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

TL;DR

This paper applies an Extended Kalman Filter to estimate states and parameters of the Lorenz system under colored noise, demonstrating effectiveness through simulations in both known and unknown parameter scenarios.

Contribution

It extends EKF application to chaotic systems with colored noise, including simultaneous state and parameter estimation, which is less explored in existing literature.

Findings

EKF effectively estimates states in chaotic systems with colored noise.

Simultaneous state and parameter estimation is feasible with the proposed method.

Simulation results confirm the method's efficiency in different noise conditions.

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.