Spelling suggestions: "subject:"robuste abschätzung"" "subject:"robuste ernteschätzung""
1 |
The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshesGrosman, Serguei 01 September 2006 (has links) (PDF)
Singularly perturbed reaction-diffusion problems
exhibit in general solutions with anisotropic
features, e.g. strong boundary and/or interior
layers. This anisotropy is reflected in the
discretization by using meshes with anisotropic
elements. The quality of the numerical solution
rests on the robustness of the a posteriori error
estimator with respect to both the perturbation
parameters of the problem and the anisotropy of the
mesh. The simplest local error estimator from the
implementation point of view is the so-called
hierarchical error estimator. The reliability
proof is usually based on two prerequisites:
the saturation assumption and the strengthened
Cauchy-Schwarz inequality. The proofs of these
facts are extended in the present work for the
case of the singularly perturbed reaction-diffusion
equation and of the meshes with anisotropic elements.
It is shown that the constants in the corresponding
estimates do neither depend on the aspect ratio
of the elements, nor on the perturbation parameters.
Utilizing the above arguments the concluding
reliability proof is provided as well as the
efficiency proof of the estimator, both
independent of the aspect ratio and perturbation
parameters.
|
2 |
Geodätische Fehlerrechnung mit der skalenkontaminierten Normalverteilung / Geodetic Error Calculus by the Scale Contaminated Normal DistributionLehmann, Rüdiger 22 January 2015 (has links) (PDF)
Geodätische Messabweichungen werden oft gut durch Wahrscheinlichkeitsverteilungen beschrieben, die steilgipfliger als die Gaußsche Normalverteilung sind. Das gilt besonders, wenn grobe Messabweichungen nicht völlig ausgeschlossen werden können. Neben einigen in der Geodäsie bisher verwendeten Verteilungen (verallgemeinerte Normalverteilung, Hubers Verteilung) diskutieren wir hier die skalenkontaminierte Normalverteilung, die für die praktische Rechnung einige Vorteile bietet. / Geodetic measurement errors are frequently well described by probability distributions, which are more peak-shaped than the Gaussian normal distribution. This is especially true when gross errors cannot be excluded. Besides some distributions used so far in geodesy (generalized normal distribution, Huber’s distribution) we discuss the scale contaminated normal distribution, which offers some advantages in practical calculations.
|
3 |
The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshesGrosman, Serguei 01 September 2006 (has links)
Singularly perturbed reaction-diffusion problems
exhibit in general solutions with anisotropic
features, e.g. strong boundary and/or interior
layers. This anisotropy is reflected in the
discretization by using meshes with anisotropic
elements. The quality of the numerical solution
rests on the robustness of the a posteriori error
estimator with respect to both the perturbation
parameters of the problem and the anisotropy of the
mesh. The simplest local error estimator from the
implementation point of view is the so-called
hierarchical error estimator. The reliability
proof is usually based on two prerequisites:
the saturation assumption and the strengthened
Cauchy-Schwarz inequality. The proofs of these
facts are extended in the present work for the
case of the singularly perturbed reaction-diffusion
equation and of the meshes with anisotropic elements.
It is shown that the constants in the corresponding
estimates do neither depend on the aspect ratio
of the elements, nor on the perturbation parameters.
Utilizing the above arguments the concluding
reliability proof is provided as well as the
efficiency proof of the estimator, both
independent of the aspect ratio and perturbation
parameters.
|
4 |
Geodätische Fehlerrechnung mit der skalenkontaminierten NormalverteilungLehmann, Rüdiger January 2012 (has links)
Geodätische Messabweichungen werden oft gut durch Wahrscheinlichkeitsverteilungen beschrieben, die steilgipfliger als die Gaußsche Normalverteilung sind. Das gilt besonders, wenn grobe Messabweichungen nicht völlig ausgeschlossen werden können. Neben einigen in der Geodäsie bisher verwendeten Verteilungen (verallgemeinerte Normalverteilung, Hubers Verteilung) diskutieren wir hier die skalenkontaminierte Normalverteilung, die für die praktische Rechnung einige Vorteile bietet. / Geodetic measurement errors are frequently well described by probability distributions, which are more peak-shaped than the Gaussian normal distribution. This is especially true when gross errors cannot be excluded. Besides some distributions used so far in geodesy (generalized normal distribution, Huber’s distribution) we discuss the scale contaminated normal distribution, which offers some advantages in practical calculations.
|
5 |
Adaptive Estimation using Gaussian MixturesPfeifer, Tim 25 October 2023 (has links)
This thesis offers a probabilistic solution to robust estimation using a novel adaptive estimator.
Reliable state estimation is a mandatory prerequisite for autonomous systems interacting with the real world.
The presence of outliers challenges the Gaussian assumption of numerous estimation algorithms, resulting in a potentially skewed estimate that compromises reliability.
Many approaches attempt to mitigate erroneous measurements by using a robust loss function – which often comes with a trade-off between robustness and numerical stability.
The proposed approach is purely probabilistic and enables adaptive large-scale estimation with non-Gaussian error models.
The introduced Adaptive Mixture algorithm combines a nonlinear least squares backend with Gaussian mixtures as the measurement error model.
Factor graphs as graphical representations allow an efficient and flexible application to real-world problems, such as simultaneous localization and mapping or satellite navigation.
The proposed algorithms are constructed using an approximate expectation-maximization approach, which justifies their design probabilistically.
This expectation-maximization is further generalized to enable adaptive estimation with arbitrary probabilistic models.
Evaluating the proposed Adaptive Mixture algorithm in simulated and real-world scenarios demonstrates its versatility and robustness.
A synthetic range-based localization shows that it provides reliable estimation results, even under extreme outlier ratios.
Real-world satellite navigation experiments prove its robustness in harsh urban environments.
The evaluation on indoor simultaneous localization and mapping datasets extends these results to typical robotic use cases.
The proposed adaptive estimator provides robust and reliable estimation under various instances of non-Gaussian measurement errors.
|
6 |
Observation error model selection by information criteria vs. normality testingLehmann, Rüdiger 17 October 2016 (has links) (PDF)
To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test.
|
7 |
Observation error model selection by information criteria vs. normality testingLehmann, Rüdiger January 2015 (has links)
To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test.
|
Page generated in 0.0385 seconds