Train localization during Global Navigation Satellite Systems (GNSS) outages presents challenges for ensuring failsafe and accurate positioning in railway networks. This paper proposes a minimalist approach exploiting track geometry and Inertial Measurement Unit (IMU) sensor data. By integrating a discrete track map as a Look-Up Table (LUT) into a Particle Filter (PF) based solution, accurate train positioning is achieved with only an IMU sensor and track map data. The approach is tested on an open railway positioning data set, showing that accurate positioning (absolute errors below 10 m) can be maintained during GNSS outages up to 30 s in the given data. We simulate outages on different track segments and show that accurate positioning is reached during track curves and curvy railway lines. The approach can be used as a redundant complement to established positioning solutions to increase the position estimate's reliability and robustness.

High-precision vehicle positioning is key to the implementation of modern driving systems in urban environments. Global Navigation Satellite System (GNSS) carrier phase measurements can provide millimeter- to centimeter-level positioning, provided that the integer ambiguities are correctly resolved. Abundant code measurements are often used to facilitate integer ambiguity resolution (IAR), however, they suffer from signal blockage and multipath in urban canyons. In this contribution, a lidar-aided instantaneous ambiguity resolution method is proposed. Lidar measurements, in the form of 3D keypoints, are generated by a learning-based point cloud registration method using a pre-built HD map and integrated with GNSS observations in a mixed measurement model to produce precise float solutions, which in turn increase the ambiguity success rate. Closed-form expressions of the ambiguity variance matrix and the associated Ambiguity Dilution of Precision (ADOP) are developed to provide a priori evaluation of such lidar-aided ambiguity resolution performance. Both analytical and experimental results show that the proposed method enables successful instantaneous IAR with limited GNSS satellites and frequencies, leading to centimeter-level vehicle positioning.