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Sensors 2014, 14(1), 1249-1266; doi:10.3390/s140101249

Adjustment of Measurements with Multiplicative Errors: Error Analysis, Estimates of the Variance of Unit Weight, and Effect on Volume Estimation from LiDAR-Type Digital Elevation Models

1
School of Geomatics, Xi'an University of Science and Technology, Xi'an 710054, China
2
Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan
3
School of Land Science and Geomatics, China University of Geosciences, Beijing 100083, China
4
GNSS Research Center, Wuhan University, Wuhan 430071, China
*
Author to whom correspondence should be addressed.
Received: 3 November 2013 / Revised: 17 December 2013 / Accepted: 24 December 2013 / Published: 10 January 2014
(This article belongs to the Section Remote Sensors)
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Abstract

Modern observation technology has verified that measurement errors can be proportional to the true values of measurements such as GPS, VLBI baselines and LiDAR. Observational models of this type are called multiplicative error models. This paper is to extend the work of Xu and Shimada published in 2000 on multiplicative error models to analytical error analysis of quantities of practical interest and estimates of the variance of unit weight. We analytically derive the variance-covariance matrices of the three least squares (LS) adjustments, the adjusted measurements and the corrections of measurements in multiplicative error models. For quality evaluation, we construct five estimators for the variance of unit weight in association of the three LS adjustment methods. Although LiDAR measurements are contaminated with multiplicative random errors, LiDAR-based digital elevation models (DEM) have been constructed as if they were of additive random errors. We will simulate a model landslide, which is assumed to be surveyed with LiDAR, and investigate the effect of LiDAR-type multiplicative error measurements on DEM construction and its effect on the estimate of landslide mass volume from the constructed DEM.
Keywords: adjustment; multiplicative errors; error analysis; least squares; digital elevation model; landslide; hazard evaluation adjustment; multiplicative errors; error analysis; least squares; digital elevation model; landslide; hazard evaluation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Shi, Y.; Xu, P.; Peng, J.; Shi, C.; Liu, J. Adjustment of Measurements with Multiplicative Errors: Error Analysis, Estimates of the Variance of Unit Weight, and Effect on Volume Estimation from LiDAR-Type Digital Elevation Models. Sensors 2014, 14, 1249-1266.

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