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

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