Prediction, filtering and smoothing using LSCR: State estimation algorithms with guaranteed confidence sets

In this paper we present a new approach to state estimation based on the Leave-out Sign-dominant Correlation Regions (LSCR) principle from system identification. The LSCR approach constructs a confidence set for the state which has the property that, regardless of the value of the true state, the constructed confidence set will contain it with a guaranteed user chosen probability. This property makes the approach potentially very useful in monitoring and detection applications. The proposed approach is illustrated in simulation examples.