RESEARCH OF METHODS FOR EXAMINATION OF THE SIGNIFICANCE OF THE SMOOTHING POLYNOMIAL COEFFICIENTS

Abstract

The aim of the work is to study the procedure for checking the significance of the coefficients of the smoothing polynomial based on the criteria for testing statistical hypotheses in order to form a vector of coefficients of the smoothing polynomial. The developed methods of nonlinear adaptive smoothing with optimization of the degree of the smoothing polynomial with optimization of the structure of the smoothing polynomial were studied. The study was carried out by simulating the value of secondary coordinates, which, according to the formulas of simple methods, were converted into primary coordinates, taking into account the location and type of measuring instruments. Then, the values of measurement errors distributed according to the normal law were added to the obtained values of the primary coordinates. The primary measurement data thus obtained were subjected to nonlinear adaptive smoothing. The formation of the coefficient vector of the smoothing polynomial was carried out on the basis of the criteria for testing statistical hypotheses in the following sequence: formation of the corresponding statistics according to the measurement data; comparison of these statistics with a threshold level depending on the confidence level and the number of degrees of freedom; making a decision on the inclusion of this component in the polynomial. The formation of the coefficient vector of the smoothing polynomial was carried out on the basis of the Fisher criterion. Based on the results of the study, the following conclusions can be drawn: methods of nonlinear adaptive smoothing with optimization of the structure of the smoothing polynomial are superior in terms of quality and efficiency to the method with optimization of the degree of the smoothing polynomial; the method of non-linear adaptive smoothing with optimization of the structure of the smoothing polynomial Structure 1 is superior in terms of quality and efficiency to the method with optimization of the structure of the smoothing polynomial Structure 2; The greatest gains in quality and efficiency for all the studied methods are achieved in the middle part within 3/5 of the smoothing interval; for all the studied methods, the quality and efficiency indicators decrease at the edges of the smoothing interval