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Karl-Rudolf Koch 《Studia Geophysica et Geodaetica》2017,61(1):1-18
Minimal Detectable Biases (MDBs) or Minimal Detectable Outliers for the Expectation Maximization (EM) algorithm based on the variance-inflation and the mean-shift model are determined for an example. A Monte Carlo method is applied with no outlier and with one, two and three randomly chosen outliers. The outliers introduced are recovered and the corresponding MDBs are almost independent from the number of outliers. The results are compared to the MDB derived earlier by the author. This MDB approximately agrees with the MDB for one outlier of the EM algorithm. The MDBs for two and three outliers are considerably larger than MDBs of the EM algorithm. 相似文献
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A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model. 相似文献
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Karl-Rudolf Koch 《Journal of Geodesy》2014,88(3):263-271
For deriving the robust estimation by the EM (expectation maximization) algorithm for a model, which is more general than the linear model, the nonlinear Gauss Helmert (GH) model is chosen. It contains the errors-in-variables model as a special case. The nonlinear GH model is difficult to handle because of the linearization and the Gauss Newton iterations. Approximate values for the observations have to be introduced for the linearization. Robust estimates by the EM algorithm based on the variance-inflation model and the mean-shift model have been derived for the linear model in case of homoscedasticity. To derive these two EM algorithms for the GH model, different variances are introduced for the observations and the expectations of the measurements defined by the linear model are replaced by the ones of the GH model. The two robust methods are applied to fit by the GH model a polynomial surface of second degree to the measured three-dimensional coordinates of a laser scanner. This results in detecting more outliers than by the linear model. 相似文献
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Karl-Rudolf Koch 《Journal of Geodesy》1975,49(1):35-40
Summary Two methods are discussed for the processing of altimetry data. For the first method it is assumed that the altimetry data,
may be analyzed independent of the orbit computation for the satellite that carries the altimeter. Because of the high accuracy
of the altimetry data, which can only be fully utilized if it is also introduced into the orbit computations, the second method
deals with a simultaneous processing of altimetry data, orbit tracking, and gravity anomalies for the continents. To represent
the gravity field, the potential of a simple layer is chosen whose unknown density is assumed to be constant over surface
elements into which the surface of the earth is divided. Depending on the accuracy and the amount of the altimetry data, the
surface elements for the density values are chosen smaller or larger, so that a very flexible representation of the earth’s
gravity field is obtained. Because of the amount and the resolution of the altimetry data a large number of density values
have to be determined in a least squares adjustment. To facilitate the computations, buffer zones are introduced so that the
large system of normal equations can be broken up into small independent subsystems.
Shortened version of a paper presented to the 14 th International Congress of Surveyors in Washington, Sept. 1974. 相似文献
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