OPTIMIZATION OF THE PARAMETERS OF SYNTHESIZED SIGNALS USING LINEAR APPROXIMATIONS BY THE NELDER-MEAD METHOD

Abstract

Context. The article presents the results of a study of the effectiveness of using the Nelder-Mead method to optimize the parameters of linear approximations of synthesized signals. Algorithms have been developed and tested that integrate spectral, temporal, and statistical analyzes and provide reasonable optimization. The effectiveness of the application of the Nelder-Mead method was proven by experiment. The obtained results substantiate the improvement of the properties of the mutual correlation of signals and the reduction of the maximum deviations of the side lobes, which opens up prospects for the further application of the method in complex scenarios of signal synthesis. Objective. The purpose of the work is to evaluate the effectiveness of the application of the Nelder-Mead method when adjusting the parameters of linear approximations to optimize the mutual correlation and minimize side deviations of complex synthesized signals. Method. The main research method is the comparison of various optimization algorithms for the selection of the most effective approaches in linear approximations of synthesized signals, taking into account such criteria as accuracy, speed and minimization of deviations. Scientific works [1, 2, 4–6, 8, 9] present algorithms, including the Nelder-Mead method and differential evolution. The effectiveness of these methods is achieved due to adaptive optimization procedures that improve the characteristics of signals. It is worth noting that the methods have disadvantages associated with high requirements for computing resources, especially when processing large data. This can be minimized using combined optimization methods that take into account the interaction of signal parameters. Another important direction of improvement is the optimization of methods for adaptation to dynamic changes in the characteristics of complex signals, which allows to achieve high adaptability and reliability of real-time systems. Results. As a result of the experiment using the Nelder-Mead method, an increase in the similarity of spectral densities was achieved from 0.52 in the first iteration to 0.90 in the fourth, with a significant decrease in the distance between the peaks of the spectrum from 1.2 to 0.4, which indicates high adaptability and the accuracy of the method in adjusting the parameters of the synthesizedsignals. Conclusions. The effectiveness of the Nelder-Mead method for adjusting the specified parameters of the synthesized signals was experimentally proven, which is confirmed by a significant improvement in the similarity of the spectra with each iteration. This opens the way for additional optimizations and application of the method in various technological areas.