Long-Term Trajectory Prediction Model Based on Points of Interest and Joint Loss Function

ZHOU Chuanxin; JIAN Gang; LI Lingshu; YANG Yi; HU Yu; LIU Zhengming; ZHANG Wei; RAO Zhenzhen; LI Yunxiao; WU Chao

doi:10.11999/JEIT250011

Volume 47 Issue 8

Aug. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(8): 2841-2849

ZHOU Chuanxin, JIAN Gang, LI Lingshu, YANG Yi, HU Yu, LIU Zhengming, ZHANG Wei, RAO Zhenzhen, LI Yunxiao, WU Chao. Long-Term Trajectory Prediction Model Based on Points of Interest and Joint Loss Function[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2841-2849. doi: 10.11999/JEIT250011

Citation:

ZHOU Chuanxin, JIAN Gang, LI Lingshu, YANG Yi, HU Yu, LIU Zhengming, ZHANG Wei, RAO Zhenzhen, LI Yunxiao, WU Chao. Long-Term Trajectory Prediction Model Based on Points of Interest and Joint Loss Function[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2841-2849. doi: 10.11999/JEIT250011

Citation:

ZHOU Chuanxin, JIAN Gang, LI Lingshu, YANG Yi, HU Yu, LIU Zhengming, ZHANG Wei, RAO Zhenzhen, LI Yunxiao, WU Chao. Long-Term Trajectory Prediction Model Based on Points of Interest and Joint Loss Function[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2841-2849. doi: 10.11999/JEIT250011

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Long-Term Trajectory Prediction Model Based on Points of Interest and Joint Loss Function

doi: 10.11999/JEIT250011 cstr: 32379.14.JEIT250011

Southwest Electronics and Telecommunications Institute, Chengdu 610000, China

Received Date: 2025-01-07
Rev Recd Date: 2025-07-10

Available Online: 2025-07-17

Publish Date: 2025-08-27

Abstract

Abstract

Objective With the rapid development of modern maritime and aerospace sectors, trajectory prediction plays an increasingly critical role in applications such as ship scheduling, aviation, and security. Growing demand for higher prediction accuracy exposes limitations in traditional methods, such as Kalman filtering and Markov chains, which struggle with complex, nonlinear trajectory patterns and fail to meet practical needs. In recent years, deep learning techniques, including LSTM, GRU, CNN, and TCN models, have demonstrated notable advantages in trajectory prediction by effectively capturing time series features. However, these models still face challenges in representing the heterogeneity and diversity of trajectory data, with limited capacity to extract features from multidimensional inputs. To address these gaps, this study proposes a long-term trajectory prediction model, PL-Transformer, based on points of interest and a joint loss function. Methods Building on the TrAISformer framework, the proposed PL-Transformer incorporates points of interest and a joint loss function to enhance long-term trajectory prediction. The model defines the positions of points of interest within the prediction range using expert knowledge and introduces correlation features between trajectory points and points of interest. These features are integrated into a sparse data representation that improves the model’s ability to capture global trajectory patterns, addressing the limitation of conventional Transformer models, which primarily focus on local feature changes. Additionally, the model employs a joint loss function that links latitude and longitude predictions with feature losses associated with points of interest. This approach leverages inter-feature loss relationships to enhance the model’s capability for accurate long-term trajectory prediction. Results and Discussions The convergence performance of the PL-Transformer model is evaluated by analyzing the variation in training and validation losses and comparing them with those of the TrAISformer model. The corresponding loss curves are presented in (Fig. 5). The PL-Transformer model exhibits faster convergence and improved training stability on both datasets. These results indicate that the introduction of the joint loss function enhances convergence efficiency and training stability, yielding performance superior to the TrAISformer model. In terms of short-term prediction accuracy, the results in Table 1 show that the PL-Transformer model achieves comparable overall prediction accuracy to the TrAISformer model. The PL-Transformer model performs better in terms of the Mean Absolute Percentage Error (MAPE) metric, while it shows slightly higher errors than the TrAISformer model for Mean Absolute Error (MAE), median Absolute Error (MdAE), and coefficient of determination (R²). For the widely used Mean Squared Error (MSE) metric, both models perform similarly. These results indicate that after incorporating points of interest and optimizing the loss function, the PL-Transformer model retains competitive performance in relative error control and fitting accuracy, while preserving the stability and robustness of the TrAISformer model in complex trajectory prediction tasks. For long-term prediction visualization, Table 2 presents the loss values for both models across medium to long-term prediction horizons (1 to 3 h). The PL-Transformer model achieves better long-term prediction accuracy than the TrAISformer model. Specifically, the loss for the PL-Transformer model increases from 2.058 (1 h) to 5.561 (3 h), whereas the TrAISformer model’s loss rises from 2.160 to 6.145 over the same period. In terms of time complexity analysis, although the PL-Transformer model incorporates additional feature engineering and joint loss computation steps, these enhancements do not substantially increase the overall time complexity. The total computational complexity of the PL-Transformer model remains consistent with that of the TrAISformer model. Conclusions This study proposes the PL-Transformer model, which incorporates points of interest and an optimized loss function to address the challenges posed by complex dynamic features and heterogeneity in trajectory prediction tasks. By introducing distance and bearing angle through feature engineering and designing a joint loss function, the model effectively learns and captures spatial and motion characteristics within trajectory data. Experimental results demonstrate that the PL-Transformer model achieves higher prediction accuracy, faster convergence, and greater robustness than the TrAISformer model and other widely used baseline models, particularly in long-term and complex dynamic trajectory prediction scenarios. Despite the strong performance of the PL-Transformer model in experimental settings, trajectory prediction tasks in real-world applications remain affected by various challenges, including data noise, high-frequency trajectory fluctuations, and the influence of external environmental factors. Future research will focus on improving the model’s adaptability to multimodal trajectory data, integrating multi-source information to enhance generalization capability, and incorporating additional feature engineering and optimization strategies to address more complex prediction tasks. In summary, the proposed PL-Transformer model provides an effective advancement for Transformer-based trajectory prediction frameworks and offers valuable reference for practical applications in trajectory forecasting and related fields.
- Trajectory prediction,
- Transformer,
- Points of interest,
- Loss function optimization

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References(14)

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