Scientific Journal of KubSAU

The main task in the analysis of time series is the reconstruction of the dynamical system that generated this series. To illustrate the nature of the behavior of a dynamic system described by a nonstationary time series, a «phase portrait» method is proposed. An acceptable description of the phase space of a dynamical system can be obtained if we take instead of real variables of the system delay vectors composed of the values of the series at consecutive moments of time. Restoration in a given class of a system of differential or difference equations is performed based on the scalar time series of the observed process. In order to eliminate the measurement error and accurately represent the position of the object in the current, future, or any of the past moments, it is proposed to apply the Kalman filter using the known mathematical model of object dynamics