This work addresses the challenge of developing a localization system for an uncrewed ground vehicle (UGV) operating autonomously in unstructured outdoor Global Navigation Satellite System (GNSS)-denied environments. The goal is to enable accurate mapping and long-range navigation with practical applications in domains such as autonomous construction, military engineering missions, and exploration of non-Earth planets. The proposed system - Terrain-Referenced Assured Engineer Localization System (TRAELS) - integrates pose estimates produced by two complementary terrain referenced navigation (TRN) methods with wheel odometry and inertial measurement unit (IMU) measurements using an Extended Kalman Filter (EKF). Unlike simultaneous localization and mapping (SLAM) systems that require loop closures, the described approach maintains accuracy over long distances and one-way missions without the need to revisit previous positions. Evaluation of TRAELS is performed across a range of environments. In regions where a combination of distinctive geometric and ground surface features are present, the developed TRN methods are leveraged by TRAELS to consistently achieve an absolute trajectory error of less than 3.0 m. The approach is also shown to be capable of recovering from large accumulated drift when traversing feature-sparse areas, which is essential in ensuring robust performance of the system across a wide variety of challenging GNSS-denied environments. Overall, the effectiveness of the system in providing precise localization and mapping capabilities in challenging GNSS-denied environments is demonstrated and an analysis is performed leading to insights for improving TRN approaches for UGVs.