Browsing by Subject "Hausdorff metric"
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Item Open Access Objective error criterion for evaluation of mapping accuracy based on sensor time-of-flight measurements(2008) Barshan, B.An objective error criterion is proposed for evaluating the accuracy of maps of unknown environments acquired by making range measurements with different sensing modalities and processing them with different techniques. The criterion can also be used for the assessment of goodness of fit of curves or shapes fitted to map points. A demonstrative example from ultrasonic mapping is given based on experimentally acquired time-of-flight measurements and compared with a very accurate laser map, considered as absolute reference. The results of the proposed criterion are compared with the Hausdorff metric and the median error criterion results. The error criterion is sufficiently general and flexible that it can be applied to discrete point maps acquired with other mapping techniques and sensing modalities as well.Item Open Access On convergence of attainability sets for controlled two-scale stochastic linear systems(Society for Industrial and Applied Mathematics, 1997) Kabanov, Y.; Pergamenshchikov, S.A limit of attainability sets is found for a linear two-scale stochastic system for the case when the diffusion coefficient of the fast variable is of order ε1/2. The attainability set is defined as the set of distributions of attainable terminal values of solutions of stochastic differential equations. As a corollary we calculate a limit of the optimal value of the terminal cost in the stochastic Mayer problem.