Details
| Original language | English |
|---|---|
| Pages (from-to) | 93-104 |
| Number of pages | 12 |
| Journal | Journal of Applied Geodesy |
| Volume | 13 |
| Issue number | 2 |
| Early online date | 24 Jan 2019 |
| Publication status | Published - 26 Apr 2019 |
Abstract
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.
Keywords
- correlation model, GNSS, stochastic model, terrestrial laser scanner, variance model
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Earth and Planetary Sciences(all)
- Earth and Planetary Sciences (miscellaneous)
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In: Journal of Applied Geodesy, Vol. 13, No. 2, 26.04.2019, p. 93-104.
Research output: Contribution to journal › Article › Research › peer review
}
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 -