Details
| Original language | English |
|---|---|
| Pages (from-to) | 243-267 |
| Number of pages | 25 |
| Journal | Journal of Applied Geodesy |
| Volume | 15 |
| Issue number | 3 |
| Early online date | 11 May 2021 |
| Publication status | Published - 27 Jul 2021 |
Abstract
Keywords
- Gauss-Helmert model, Gauss-Markov model, accelerometer time series, auto-correlations, cross-correlations, expectation maximization algorithm, iteratively reweighted least squares, multivariate t-distribution, vector-autoregressive model
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Earth and Planetary Sciences(all)
- Earth and Planetary Sciences (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Applied Geodesy, Vol. 15, No. 3, 27.07.2021, p. 243-267.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors
AU - Kargoll, Boris
AU - Dorndorf, Alexander
AU - Omidalizarandi, Mohammad
AU - Paffenholz, Jens-André
AU - Alkhatib, Hamza
N1 - Funding Information: Este trabajo se desarroll? en el marco del proyecto Fondecyt 11110246 "Etnicidad y procesos translocales en espacios de frontera".
PY - 2021/7/27
Y1 - 2021/7/27
N2 - In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.
AB - In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.
KW - Gauss-Helmert model
KW - Gauss-Markov model
KW - accelerometer time series
KW - auto-correlations
KW - cross-correlations
KW - expectation maximization algorithm
KW - iteratively reweighted least squares
KW - multivariate t-distribution
KW - vector-autoregressive model
UR - http://www.scopus.com/inward/record.url?scp=85106384939&partnerID=8YFLogxK
U2 - 10.1515/jag-2021-0013
DO - 10.1515/jag-2021-0013
M3 - Article
VL - 15
SP - 243
EP - 267
JO - Journal of Applied Geodesy
JF - Journal of Applied Geodesy
SN - 1862-9016
IS - 3
ER -