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Map matching is a key preprocess of trajectory data which recently have become a major data source for various transport applications and location-based services. In this paper, an online map matching algorithm based on the second-order hidden Markov model (HMM) is proposed for processing trajectory data in complex urban road networks such as parallel road segments and various road intersections. Several factors such as driver's travel preference, network topology, road level, and vehicle heading are well considered. An extended Viterbi algorithm and a self-adaptive sliding window mechanism are adopted to solve the map matching problem efficiently. To demonstrate the effectiveness of the proposed algorithm, a case study is carried out using a massive taxi trajectory dataset in Nanjing, China. Case study results show that the accuracy of the proposed algorithm outperforms the baseline algorithm built on the first-order HMM in various testing experiments. [ABSTRACT FROM AUTHOR]