Development of technologies for reducing the error of traditional algorithms of correlation analysis of noisy signals

Abstract

The authors analyze the factors affecting the errors in the estimates of the correlation functions of the noisy signals when using traditional calculation algorithms. It is shown that the sum noise of the noisy signal in many cases consists of the noise caused by external factors and the noise caused by the initiation of various defects during the operation of control objects. For this reason, in order to eliminate the error in the results of the correlation analysis of noisy signals, it is necessary to create algorithms and technologies for determining the estimate of the noise variance and the cross-correlation functions between the useful signal and the noise. For this purpose, appropriate algorithms and technologies are proposed that open up the possibility of reducing the error of traditional technologies for determining the estimates of correlation functions. With the purpose of reducing the error of the results of correlation analysis, a technology is proposed for determining the approximate equivalent samples of the noise of the noisy signals. It is shown that using the equivalent noise samples, it is possible to obtain results that are identical to the results of using real samples of the noise in the correlation analysis of the same signals. Moreover, by extracting the equivalent noise samples from the noisy signal, the equivalent samples of the useful signal are also determined, which allow determining the estimates equivalent to the estimates of the correlation functions of the useful signal. At the same time, having equivalent noise samples and useful signal samples, the estimates of the cross-correlation function between the useful signal and the noise are determined. The study have shown that despite certain errors in the equivalent samples compared to the true samples, with a sufficient observation time using equivalent samples, the error of traditional technologies for the correlation analysis of noisy signals can be significantly reduced. These technologies can also be used to correct errors in the results of the analysis of experimental data in information-measuring and other measuring complexes and systems, which will significantly improve their metrological characteristics.