State and Parameter Estimation of the Lorenz System in Existence of Colored Noise

Abstract

Many researchers are interested to use Extended Kalman Filter (EKF) for state estimation of complex nonlinear dynamics with uncertainties which modeled with white noises. On the other hand behavior of the chaotic systems in time domain itself is similar to noise too. In this paper, states of the chaotic Lorenz system that its uncertainties modeled with colored noise on states and also on output are considered. For both cases, the case that parameters of Lorenz system are known and the case that parameters of the Lorenz system are unknown, EKF is used to estimate the states. In the case that parameters are unknown using a stochastic viewpoint parameters of the system and parameters of the first order filter of the colored noise are estimated. Efficiency of the method is shown with simulation.