Koreliuotų geodezinių matavimų rezultatų matematinis apdorojimas

Abstract

Pirmų kartų pateiktas problemos, susijusios su tolerancijomis kontroliuojamų matavimo rezultatų apdorojimu, sprendimas. Apibrėžta normatyvinės koreliacijos sųvoka. Gautos formulės matavimo rezultatų klaidų, kontroliuojamų tolerancijomis, pasiskirstymo dėsniui nustatyti, matavimo rezultatų tikslumo kriterijams skaičiuoti. Išnagrinėtas išmatuotų ir išlygintų dydžių tikslumo įvertinimas, atsižvelgiant į tolerancijas. Knyga bus naudinga magistrams, doktorantams, moksliniams darbuotojams, dirbantiems geodezinių matavimo rezultatų apdorojimo srityje.

In this book processing theory and computational procedures of the correlated measurements are presented. At present, during measurements processing the influence of distribution laws of measured quantities towards parameters and accuracy estimation is ignored. Using tolerancies, the errors of functions of measured quantities may be controlled and in the same time this procedure permits to control the quality of measuring information. Tolerancies of function errors of observed quantities are increasing in precision of the actual measurements, also they do influence to the correlation between independently observed quantities. The probability of smoothing and eliminating (filtering) of functional measurement errors does actual effect on the corresponding probability of smoothing errors of observational results. In surveying literature are given formulae that may be applied for estimating the precision either measures or adjusted quantities, but there the influence of tolerancies is ignored. However, under their influence calculated accuracy values for corresponding parameters are gained less than they should be in reality. Therefore in procedures of estimating the accuracy of various quantities and parameters it is necessary to take into consideration this above mentioned aspect. The errors of direct measurements are distributed in accordance with the normal law of distribution. In the case, however, when the tolerancies are in action, then the errors of observations have been submitted according to so called cut-off normal distribution. In the mathematical processing procedures of observations it is necessary to determine correlation between independently measured quantities and consequently to take it into account. The latest correlation appears due to the tolerancies. Consequently the perfection of mathematical processing theory, creation of computation algorithms and softwares when influence of tolerancies is taken into consideration is one of actual problems.