Position Measurement Outlier Detection for Lie-Group-Based Navigation Filters Utilizing Gaussian Mixtures

GNSS integrity is essential for safe and robust navigation, especially in automated and autonomous systems. A key component to achieve integrity within filtering frameworks is the accurate modeling of uncertainties in the estimation problem, enabling the use of prior information to assess the integrity of new observations. Leveraging the Lie group extended Kalman filters (EKF) capability to capture the uncertainties inherent in loosely coupled GNSS-aided inertial navigation, this work presents a position measurement outlier detection method derived explicitly for the Lie group EKF. The method uses a Gaussian mixture to provide a more accurate approximation of the non-Gaussian distributed innovation that arises from the use of the Lie group EKF. A planar simulation demonstrates that the proposed method fully utilizes the Lie group EKF's uncertainty information, enabling more accurate detection and rejection of false position measurements, even in scenarios with high orientation uncertainty.