State and Parametric Fault Estimation Using Extended Kitanidis Kalman Filter for Chaotic Rössler System

This paper analyzes the simultaneous estimation of states and parametric faults of a chaotic Rössler system in the presence of process and measurement noise. The parametric fault causes a bifurcation in the Rössler system. The problem of state and parametric fault estimation for nonlinear systems can be solved through the extended Kitanidis Kalman filter (EKKF). In fact, the EKKF makes a perfect estimate merely for states in the presence of unknown parameters for nonlinear systems. In this paper, an EKKF is developed to estimate states. Since the EKKF-generated innovation is a colored Gaussian stochastic process, its covariance kernel is also computed through a recursive approach. However, the parametric fault is estimated through the maximum likelihood (ML) framework based on the moving window in the EKKF-generated innovation. In the simulation section, the parametric fault occurs and causes the system to show chaotic behavior, which is described through the bifurcation diagram. According to the simulation results, the proposed approach succeeded in estimating states and parametric faults. Moreover, a low parametric fault can also cause a bifurcation in the system.