[J]. Geomatics and Information Science of Wuhan University, 2021, 46(11): 1636-1640. DOI: 10.13203/j.whugis20190166

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MAD Estimate of Scale Factor and Its Applications in Measurement Adjustment

GUO Jianfeng^1,

1.
College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Funds:

The National Natural Science Foundation of China 41674020

The National Natural Science Foundation of China 40874007

the Henan Key Laboratory of Intelligent Public Opinion Analysis

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Author Bio:
GUO Jianfeng, PhD, specializes in geodesy and GNSS data processing. E-mail: jianfeng.guo@gmail.com
Received Date: April 17, 2020
Published Date: November 04, 2021

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Abstract

Abstract

Objectives The least-squares method is very sensitive to outliers, and the adjustment outputs will usually be unacceptable when some of the observations are contaminated. Selection of appropriate statistical tests plays a pivotal role both in robust estimation and conventional outlier detection procedures.
Methods The MAD (median absolute deviation) estimate of scale factor in the univariate case is discussed firstly. Determination of the Fisher-consistency factor is described for Gaussian normal distribution. Robust estimates of scale factor in linear adjustment model are addressed based on standardized least-squares residuals and the uniformly most powerful test statistics, respectively. Both of them can be used for constructing statistical tests, to identify the potential outlying observations, and therefore their deterioration effect will be mitigated. For illustrative purpose, Monte Carlo simulations in GPS network adjustment scenario are performed.
Results Numerical results show that the MAD-based estimate of scale factor is robust and works well in accuracy assessment for adjustment outputs.
Conclusions Explicit formula for estimating the scale factor, the MAD is a very robust scale estimator and has low computation complexity. It is therefore appropriate to use the MAD for adjustment computations and accuracy assessment when outliers are present.
- scale factor,
- outlier detection,
- robust estimation,
- MAD estimate

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