Online adaptive shockwave detection and inpainting based on vehicle trajectory data: rigorous algorithm design and theory development

Traffic shockwaves, as the boundary of distinct traffic states, capture the temporal-spatial characteristics of traffic fluctuation formation and propagation. Monitoring shockwaves facilitates real-time traffic management and control to improve traffic efficiency and safety. However, detecting shockwaves is challenging due to the complex nature of traffic dynamics and limited data collection. Existing methods either require prior knowledge of shockwaves to detect them in specific traffic scenarios or are capable of detecting only partial shockwaves with approximated propagation speed. To address these limitations, this study develops an eFfective online ShockWave deTection and Inpainting approach using vehicle trajectory data (labeled as SWIFT) collected in broad traffic scenarios. Briefly, first noticing the correlation between turning points for piecewise linear regression and breakpoints on each individual trajectory curve where a vehicle experiences significant speed changes, we develop a novel automatic breakpoint identification method by renovating the piecewise linear regression with shockwave features’ constraint. Next, we design an adaptive data-driven online shockwave detection approach that operates without any prior knowledge of shockwaves. This approach sequentially classifies and connects breakpoints based on shockwave propagation characteristics to generate distinct piecewise linear shape shockwave traces with mathematically guaranteed error bounds. Considering the shockwaves detected from data-driven approaches are usually incomplete, we establish the theoretical foundation including critical definitions, corollaries, and a theorem to guide shockwave inpainting and missing shockwave revealing based on the geometry representation of shockwave features. Built upon that, we develop a generative algorithm that verifies shockwave endpoints one by one based on partial trajectory data to repair incomplete shockwaves and reveal missing shockwaves. The numerical experiments using the NGSIM dataset demonstrated the accuracy, adaptiveness, and robustness of the SWIFT under various data collection settings (e.g., penetration rates, detection window sizes, sampling intervals) and different traffic scenarios.