Nonlinearity in Sensor Fusion: Divergence Issues in EKF, Modified Truncated GSF, and UKF

Relative navigation is a challenging technological component of many planned NASA and ESA missions. It typically uses recursive filters to fuse measurements (e.g., range and angle) from sensors with contrasting accuracies to estimate the vehicle state vectors in real time. The tendency of Extended Kalman filter to diverge under these conditions is well documented in the literature. As such, we have investigated the application of the modified truncated Second-Order Filter (mtSOF) and the Unscented Kalman filter (UKF) to those mission scenarios using numerical simulations of a representative experimental configuration: estimation of a static position in space using distance and angle measurements. These simulation results showed that the mtSOF and UKF may also converge to an incorrect state estimate. A detailed study establishes the divergence process of the mtSOF and UKF, and designs new strategies that improve the accuracy of these filters.