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.

Traffic signal phase and timing (TSPaT) information is valuable for various applications, such as velocity advisory systems, navigation systems, collision warning systems, and so forth. In this paper, we focus on learning baseline timing cycle lengths for fixed-time traffic signals. The cycle length is the most important parameter among all timing parameters, such as green lengths. We formulate the cycle length learning problem as a period estimation problem using a sparse set of noisy observations, and propose the most frequent approximate greatest common divisor (MFAGCD) algorithms to solve the problem. The accuracy performance of our proposed algorithms is experimentally evaluated on both simulation data and the real taxi GPS trajectory data collected in Shanghai, China. Experimental results show that the MFAGCD algorithms have better sparsity and outliers tolerant capabilities than existing cycle length estimation algorithms.