A Comparison of Two Methods for State Estimation: A Statistical Kalman Filter, and a Deterministic Interval-Based Approach

In an uncertain framework the performance of two methods of state estimation for discrete-time linear systems are compared on a pedagogical example. The first one is the well known Kalman filter, which is accurate when the measurement noises and the state disturbances are assumed Gaussian white noises and their statistical properties are available. The second one is a set-membership state estimator, which is also based on the prediction-correction principle. Based on the observability assumption of linear systems combined with interval analysis, both stages of this estimator are carried out in a guaranteed and efficient way. In this study, the performance of both state estimation algorithms are evaluated under two scenarios. In the first scenario, the state disturbances and measurement noise are considered Gaussian and in the second scenario these signals are considered unknown-but-bounded with known bounds.