This paper concerns a new methodology for accuracy assessment of global positioning system verified experimentally with LiDAR (Light Detection and Ranging) data alignment at continent scale for autonomous driving safety analysis. Accuracy of GPS (Global Positioning System) positioning of an autonomous driving vehicle within a lane on the road is one of the key safety considerations. Safety is addressed as a geometry of the problem, where the aim is to maintain knowledge that the vehicle (its bounding box) is within its lane. Accuracy of GPS positioning is checked by comparing it with mobile mapping tracks in the recorded high definition source. The aim of the comparison is to see if the GPS positioning remains accurate up to the dimensions of the lane where the vehicle is driving. For this reason, a new methodology is proposed. Methodology is composed of six elements: 1) Mobile mapping system minimal setup, 2) Global positioning data processing, 3) LiDAR data processing, 4) Alignment algorithm, 5) Accuracy assessment confirmation and 6) Autonomous driving safety analysis. The research challenge is to assess positioning accuracy of moving cars taking into account the constraints of the coverage of limited access highways in the United States of America. The available coverage limits the possibility of repeatable measurements and introduces an important challenge being the lack the ground truth data. State-of-the-art methods are not applicable for this particular application, therefore a novel approach is proposed. The method is to align all the available LiDAR car trajectories to confirm the GNSS+INS (Global Navigation Satellite System + Inertial Navigation System) accuracy. For this reason, the use of LiDAR metric measurements for data alignment implemented using SLAM (Simultaneous Localization and Mapping) was investigated, assuring no systematic drift by applying GNSS+INS constraints. SLAM implementation used state-of-the-art observation equations and the Weighted Non-Linear Least Square optimization technique that enables integration of the required constraints. The methodology was verified experimentally using arbitrarily chosen measurement instruments (NovAtel GNSS+INS, LiDAR Velodyne HDL32) mounted onto mobile mapping systems. The accuracy was assessed and confirmed by the alignment of 32785 trajectories with total length of 1,159,956.9~km and of total $186.4*10^{9}$~optimized parameters (six degrees of freedom of poses) that cover the United States region in the 2016--2019 period. It is demonstrated that the alignment improves the trajectories, thus final map is consistent. The proposed methodology extends the existing methods of global positioning system accuracy assessment focusing on realistic environmental and driving conditions. The impact of global positioning system accuracy on autonomous car safety is discussed. It is shown that 99\% of the assessed data satisfies the safety requirements (driving within lanes of 3.6~m) for Mid-Size (width 1.85~m, length 4.87~m) vehicle and 95\% for 6-Wheel Pickup (width 2.03--2.43~m, length 5.32--6.76~m). The conclusion is that this methodology has great potential for global positioning accuracy assessment at global scale for autonomous driving applications. LiDAR data alignment is introduced as a novel approach to GNSS+INS accuracy confirmation. Further research is needed to solve the identified challenges.