Extended and unscented Kalman filters for the identification of uncertainties in a process

This paper describes the application of extended and unscented Kalman filters for the identification of uncertainties in a process. The extended Kalman filter (EKF) is an optimal linear recursive algorithm that offers a solution to the filtering problem. The EKF is based on a first-order Taylor expansion to approximate the measurement and process models. This approach may cause the estimation process to diverge. Consequently, alternatives (e.g., the unscented Kalman filter, UKF) based on a fixed number of points to represent a Gaussian distribution have been introduced. The EKF and UKF have been applied for the identification of uncertainty in the attitude determination process for small satellites based on noisy measurements collected from Sun sensors and three-axis magnetometers. Simulation results indicate that the EKF and UKF perform equally well when small initial errors are present. However, when large errors are introduced, the UKF leads to a faster convergence and achieves a higher more accurate estimate of the state of the system.