Ellipsoidal Set Membership Filtering with Reduced Conservatism Applied to Relative Localization Between Aircraft Based on GNSS and UWB Ranging

For automatic formation flight and applications such as automatic aerial refueling, relative positions between aircraft need to be accurately estimated. However, to ensure flight safety, guaranteed consistent uncertainty estimates are of equally crucial importance. This paper presents a novel Iterated Extended Set Membership Filter (IESMF) providing ellipsoidal regions guaranteed to contain another aircraft's position in a formation. Two easily implementable modifications to the Extended Set Membership Filter are shown to greatly reduce its conservatism. The filter runs in fixed time and handles asynchronous observations. As another novelty, we take into account parametric uncertainty of the observation equation. The proposed filter is applied to a realistic UAS localization benchmark simulation. We compare the new filter to a computationally very strong but much more expensive nonlinear set inversion algorithm and find that similar performances can be achieved. Also, simulation results illustrate the effective reduction of filter conservatism by a few iterative updates.