ON THE DEVELOPMENT OF THE ALGORITHM FOR DETERMINATION OF STADIA CONSTANT OF ELECTRONIC TACHOMETERS

Abstract

An algorithm for determining the stadia constant of the rangefinder is developed and tested. This algorithm is based on the generalized reduced gradient (GRG) method with consistent use of criteria of minimizing the maximum deviation and minimizing the total sum of squares of deviations. There were some stages of the research. First, we carried out 200 measurements with equal accuracy by a SOUTH NTS-350 electronic tachometer. The statistical processing of measurement results enabled specification of the optimal number of measurements for the device taking into account the dependence of the correlation values of instrumental and random errors. Having determined the optimal number of measurements, we continued the study of the proposed method of calculating the stadia constant of electronic tachometers. According to the data obtained during the measurement of the range of the target, which consisted of four points, conditional equations were compiled. These conditional equations are based on the relationships between the length of the measured target and its segments in all combinations, taking into account the stadia constant of the rangefinder. Due to the large number of measurements, the solution of such system of equations is to find the minimum of some function for determining the errors of the measured distances. Our methodology is based on the use of the Lagrange multiplier method in finding the solution of a nonlinear programming problem, which in most software resources is called the Nonlinear Generalized Consolidated Gradient (GRG). The essence of this solution is to find a conditional local extremum. In this case, it is most appropriate to consistently use the criteria of minimizing the maximum deviation and minimizing the total sum of squares of deviations. The method of minimizing the maximum deviation makes it possible to reject gross errors in the measured values. The following minimization of the total sum of squares of deviations will allow to minimize random errors of the measured distances, as the selected samples are subject to the normal distribution law. Thus, the most probable value of the constant correction of the rangefinder and lengths of the measured target and its segments for all possible combinations has been obtained.