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Matrix Strengthening the Identification of Observations with Split Functional Models in the Squared Msplit(q) Estimation Process
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Matrix Strengthening the Identification of Observations with Split Functional Models in the Squared Msplit(q) Estimation Process
PublicationThis article addresses the issue of raising the level of identification of observations with either single or more split functional models in the squared Msplit(q) estimation process. The theoretical part of the study presents the theoretical grounds for the classical method for estimating parameters in a split functional model and proposes a modification of the computational algorithm to increase the quality of the determinations...
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ESPRIT
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The circle object detection with the use of Msplit estimation
PublicationThe paper presents the use of Msplit(q) - estimation in the filtration and aggregation of point clouds containing a known number of elliptical shapes with preliminary unknown - locations and dimensions. These theoretical solutions may have practical relevance especially in the modelling of terrestrial laser scanning data of objects that have similar shape to circles. Mentioned shapes can be scanned of tree trunks, columns, gutters,...
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Estimators of covariance matrices in Msplit(q) estimation
PublicationThis paper proposes methods for the determination of covariance matrices of Msplit(q) estimators. The solutions presented here allow Msplit(q) estimation to be supplemented by the operations from the domain of accuracy analysis (especially that concerning estimators of parameters). Theoretical forms of covariance matrices of Msplit(q) estimators were established using the empirical influence functions and the equivalent covariance...
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Empirical analyses of robustness of the square Msplit estimation
PublicationThe paper presents Msplit estimation as an alternative to methods in the class of robust M-estimation. The analysis conducted showed that Msplit estimation is highly efficient in the identification of observations encumbered by gross errors, especially those of small or moderate values. The classical methods of robust estimation provide then unsatisfactory results. Msplit estimation also shows high robustness to single gross errors...
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On-line ranking of split graphs
PublicationA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Esprit créateur
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Identification of Unstable Reference Points and Estimation of Displacements Using Squared Msplit Estimation
PublicationThe article presents a new version of the method for estimating parameters in a split functional model, which enables the determination of displacements of geodetic network points with constrained datum. The main aim of the study is to present theoretical foundations of Msplit CD estimation and its basic properties and possible applications. Particular attention was paid to the efficacy of the method in the context of geodetic...
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The Use of Free Adjustment and Msplit-Estimation for Determination of the Vertical Displacements in Unstable Reference System
PublicationThe problem of the determining of the displacements of engineering objects and their surroundings is the current and important issue in the field of engineering geodesy. Most control measurements are made in relation to reference points (stable points). On the other hand, sometimes it happens that it is not possible perform the measurements with reference to the stable points or identification of stable points is difficult. Therefore,...