Interval state estimation for bounded noise and its applications

Abstract

Consider the problem of state estimation in identification and control theory, the traditional Kalman filter method and its modified forms can estimate the unknown state only on the condition of probabilistic distribution on external noise, such as white noise or colored noise. To relax this strict condition on external noise, interval state estimation is proposed to achieve the goal in case of the unknown but bounded noise, due to external noise with unknown but bounded property is more realistic then white noise. Given one state space form with bounded noises and bounded initial state, two intervals are constructed to include the state estimation and output prediction respectively through our own derivations. One easy way to determine the terminate state estimation is to choose the center of midpoint of the constructed interval. The equivalent property between interval state estimation and our previous zonotope state estimation is also described.