State estimation algorithms with guaranteed confidence intervals for first order systems

In a recent paper (Weyer and Campi (2011)) a new approach to state estimation based on the Leaveout Sign-dominant Correlation Regions (LSCR) algorithm was introduced. The algorithm has the property that it delivers guaranteed confidence regions for the true state without knowledge of the variance of the process noise and measurement noise. For first order systems there is additional freedom in the choice of the correlation functions computed in the LSCR algorithm, and in this paper we investigate through a simulation study how these design choices affect the performance of the algorithm under different levels of process- and measurement noise.