Due to the prevalence of GPS-enabled devices and wireless communications technologies, spatial trajectories that describe the movement history of moving objects are being generated and accumulated at an unprecedented pace. Trajectory data in a database are intrinsically heterogeneous, as they represent discrete approximations of original continuous paths derived using different sampling strategies and different sampling rates. Such heterogeneity can have a negative impact on the effectiveness of trajectory similarity measures, which are the basis of many crucial trajectory processing tasks. In this paper, we pioneer a systematic approach to trajectory calibration that is a process to transform a heterogeneous trajectory dataset to one with (almost) unified sampling strategies. Specifically, we propose an anchor-based calibration system that aligns trajectories to a set of anchor points, which are fixed locations independent of trajectory data. After examining four different types of anchor points for the purpose of building a stable reference system, we propose a spatial-only geometry-based calibration approach that considers the spatial relationship between anchor points and trajectories. Then a more advanced spatial-only model-based calibration method is presented, which exploits the power of machine learning techniques to train inference models from historical trajectory data to improve calibration effectiveness. Afterward, since trajectory has temporal information, we extend these two spatial-only trajectory calibration algorithms to incorporate the temporal information, which can infer a proper time stamp to each anchor point of a calibrated trajectory. At last, we provide a solution to reduce cost, i.e., the number of trajectories that is necessary to be re-calibrated, of the updating of the reference system. Finally, we conduct extensive experiments using real trajectory datasets to demonstrate the effectiveness and efficiency of the proposed calibration system.