ISSN 0536-101X (print)
ISSN 2618-7299 (online)
+7 (499) 261-82-86
Русская версия
English version

О соотношении точностей линейных и угловых измерений в линейно-угловых сетях

Р.А. Губайдуллина, Ю.Н. Корнилов

Страницы: 145–149

Аннотация. Вопрос о соотношении точности линейных и угловых измерений в различных линейно-угловых геодезических построениях по известным причинам волновал, волнует и будет волновать специалистов. В статье показано, что для ответа на него может быть с успехом использован принцип отношений (подобия). Приведены соответствующие примеры. В ходе данного исследования выяснилось, что в случае, когда точность линейных измерений выше точности угловых, целесообразно вычислять координаты искомой точки по методике, изложенной в работе [1].

Ключевые слова: засечка, однородные элементы, относительная ошибка, теория подобия, точность измерений, трилатерация, триангуляция, intersection, homogeneous elements, measurement accuracy, position resection, relative error, similarity theory, triangulation, trilateration

About comparison of linear and angular measurement accuracy in linear-angulargeodetic networks

R.A. Gubaydullina, Yu.N. Kornilov

Pages: 145–149

Summary. In paper [1] some practical applications of relationship (similarity) principle applied to linear measurements in various geodetic constructions were presented.Here we are going to demonstrate that this principle could be generalized for angular measurements too, since the sine ratio in triangle coincides with the homogeneous elements (similarity coefficient Ki) considered in [1]. That leads to evaluate correlation of linear and angular accuracy in linear-angular constructions. Using various linear-angular serif equation solutions, we showcase when linear and angular measurements might be comparable in their accuracy. It should be taken into account in order to comply with the equivalence principle for calculating the accuracy of linear and angular measurements because configuration of triangles are usually different when designing linear-angular networks. We believe that this research proves the concept and allows equalization of linear measurements to angular in some network construction variants, in that case joint equalization of linear and angular measurements might be used for calculation the coordinates of point. But when their accuracies are unequal it is necessary to refuse from angular or linear measurements, or to introduce the weight coefficients. On top of that, in some cases of serif construction - linear measurements might actually outperform the angular ones in accuracy, so in this case it is advisable to calculate the coordinates of the desired point using method described in [1].

Скачать статью