An Aperiodic Phenomenon of the Unscented Kalman Filter in Filtering Noisy Chaotic Signals

An interesting behavior of the unscented Kalman filter (UKF) when it is used to filter chaotic systems, is reported in this paper. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, it either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.