Improvement of State Estimation for Systems with Chaotic Noise

To estimate the state of the system, one needs the covariance matrices as the inputs. The accuracy of the new prediction of the estimation is based recursively on the previous ones. To search for the optimal solution, researchers try to obtain best closed-state approximation for the covariance inputs using the Kalman filtering technique. Many variations of the technique have been proposed for many years. However, in this chapter, our version presents a new improvement of state estimation of the systems with various chaotic noises. Introducing an updated scaling factor to the covariance matrices is a simple modification yet provides a highly effective way to estimate the state of the system in the presence of chaotic noises. Performance comparison among the original Kalman filter, an adaptive version, and our enhanced one is carried out. Computer simulation shows remarkable improvement of the proposed method for estimation of the state of the systems with chaotic noises.