Enhanced trajectory reconstruction from sparse and noisy GPS data: A progressive chunked transformer approach

Trajectory reconstruction from sparse and noisy GPS data is critical for applications such as urban mobility analysis, transportation planning, and navigation systems. However, large sampling intervals and the typically long output sequences required to reconstruct coherent travel trajectories significantly increase computational complexity, particularly in the presence of noise. To address these challenges, we propose a progressive chunked transformer (ProChunkFormer), which is a deep learning method for trajectory reconstruction that employs self-attention mechanisms and chunked processing to balance efficiency with accuracy. ProChunkFormer first generates intermediate trajectories at a semi-high frequency from low-frequency sampled data, and then the remaining trajectory is divided into manageable blocks and reconstructed parallelly in the condition of the semi-high-frequency trajectory. By combining progressive reconstruction with chunk processing, ProChunkFormer not only mitigates the cumulative errors commonly observed in autoregressive models but also alleviates the rapid increase in complexity associated with reconstructing ultralong trajectories. Specifically, our approach achieves quadratic optimization in time and space for attention modules, with cubic time savings compared with autoregressive decoding. A case study using an open-source taxi trajectory dataset confirms the effectiveness of our approach. The performance of ProChunkFormer is comparable to that of autoregressive transformers while offering better running efficiency. It improves the accuracy, F1 score (F1), mean absolute error (MAE), and road network mean absolute error (MAE_RN) by 23.1%, 18.6%, 22.3%, and 25.1%, respectively, for trajectories with a long interval time of up to 240 ​s. Furthermore, we investigate incorporating heuristic information to guide trajectory reconstruction for each block. The experimental results indicate an improvement in both the overall performance and convergence speed of the model.