An interval Kalman filtering with minimal conservatism

The interval Kalman filtering (IKF) can handle parametric interval uncertainties of the system matrices, and it computes the lower and upper boundaries of the estimated states. In this paper, we propose an alternative form of interval Kalman filtering to reduce the conservatism inherent to the existing interval Kalman filtering. First, we address why the existing interval Kalman filtering scheme induces conservatism in the boundary estimation. Then, to remove the conservatism, we derive noise covariance matrices taking into account of interval uncertainties as well as process and measurement noises. Following the typical derivation process of the standard Kalman filtering, a new recursive form of interval Kalman filtering is derived. Through numerical simulations, the superiority of the new algorithm over existing IKF is illustrated.