1658434 - Online adaptive shockwave detection and completion based on vehicle trajectory data

Abstract:
This study is devoted to detecting online precise shockwave propagation on a road segment using real-time trajectory data. To adapt to traffic dynamics and non-uniform data collection rates, we discretize time dimension into detection epochs and enable iterative shockwave detection by developing the following methods. We first develop a novel ordinary least square regression model constrained by shockwave features, which describes vehicle trajectory curves as piecewise linear functions, enabling to capture traffic state transitions at trajectory breakpoints. Next, we develop an adaptive wave-growing algorithm (WGA) that sequentially classifies and connects breakpoints to generate distinct piecewise linear shockwave traces with mathematically guaranteed error bounds. The WGA incorporates shockwave propagation rules, nearest neighbor classification, and piecewise linear approximation. It also embeds an optimization model that fine-tunes key parameters such as the search area size to accommodate traffic dynamics and non-uniform data collection. To further enhance the precision of shockwave detection, we develop a shockwave completion theory to adjust the incorrect endpoints of detected shockwaves and reveal the missing shockwaves caused by partial trajectory data and detection errors. Accordingly, we propose a shockwave completion algorithm (SCA) that utilizes discrete trajectory data to iteratively correct four types of errors through five maps. The SCA incorporates two sub-algorithms: geometric disjoint polygon identification and missing shockwave revealing. The numerical experiments using the NGSIM dataset demonstrated the accuracy, adaptiveness, and robustness of our approaches under various data collection penetration rates and complex traffic dynamics.