Сравнение качества оптимальной фильтрации наклона дисперсионной характеристики фильтром Стратоновича и сигма-точечным фильтром Калмана

Abstract

The article deals with the reception and transmission of broadband signals through the ionospheric channel. An increase in the width of the spectrum of transmitted signals leads to a significant effect of the frequency dispersion of the Earth's ionosphere on the quality of information reception. Estimation of dispersion distortions of broadband signals and compensation of their influence in the article is carried out by methods of optimal filtering. Two algorithms for nonlinear optimal filtering of the slope of the dispersion characteristic of the ionospheric channel are compared: using the Stratonovich filter and using the sigma-point Kalman filter. The article presents general analytical expressions for calculating the estimate of the slope of the dispersion characteristic for both algorithms: Stratonovich filtering and filtering using the unscented Kalman filter. In addition, the results of simulation modeling are presented, the purpose of which was to compare the two above-mentioned filtering algorithms within the framework of the task. Three cases of the dependence of the slope of the DC on time are studied: a Markov damped process, a constant process, and a process with random increments for phase-shift keyed signals with different spectral widths under the assumption of large signal-to-noise ratios. It is shown that for signals with a spectral width from 500 kHz to 1 MHz, the unscented Kalman filter adjusts on average 2 times faster, however, the standard deviation of the estimate of the slope of the dispersion characteristic from the true value is up to 1.5 times larger compared to the Stratonovich filter. The duration of the filter adjustment decreases with a decrease in the width of the signal spectrum from 1 MHz to 250 kHz. In the 250 kHz band, both considered filters have approximately the same tuning speed and filtering quality.