An aperiodic phenomenon of the extended Kalman filter in filtering noisy chaotic signals

In this correspondence, we report an interesting behavior of the extended k alman filter (EKF) when it is used to filter a chaotic system. We show both theoretically and experimentally that the gain of the EKF may not converge or diverge but oscillates aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the EKF converg e to zero. However, when the system is chaotic, they either converge to a f iled pl,int with magnitude larger than zero or oscillate aperiodically. Our theoretical analyses are verified using Monte Carlo simulations based on s ome popular chaotic systems.