Details
| Original language | English |
|---|---|
| Article number | 5 |
| Journal | Journal of geodesy |
| Volume | 95 |
| Issue number | 1 |
| Early online date | 23 Dec 2020 |
| Publication status | Published - Jan 2021 |
Abstract
To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).
Keywords
- Bias, Correlations Matérn, Covariance function, Diagonal correlation model, Nonlinear model, Taylor expansion, Terrestrial laser scanner
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Geophysics
- Earth and Planetary Sciences(all)
- Geochemistry and Petrology
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
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In: Journal of geodesy, Vol. 95, No. 1, 5, 01.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements
AU - Kermarrec, Gaël
AU - Lösler, Michael
N1 - Funding Information: This study was supported by the Deutsche Forschungsgemeinschaft under the project KE2453/2-1.
PY - 2021/1
Y1 - 2021/1
N2 - To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).
AB - To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).
KW - Bias
KW - Correlations Matérn
KW - Covariance function
KW - Diagonal correlation model
KW - Nonlinear model
KW - Taylor expansion
KW - Terrestrial laser scanner
UR - http://www.scopus.com/inward/record.url?scp=85098004732&partnerID=8YFLogxK
U2 - 10.1007/s00190-020-01456-7
DO - 10.1007/s00190-020-01456-7
M3 - Article
VL - 95
JO - Journal of geodesy
JF - Journal of geodesy
SN - 0949-7714
IS - 1
M1 - 5
ER -