Correlated Estimation Problems and the Ensemble Kalman Filter
Jan Čurn · Trinity's Access to Research Output (TARA) (Trinity College Dublin) · 2014
Ph.D. Thesis Title: Correlated Estimation Problems and the Ensemble Kalman Filter Author: Jan Čurn Abstract: The Kalman filter is a recursive algorithm that estimates the state of a linear dynamic system from a sequence of noisy sensor measurements. Due to its relative simplicity, numerical efficiency and optimality, the Kalman filter and its variants have been applied to a wide range of problems in technology, notably in the areas of guidance, navigation, and control. The traditional definition of the Kalman filter is based on the assumption that at any given time, the errors associated with the predicted state estimate and the observation are statistically independent. However, in many practical problems, this assumption is not satisfied, and as such the Kalman filter may provide overconfident state estimates and diverge. This can have serious consequences in the context of safety-critical systems. Although there are modifications of the Kalman filter that accommodate various types of correlation in the process and observation noises, these are not suitable in the situation where the correlation between the errors associated with the predicted state estimate and the observation is caused by the presence of common past information between the state estimate and the observation, which is characteristic of...