Increase of exactness of observation of ship at the surplus measuring
Journal Title: Автоматизация судовых технических средств - Year 2018, Vol 1, Issue 24
Abstract
The analysis of statistical these errors of the navigation measuring, got last thirty years in the model supervisions, showed that errors did not submit to the normal law of distributing, and the histograms of their selections are contained by surplus members in extreme digits, that testifies to the positive excess of law of distributing. Therefore as alternative the models of the mixed laws of distributing of errors were offered to the normal law, for which characteristic positive excess. For providing of maximally possible exactness of observations of place of ship it is necessary to know the law of distributing of errors of the navigation measuring. However at the limited sample size of statistical materials of errors it is not succeeded by standard procedure to define the law of their distributing, although is present possibility to estimate the central moments of distributing. Thus if the histogram of selection has a positive excess, it is possible to use decomposition of closeness of distributing of errors by the ortogonal polynomials of Ermyt, indisposing its by analytical expression, and to apply him as the closeness of distributing. The analysis of the considered works shows that the variety of laws of probability distribution of casual sizes, the feature of which there is the presence of positive excess, can be compatible by the use of ortogonal decomposition with the got values of central moments of higher orders. Decomposition of normal closeness of the rationed error in a row Gramme - Sharl'e type A by the orthogonal polynomials of Ermyt is a classic result, however for the standard closeness of law of Gauss of the unrationed error in work the coefficients of row are certain Gramme - Sharl'e type A, and proved the ortogonal polynomials of Ermyt. The got result allows to offer the universal method of description of closeness of distributing of the unrationed casual size by its decomposition in a row Gramme - Sharl'e type A, that provides maximal exactness of observation of place of ship at the unknown law of distributing of errors of measuring, having a positive excess.
Authors and Affiliations
Igor Vorokhobin
Keywords
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