To achieve higher automation level of vehicles defined by the Society of Automotive Engineers, safety is a key requirement affecting navigation accuracy. We apply Light Detection and Ranging (LiDAR) as a main auxiliary sensor and propose LiDAR-based Simultaneously Localization and Mapping (SLAM) approach for Positioning, Navigation, and Timing. Furthermore, point cloud registration is handled with 3D Normal Distribution Transform (NDT) method. The initial guess of the LiDAR pose for LiDAR-based SLAM comes from two sources: one is the differential Global Navigation Satellite System (GNSS) solution; the other is Inertial Navigation System (INS) and GNSS integrated solution, generated with Extended Kalman Filter and motion constraints added, including Zero Velocity Update and Non-Holonomic Constraint. The experiment compares two initial guesses for scan matching in terms navigation accuracy. To emphasize the importance of a multi-sensor scheme in contrast to the conventional navigation method using the stand-alone system, the tests are conducted in both open sky area and GNSS signal block area, the latter might cause Multipath and Non-Line-Of-Sight effects. To enhance the navigation accuracy, the Fault Detection and Exclusion (FDE) mechanism is applied to correct the navigation outcome. The results show that the application of NDT and FDE for INS/GNSS integrated system can not only reach where-in-lane level navigation accuracy (0.5 m), but also enable constructing the dynamic map.