With the extensive use of location based devices, trajectories of various kinds of moving objects can be collected and stored. As time going on, the volume of trajectory data increases exponentially, which presents a series of problems in storage, transmission and analysis. Moreover, GPS trajectories are never perfectly accurate and sometimes with high noise. Therefore, how to overcome these problems becomes an urgent task in trajectory data mining and related applications. In this paper, an adaptive noise filtering trajectory compression and recovery algorithm based on Compressed Sensing (CS) is proposed. Firstly, a noise reduction model is introduced to filter the high noise in GPS trajectories. Secondly, the compressed data can be obtained by the improved GPS Trajectory Data Compression Algorithm. Thirdly, an adaptive GPS trajectory data recovery algorithm is adopted to restore the compressed trajectories to their original status approximately. Finally, comprehensive experiments on real and synthetic datasets demonstrate that the proposed algorithm is not only good at noise filtering, but also with high compression ratio and recovery performance compared to current algorithms.