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In this paper, we introduce a real-time parallel-serial algorithm for autonomous robot positioning for GPS-denied, dark environments, such as caves and mine galleries. To achieve a good complexity-accuracy trade-off, we fuse data from light detection and ranging (LiDAR) and an inertial measurement unit (IMU). The proposed algorithm’s main novelty is that, unlike in most algorithms, we apply an extended Kalman filter (EKF) to each LiDAR scan point and calculate the location relative to a triangular mesh. We also introduce three implementations of the algorithm: serial, parallel, and parallel-serial. The first implementation verifies the correctness of our innovative approach, but is too slow for real-time execution. The second approach implements a well-known parallel data fusion approach, but is still too slow for our application. The third and final implementation of the presented algorithm along with the state-of-the-art GPU data structures achieves real-time performance. According to our experimental findings, our algorithm outperforms the reference Gaussian mixture model (GMM) localization algorithm in terms of accuracy by a factor of two.

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