High penetration rate of Smartphones and their increased capabilities to sense, compute, store and communicate have made the devices vital components of intelligent transportation systems. However, their GPS positions accuracy remains insufficient for a lot of location-based applications especially traffic safety ones. In this paper, we developed a new algorithm which is able to improve smartphones GPS accuracy for vulnerable road users' traffic safety. It is a two-stage algorithm: in the first stage GPS readings obtained from smartphones are passed through Kalman filter to smooth deviated reading. Then an adaptive online time warping based map matching is applied to map the improved new locations to corresponding road segments. The incremental alignment is made in real-time based on two similarity metrics - distance and direction difference. Different online time warping variants are formulated and compared with the naïve dynamic time warping algorithm in terms of accuracy and response time. We tested them on GPS trajectories collected from smartphones and reference points extracted from road network data. Test results show that while the proposed algorithms have comparable accuracy with existing algorithms, they largely outperform in terms of response time. For the dataset used, average ratios of correct matches are 91.4% and 93.2% for newly proposed algorithms and for existing algorithm respectively. Negligible accuracy inferiority of the new algorithms is compensated by large improvement on response times which are meliorated from seconds to instant responses.