Journal ArticleDOI
On the sensitivity of the results of least-squares adjustments concerning the stochastic model
TLDR
In this article, the sensitivity of some characteristic results of least-squares adjustments such as the estimated values of the parameters and their variance-covariance matrix due to imminent uncertainties of the stochastic model is discussed in detail.Abstract:
A proper perturbation theory of a mathematical model and the quantities derived by means of least-squares adjustments is indispensable if the results have to be interpreted in a wider context. The sensitivity of some characteristic results of least-squares adjustments such as the estimated values of the parameters and their variance–covariance matrix due to imminent uncertainties of the stochastic model is discussed in detail. Linearizations are used with rigorous error measures and interval mathematics. Numerical examples conclude the investigations.read more
Citations
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Journal ArticleDOI
Impact of temporal correlations on GPS-derived relative point positions
TL;DR: The sensitivity and reliability of GPS positioning over long baselines when temporal correlations are modelled with the aid of a correlation function are discussed and exemplary results are given to illustrate the effects on position and accuracy of GPS stations.
Journal ArticleDOI
On the Mátern covariance family: a proposal for modeling temporal correlations based on turbulence theory
Gaël Kermarrec,Steffen Schön +1 more
TL;DR: In this paper, a new model for temporal correlations of GPS phase measurements based on turbulence theory is proposed that overcomes this issue and the obtained model belongs to the Matern covariance family with a smoothness of 5/6 as well as a correlation time between 125-175 s.
National Report of the Federal Republic of Germany on the Geodetic Activities in the years 1995-1999
TL;DR: A major role played the monitoring of environmental effects on both the instruments and the gravity signal in this paper, and a network for geodynamical studies and for environmental hazard prevention were set up in several projects within and outside of Germany.
Journal ArticleDOI
Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix
Gaël Kermarrec,Steffen Schön +1 more
TL;DR: In this article, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented, which can be seen as a reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix.
Journal ArticleDOI
A priori fully populated covariance matrices in least-squares adjustment—case study: GPS relative positioning
Gaël Kermarrec,Steffen Schön +1 more
TL;DR: In this paper, the effect of apriori fully populated variance covariance matrices (VCM) in the Gauss-Markov model, by varying both the smoothness and the correlation length of the covariance function, is analyzed.
References
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Book
Introduction to Interval Computation
TL;DR: In this paper, the authors present an ALGOLGOL-based approach for the inclusion of complex Zeros of polynomials of a function of one real variable in a system of linear systems of equations.
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Interval methods for systems of equations
TL;DR: In this paper, the authors describe the basic properties of interval arithmetic and the solution of square linear systems of equations, and the Hull computation of nonlinear systems of equation 6, 7, 8.
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Applied Linear Algebra
TL;DR: In this article, the authors introduce geometric vectors and vector spaces, as well as linear transformations and matrix algebras, for solving equations and finding inverses in matrix algebra.
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Sensitivity analysis in linear systems
TL;DR: In this article, the problem of estimating error bounds in linear programming has been studied in the context of circuit theory interpretation of sensitivity analysis, and an alternative bound for the Moore-Penrose inverse has been proposed.