Trajectory prediction is an important problem that has a large number of applications. A common approach to trajectory prediction is based on historical trajectories. However, existing techniques suffer from the "data sparsity problem". The available historical trajectories are far from enough to cover all possible query trajectories. We propose the sparsity trajectory prediction algorithm based on multiple entropy measures (STP-ME) to address the data sparsity problem. Firstly, the moving region is iteratively divided into a two-dimensional plane grid graph, and each trajectory is represented as a grid sequence with temporal information. Secondly, trajectory entropy is used to evaluate trajectory's regularity, the L-Z entropy estimator is implemented to calculate trajectory entropy, and a new trajectory space is generated through trajectory synthesis. We define location entropy and time entropy to measure the popularity of locations and timeslots respectively. Finally, a second-order Markov model that contains a temporal dimension is adopted to perform sparse trajectory prediction. The experiments show that when trip completed percentage increases towards 90%, the coverage of the baseline algorithm decreases to almost 25%, while the STP-ME algorithm successfully copes with it as expected with only an unnoticeable drop in coverage, and can constantly answer almost 100% of query trajectories. It is found that the STP-ME algorithm improves the prediction accuracy generally by as much as 8%, 3%, and 4%, compared to the baseline algorithm, the second-order Markov model (2-MM), and sub-trajectory synthesis (SubSyn) algorithm, respectively. At the same time, the prediction time of STP-ME algorithm is negligible (10 µs), greatly outperforming the baseline algorithm (100 ms).

SUMMARYMost of the existing algorithms cannot effectively solve the data sparse problem of trajectory prediction. This paper proposes a novel sparse trajectory prediction method based on L-Z entropy estimation. Firstly, the moving region of trajectories is divided into a two-dimensional plane grid graph, and then the original trajectories are mapped to the grid graph so that each trajectory can be represented as a grid sequence. Secondly, an L-Z entropy estimator is used to calculate the entropy value of each grid sequence, and then the trajectory which has a comparatively low entropy value is segmented into several sub-trajectories. The new trajectory space is synthesised by these sub-trajectories based on trajectory entropy. The trajectory synthesis can not only resolve the sparse problem of trajectory data, but also make the new trajectory space more credible. In addition, the trajectory scale is limited in a certain range. Finally, under the new trajectory space, Markov model and Bayesian Inference is applied to trajectory prediction with data sparsity. The experiments based on the taxi trajectory dataset of Microsoft Research Asia show the proposed method can make an effective prediction for the sparse trajectory. Compared with the existing methods, our method needs a smaller trajectory space and provides much wider predicting range, faster predicting speed and better predicting accuracy.