Nowadays, a lot of mobile devices have been equipped with GPS sensors to collect and upload time-stamped trajectories for more personalized services such as navigation and route planner. However, it is a challenging work to process large amount of trajectories due to high cost transmission and computation in the real time case. Although, it can be addressed by highly efficient compression algorithms which aim to reduce the size of uploaded trajectory data and maintain spatial-temporal information as much as possible, existing methods lack of consideration regarding the correlation between the longitude and the latitude. In this paper, a Distributed Compressive Approximation of Trajectory (DCAT) based on Distributed Compressive Sensing (DCS) is proposed to incorporate the correlation between the longitude and the latitude for better compression performance. In addition, we propose a method for training a correlation matrix which aims to decrease the total sparsity. Finally, a series of experiments have been conducted to compare with other state-of-the-art compression algorithms, and our model shows significant improvements in the accuracy (more than 10 percent).