TY - JOUR

T1 - The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations

T2 - A proposal to account for correlations in least squares adjustment

AU - Kermarrec, Gael

AU - Neumann, Ingo

AU - Alkhatib, Hamza

AU - Schon, Steffen

N1 - Funding Information: The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Maria Letizia Corradini under the direction of Editor André L. Tits. The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development is gratefully acknowledged. The authors would like to thank their colleague Markus Reichhartinger for several valuable literature references and discussions regarding this contribution.

PY - 2019/4/26

Y1 - 2019/4/26

N2 - The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance-covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment.

AB - The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance-covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment.

KW - correlation model

KW - GNSS

KW - stochastic model

KW - terrestrial laser scanner

KW - variance model

UR - http://www.scopus.com/inward/record.url?scp=85060671846&partnerID=8YFLogxK

U2 - 10.1515/jag-2018-0019

DO - 10.1515/jag-2018-0019

M3 - Article

AN - SCOPUS:85060671846

VL - 13

SP - 93

EP - 104

JO - Journal of Applied Geodesy

JF - Journal of Applied Geodesy

SN - 1862-9016

IS - 2

ER -