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Article
Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances
Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances ...
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Article
Identity of simultaneous estimates of control points and of their estimates by the lofting method for NURBS surface fitting
For reverse engineering, nonuniform rational B-spline surfaces are fitted to measured coordinates of points. Two methods are often applied. The first one consists of simultaneously estimating the unknown contr...
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Article
Comments on Xu et al. (2006) Variance component estimation in linear inverse ill-posed models, J Geod 80(1):69–81
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Article
Gibbs sampler by sampling-importance-resampling
Among the Markov chain Monte Carlo methods, the Gibbs sampler has the advantage that it samples from the conditional distributions for each unknown parameter, thus decomposing the sample space. In the case the...
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Article
Comments and reply regarding Kotsakis (2005) “A type of biased estimators for linear models with uniformly biased data”
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Article
Determining the maximum degree of harmonic coefficients in geopotential models by Monte Carlo methods
Random errors for the harmonic coefficients of a geopotential model are generated from the matrix of normal equations by a parallel computer applying the Gibbs sampler. This leads to random values for the harm...
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Article
Gibbs sampler for computing and propagating large covariance matrices
The use of sampling-based Monte Carlo methods for the computation and propagation of large covariance matrices in geodetic applications is investigated. In particular, the so-called Gibbs sampler, and its use ...
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Article
Regularization of geopotential determination from satellite data by variance components
Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with ...
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Article
Confidence regions for GPS baselines by Bayesian statistics
The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued, the baseline coordinates, but also integers, the phase ambiguities. The GPS model ther...
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Article
Robust Kalman filter for rank deficient observation models
A robust Kalman filter is derived for rank deficient observation models. The datum for the Kalman filter is introduced at the zero epoch by the choice of a generalized inverse. The robust filter is obtained b...
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Chapter and Conference Paper
Preliminary Results for the Simultaneous Estimation of Geoid Undulations and Sea Surface Topography by Geosat Altimeter Data
Satellite altimeter data contains information about the heights of the geoid above the reference ellipsoid, the geoid undulations, the heights of the sea surface above the geoid, the sea surface topography and...
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Article
Maximum likelihood estimate of variance components
Using the orthogonal complement likehood function, an iterative procedure for the maximum likelihood estimates of the variance and covariance components is derived. It is shown that these estimates are identic...
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Article
Isomerism in parabutylchloral; x-ray crystallographic determinations of 2,4,6-tris(1′,1′,2′-trichloropropyl)-1,3,5-trioxanes
α-Parabutylchloral (2,4,6-tris(1′,1′,2′-trichloropropyl)-1,3,5-trioxane, C12H15Cl9O3) crystallizes in the orthorhombic space groupP212121 (No. 19) witha=12.165(6),b=9.964(5),c=17.433(9) Å,Z=4. The finalR value i...
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Article
Bayesian inference for the derivation of less sensitive hypothesis tests
The matrixt distribution is derived and its properties are shown which are applied for the Bayesian inference in the multivariate linear model. By this approach hypothesis tests for the multivariate model are der...
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Chapter and Conference Paper
First Order Design: Optimization of the Configuration of a Network by Introducing Small Position Changes
Free networks only, i.e. networks for which the datum has to be defined, will be considered in the following. Thus, the property of these networks, especially the dependency of the covariance matrix of the est...
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Article
Deviations from the null hypothesis to be detected by statistical tests
Deviations from the null hypothesis, which can be detected by tests in an univariate model, are derived by means of the expected value of the test criterion. As shown, the boundary of the detectable deviations...
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Article
The geopotential from gravity measurements, levelling data and satellite results
The geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of points at the surface of the continents and the potential of the geoid. These differe...
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Article
Least squares adjustment and collocation
For the estimation of parameters in linear models best linear unbiased estimates are derived in case the parameters are random variables. If their expected values are unknown, the well known formulas of least ...
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Article
Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth
The geodetic boundary value problem using the known surface of the earth is defined and shown to have at most one solution. Furthermore it is proved that the solution exists and that its harmonic part can be r...
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Article
Error study for the determination of the center of mass of the earth from Pageos observations
The least squares adjustment for the station coordinates of the worldwide satellite triangulation net gives, in addition to the station positions, the positions of the satellites observed in a simultaneous eve...
