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  • Cross-correlations  (1)
  • Forward gravity modeling  (1)
  • GPS time series  (1)
  • 1
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    Self-tuning robust adjustment within multivariate regression time series models with vector-autoregressive random errors (2020)
    Springer Berlin Heidelberg
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    Publikationsdatum: 2023-07-03
    Beschreibung: The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN).
    Beschreibung: Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659
    Schlagwort(e): ddc:526 ; Regression time series ; Vector-autoregressive model ; Cross-correlations ; Multivariate scaled t-distribution ; Self-tuning robust estimator ; Generalized expectation maximization algorithm ; Iteratively reweighted least squares ; Multivariate portmanteau test ; Monte Carlo simulation ; GPS time series
    Sprache: Englisch
    Materialart: doc-type:article
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    CITATION GEO-LEO
  • 2
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    Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction (2020)
    Springer Netherlands
    Details
    Publikationsdatum: 2023-06-09
    Beschreibung: We present an accurate method for the calculation of gravitational potential (GP), vector (GV), and gradient tensor (GGT) of a tesseroid, considering a density model in the form of a polynomial up to cubic order along the vertical direction. The method solves volume integral equations for the gravitational effects due to a tesseroid by the Gauss–Legendre quadrature rule. A two-dimensional adaptive subdivision technique, which automatically divides the tesseroids near the computation point into smaller elements, is applied to improve the computational accuracy. For those tesseroids having small vertical dimensions, an extension technique is additionally utilized to ensure acceptable accuracy, in particular for the evaluation of GV and GGT. Numerical experiments based on spherical shell models, for which analytical solutions exist, are implemented to test the accuracy of the method. The results demonstrate that the new method is capable of computing the gravitational effects of the tesseroids with various horizontal and vertical dimensions as well as density models, while the evaluation point can be on the surface of, near the surface of, outside the tesseroid, or even inside it (only suited for GP and GV). Thus, the method is attractive for many geodetic and geophysical applications on regional and global scales, including the computation of atmospheric effects for terrestrial and satellite usage. Finally, we apply this method for computing the topographic effects in the Himalaya region based on a given digital terrain model and the global atmospheric effects on the Earth’s surface by using three polynomial density models which are derived from the US Standard Atmosphere 1976.
    Schlagwort(e): ddc:550.2 ; Forward gravity modeling ; Gauss–Legendre quadrature ; Tesseroids ; Polynomial density model ; Topographic and atmospheric effects
    Sprache: Englisch
    Materialart: doc-type:article
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    CITATION GEO-LEO
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