Analysis of the accuracy of the gradient method for determining the mean integral refractive index of air

Abstract

The article is devoted to the problem of improving the accuracy of taking into account the influence of the Earth’s atmosphere on the results of distance measurements carried out using electromagnetic waves. The main influencing factors in such measurements are the difference between the speed of propagation of an electromagnetic signal in the atmosphere and the speed of light in a vacuum, as well as the refractive distortion of the trajectory along which the signal propagates.To eliminate the influence of the atmosphere, special corrections are used, which are applied into the measurement results in order to compensate for the above influencing factors. The most important among them is the correction, which takes into account the mean integral refractive index of air along the trace being measured.At present, as a rule, model methods for determining the correction are used, taking into account the mean integral refractive index of air. These methods use a point approximation of continuous functions describing the spatial distribution of temperature, pressure and air humidity on the trace being measured, as well as the representation of the finite sum of a certain integral specifying the exact correlation for the correction. Due to these limitations in the framework of the commonly used model methods, it is not always possible to achieve the required accuracy of the results of distance measurements. As for the well-known hardware methods, which are potentially more accurate, they are still under development. In this regard, new possibilities of improving the accuracy of model methods, in particular, the recently proposed gradient method, are considered.Theoretical studies of the accuracy of the gradient method for determining the mean integral refractive index of air in distance measurements on near-Earth traces are carried out. It is shown that it is more accurate than the well-known trapezium method. The equations of measurement of the gradient method obtained with the use of Hermite interpolation polynomials, which are valid for non-uniform partition of the measured trace by points in which the local values of the refractive index are determined, are considered. The requirements for the procedure and accuracy of measurements of the parameters necessary for determining the gradients of the refractive index of air at the end points of the trace in the framework of the gradient method are substantiated.The results of the studies provide a rigorous justification for new methods for determining the mean integral refractive index of air on near-Earth traces with a non-uniform profile of the underlying surface in the presence of significant elevation differences.