Comparative analysis of quadrature formulas for the mean integral refractive index of air in high-precision ranging

Volume І(39), 2020, pp.69-73

Authors:

P. NEYEZHMAKOV1, T. PANASENKO1, O. PROKOPOV1, A. SHLOMA1, I. TREVOHO2
1 National Scientific Center “Institute of Metrology”, 42, Mironositskaya str., Kharkiv, 61002, Ukraine, tel. +380577003409, E-mail: pavel.neyezhmakov@gmail.com
2 Hetman Petro Sahaidachny National Army Academy, 32, Heroes of the Maidan str., Lviv, 79026, Ukraine, tel. 38050370602, e-mail: itrevoho@gmail.com

Abstract:

Aim. The purpose of this work is to improve (improve accuracy) methods of taking into account the influence of the Earth’s atmosphere on the results of measurements of large lengths carried out by electromagnetic waves on the nearearth tracks. Method. The influence of the earth’s atmosphere on the speed of propagation of the electromagnetic signal is
considered. This effect is taken into account by introducing the correction of the mean refractive index of the air along the measured track in result of the measurements. Methods for determining this correction are selected for analysis, based on the replacement of the exact integral, which determines its value, by approximate quadrature formulas. These
quadrature formulas allow us to represent the exact integral for the mean integral refractive index of air as a function of the local values of the refractive index on the track being measured. The focus is on the quadrature formulas that underlie the recently proposed gradient method (based in particular on the use of the Euler–Maclaurin integration formula or the Hermite polynomials). Results. It is shown that the gradient method of determining the mean integral refractive index of air, which uses the Hermite interpolation polynomials, has the better precision capabilities, than the gradient method based on the Euler–Maclaurin integration formulas. Scientific novelty and practical importance. The obtained results
make it possible to determine the most appropriate method for determining the mean integral refractive index of air in geodetic applications taking into account the measurement conditions: track geometry and the type of underlying surface, the number of points to measure the local values of the refractive index and their locations.

Keywords

gradient method; mean integral refractive index of air; earth`s atmosphere.

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