Advanced data analytics have become an integral part of a number of eScience initiatives including the many challenges facing the urban sciences. Understanding the movement of people and their spatial trajectorits would greatly aid the development of policies for sustainable urban living including urban traffic analysis and smart city management. Due to the widespread popularity of mobile devices with location-aware capabilities and the extensive prevalence of location-based social networks, citizens' movements and their trajectories are being produced and gathered at an unprecedented rate. In this context, there are two fundamental issues that need to be addressed: trajectory data hold private information of citizens that require privacy preserving solutions for data release and analysis, and the heterogeneous nature of the trajectory data makes it hard to effectively measure their similarity, which is fundamental to trajectory analysis. In this paper, we address these challenges by proposing an innovative private trajectories calibration model that not only guarantees the privacy of citizens, but also increases the utility. We have conducted comprehensive experiments using real-life user trajectories extracted from Twitter data. The results reveal the effectiveness and efficiency of the proposed approach, which is also reported in this paper.