###### Abstract  
The monitoring technology for targets such as aircraft and vehicles has rapidly developed in recent years and is widely used in national airspace security supervision, urban traffic supervision, and the tracking of special targets. However, the sparse trajectories of targets, primarily caused by the insufficient density of monitoring points, significantly reduce their usability. Therefore, it is important to reconstruct the target trajectories. Existing methods for the reconstruction of target trajectories often rely on topological data and convert trajectory reconstruction into a trajectory matching problem. Such methods heavily rely on topological data and cannot reconstruct trajectories in free space. To address this issue, we proposed a trajectory reconstruction method, named Prob-Attn, which does not rely on topological data and can accurately reconstruct target trajectories in free space. This method can be divided into two steps: first, a spatial trajectory construction module is proposed to determine the spatial trajectories of targets. Then, based on the reconstructed spatial trajectory of the target, this paper proposes a time series prediction model based on historical trajectories and an attention mechanism, which considers the impact of the target's activity cycle and the surrounding status to predict the time series inside the trajectory. Finally, the proposed method is evaluated on real automatic vehicle detection datasets collected in Chongqing, China. The experimental results show that, compared with traditional methods, the proposed method can reconstruct the spatiotemporal trajectory of the target more accurately. The reconstructed trajectory data can be used for critical applications such as the intent and behavior analysis of key targets in national airspace and ground areas, providing valuable insights into security and safety. target trajectory reconstruction; automatic vehicle detection; probability model; attention network +
Footnote †: journal: applied sciences  
Although the underlying principles of different AVI systems may vary, the method of data collection is similar. Vehicle detectors are strategically placed at key locations on city roads. These detectors record information such as the license plate number and vehicle type when a vehicle passes through them, generating a record of the vehicle's time and location [3]. The advantages of automatic vehicle identification (AVI) data compared to traditional GPS trajectories are numerous [4]. Firstly, AVI data boost high accuracy, as they record vehicle identification data at specific locations, eliminating uncertainty in locations and accurately recording the vehicle's passage time. Specifically, RFID-based automatic vehicle identification systems can achieve near-perfect recognition accuracy. Secondly, AVI data have a large data volume and can be applied in various scenarios, such as toll booths and urban roads, identifying all types of vehicles in the city. Thus, the amount of data generated by AVI far exceeds what GPS can cover. Thirdly, AVI data provide rich information, such as vehicle IDs, vehicle types, and locations. AVI data are considered a typical type of automatic target position detection data. A comparison of an AVI trajectory and GPS trajectory is shown in Figure 2. The blue dots represent the GPS trajectory, showcasing densely sampled points along the vehicle's path, while the sparse red markers indicate the AVI trajectory, with only a few data points recorded at fixed collection points. This stark contrast highlights the challenges posed by the low sampling rate of AVI data in accurately capturing a vehicle's full trajectory. However, AVI data also have drawbacks. The most significant is the low sampling rate [5]. Since the automatic vehicle identification device can only record vehicle information when it passes through a collection point, the sparsely distributed collection points in the urban road network led to very sparse vehicle trajectories based on AVI data.