Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Boris Kargoll
  • Alexander Dorndorf
  • Mohammad Omidalizarandi
  • Jens-André Paffenholz
  • Hamza Alkhatib

Research Organisations

External Research Organisations

  • Anhalt University of Applied Sciences
  • Clausthal University of Technology
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Details

Original languageEnglish
Pages (from-to)243-267
Number of pages25
JournalJournal of Applied Geodesy
Volume15
Issue number3
Early online date11 May 2021
Publication statusPublished - 27 Jul 2021

Abstract

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.

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

Cite this

Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors. / Kargoll, Boris; Dorndorf, Alexander; Omidalizarandi, Mohammad et al.
In: Journal of Applied Geodesy, Vol. 15, No. 3, 27.07.2021, p. 243-267.

Research output: Contribution to journal › Article › Research › peer review

Kargoll, B, Dorndorf, A, Omidalizarandi, M, Paffenholz, J-A & Alkhatib, H 2021, 'Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors', Journal of Applied Geodesy, vol. 15, no. 3, pp. 243-267. https://doi.org/10.1515/jag-2021-0013
Kargoll, B., Dorndorf, A., Omidalizarandi, M., Paffenholz, J.-A., & Alkhatib, H. (2021). Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors. Journal of Applied Geodesy, 15(3), 243-267. https://doi.org/10.1515/jag-2021-0013
Kargoll B, Dorndorf A, Omidalizarandi M, Paffenholz JA, Alkhatib H. Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors. Journal of Applied Geodesy. 2021 Jul 27;15(3):243-267. Epub 2021 May 11. doi: 10.1515/jag-2021-0013
Kargoll, Boris ; Dorndorf, Alexander ; Omidalizarandi, Mohammad et al. / Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors. In: Journal of Applied Geodesy. 2021 ; Vol. 15, No. 3. pp. 243-267.
Download
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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".

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