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Combining Terrestrial Reference Frames (TRFs) to frames of superior quality (like the ITRF) usually involves homogenisation by an empirical weighting scheme. Different approaches on variance component estimation have been evaluated for this purpose. The statistically rigorous Helmert estimator has been compared with two other methods: the degree of freedom method and a simplified, approximate estimator. Tests have been performed, covering two elementary types of combinations.

Reference Systems --- VLBI --- Geodesy --- SLR --- GPS --- Least Squares Adjustment --- Variance Component Estimation --- ITRF

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In geodesy and geoinformation science, as well as in many other technical disciplines, it is often not possible to directly determine the desired target quantities. Therefore, the unknown parameters must be linked with the measured values by a mathematical model which consists of the functional and the stochastic models. The functional model describes the geometrical–physical relationship between the measurements and the unknown parameters. This relationship is sufficiently well known for most applications. With regard to the stochastic model, two problem domains of fundamental importance arise: 1. How can stochastic models be set up as realistically as possible for the various geodetic observation methods and sensor systems? 2. How can the stochastic information be adequately considered in appropriate least squares adjustment models? Further questions include the interpretation of the stochastic properties of the computed target values with regard to precision and reliability and the use of the results for the detection of outliers in the input data (measurements). In this Special Issue, current research results on these general questions are presented in ten peer-reviewed articles. The basic findings can be applied to all technical scientific fields where measurements are used for the determination of parameters to describe geometric or physical phenomena.

History of engineering & technology --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In geodesy and geoinformation science, as well as in many other technical disciplines, it is often not possible to directly determine the desired target quantities. Therefore, the unknown parameters must be linked with the measured values by a mathematical model which consists of the functional and the stochastic models. The functional model describes the geometrical–physical relationship between the measurements and the unknown parameters. This relationship is sufficiently well known for most applications. With regard to the stochastic model, two problem domains of fundamental importance arise: 1. How can stochastic models be set up as realistically as possible for the various geodetic observation methods and sensor systems? 2. How can the stochastic information be adequately considered in appropriate least squares adjustment models? Further questions include the interpretation of the stochastic properties of the computed target values with regard to precision and reliability and the use of the results for the detection of outliers in the input data (measurements). In this Special Issue, current research results on these general questions are presented in ten peer-reviewed articles. The basic findings can be applied to all technical scientific fields where measurements are used for the determination of parameters to describe geometric or physical phenomena.

History of engineering & technology --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data