## 2 Related Work  
### Social Interactions for Pedestrian Trajectories  
Early trajectory prediction is mainly made by manual formulas according to the attraction and repulsive force of pedestrians, such as the Social Force Model [1], which simulates the pedestrian's attractive and repulsive forces to nearby pedestrians, moving cars, other obstacles, and the pedestrian's intended destination. Ref. [2] designs a linear trajectory avoidance (LTA) model to move pedestrians in the best direction by predicting their expected closest points and using those points as the guiding factor for decision-making. They take into account that pedestrians are motivated by planned destinations and collision avoidance. Ref. [3] proposes Social LSTM, this method considers the interactions between pedestrians and increases the sensory field of the model by designing a new pooling layer to share information among multiple LSTMs. Ref. [4] designs a repulsive force on the basis of Social LSTM by investigating how pedestrians adjust their trajectories pooling layer to superimpose the repulsive force around pedestrians within a certain range and share it as a hidden state among all LSTMs. Social LSTM only considers the effects within a fixed-size local neighborhood and does not take into account the global effects. Thus, Ref. [5] proposes a spatio-temporal graph that explicitly captures the global interactions of all pedestrians in the scene as well as the local interactions with static objects, and designed a spatio-temporal attention mechanism to capture the effects of each pedestrian both spatially and temporally. In order to reason about the interaction relationship between pedestrians in a more detailed way, ref. [6] reasons about the higher-order social relationships of individuals from different social scale levels by designing a graph-based higher-order relationship inference module based on a novel collision-aware kernel function, specifically by designing a collision point for each pair of interacting pedestrians and then assigning the impact weights according to the specific different from the collision point to each pedestrian. The higher-order impacts of the pedestrians are then modeled by a graph convolutional network. Ref. [7] reflects the distance and direction relationship between any location in the environment and the target pedestrian by proposing a polar coordinate-based approach. Afterwards, the basic local features of each time-step feature map are captured through a local multimodal window and the social and environmental interaction feature maps are spliced together and trajectory prediction is performed based on a CNN. Ref. [8] designs a GATA rapid to encode past trajectories and interactions using an encoder-decoder structure, extract the spatio-temporal features through the attentional mechanism, and design a GCN to simulate the interactions between pedestrians while achieving a good balance of prediction speed and prediction accuracy. Transformer-based methods have also been applied to trajectory prediction such as refs. [9; 10]. A transformer is a fully attention-based network that reduces model complexity and is computationally efficient. Ref. [11] improves the performance of the model by considering both pedestrian trajectory data and self-motion data, and by designing a connectivity layer or by using an attentional mechanism to reweight and combine them into a single representation to fully utilize multimodal data and improve the model performance. However, the decoder in the transformer is autoregressive, which can lead to problems such as cumulative errors and delayed inference. To address this problem, ref. [12] proposesan approach based on historical trajectories and self-motion of pedestrians, the VOSTN model, which obtains the intrinsic correlation of pedestrians themselves at different time steps through a cross-modal attention module, and designs a one-time generator module responsible for generating the data and merging it with the latent distributions in order to perform parallel prediction.