## 1 Introduction
Trajectory data compression based on line segment simplification can be subdivided into two types: global-oriented method and local forward method. The representative global-oriented method is the Douglas-Peucker (DP) algorithm [12] and its related improvements [13; 14; 15; 16]. The DP algorithm uses the perpendicular Euclidean distance to measure the error. First, the straight line formed by the start and end points of the trajectory is regarded as the approximate trajectory, and the perpendicular Euclidean distance from the point to the line is calculated for all the points in the middle; the point with the largest distance is selected. If the maximum distance exceeds the preset distance threshold, the point is regarded as the segment feature point, and then the original trajectory is divided into two segments. The above steps are to be repeated for the two segments, respectively, until the maximum perpendicular Euclidean distance calculated by all sub trajectories is less than the distance threshold, or until there are only the start and end points in the trajectories. The DP algorithm is simple and practical. When the distance threshold is set well, it can meet the user's requirements for the similarity between the compressed trajectory and the original trajectory. At the same time, it can achieve high data compression rate. However, the distance threshold is often difficult to set and needs to be adjusted and tried repeatedly. Based on the DP algorithm, [PERSON] [33] established the trajectory point batch processing mode, which reduced the time complexity from \(O(N^{2})\) to \(O(N\times\log N)\), but it is difficult to realize the batch processing mode in many real trajectory data compression processing instances. Top-Down Time-Ratio (TD-TR) algorithm [34; 35] is an improvement on the basis of the DP algorithm. The main difference is that it uses the spatial distance of time scale as the distance function, finds the position corresponding to the original trajectory point on the approximate line segment according to the time scale and then calculates the Euclidean distance between the approximate point and the original trajectory point, so as to obtain a more accurate approximate trajectory. [PERSON] [36] compared the performance of the DP algorithm with TD-TR, Bellman [37], STTrace [38] and other algorithms. Finally, the DP algorithm has better performance in time efficiency, compression ratio and accuracy on multiple data sets. [PERSON] [39] used convex hull to optimize the time complexity of the DP algorithm for segmentation of online trajectory data stream. The local forward methods start from the initial point of the trajectory, and the trajectory points that meet the constraints can be classified as a local approximate line segment. On the contrary, the trajectory points that do not meet the conditions can continue to search forward as the initial point of the new segment [40]. The constraint condition can be defined as the distance function between the trajectory point and the approximate line segment, or the direction change function between the segments. A typical algorithm whose constraint condition is the distance function is the segment simplification part of the trajectory clustering (TRACLUS) algorithm proposed by [PERSON] [41]. The algorithm defines three indexes: perpendicular distance, parallel distance and angle distance, and the trajectory segmentation solution is approximately solved based on the principle of minimum description length (MDL). The segmentation method has been applied in [42; 43; 44]. [PERSON] [45] divides the trajectory into a set of stationary sub-trajectory (SST) based on the detection and evaluation of trajectory position disturbance. The HTRACLUS_DL algorithm proposed by [PERSON] [46] improved the accuracy of TRACLUS algorithm, in which a sub-trajectory parallel boundary method is constructed.