This paper presents a fast, memory-efficient, and worldwide map matching algorithm based on raw geographic coordinates and enriched open map data with support for trajectories on foot, by bike, and motorized vehicles. The proposed algorithm combines the Markovian behavior and the shortest path aspect while taking into account the type and direction of all road segments, information about one-way traffic, maximum allowed speed per road segment, and driving behavior. Furthermore, a self-adapting lane detection algorithm based solely on accelerometer readings is added on top of the map matching algorithm. An experimental validation consisting of 30 trajectories on foot, by bike, and by car, showed the efficiency and accuracy of the proposed algorithms, with an average F1-score and median error of 99.5% and 1.89 m for the map matching algorithm and an average F1-score of 86.7% for the lane detection algorithm, which resulted in the correctly estimated lane 93.0% of the time. Moreover, the proposed technique outperforms existing state of the art techniques with accuracy improvements up to 45.2%.