Beyond 1D and oversimplified kinematics: A generic analytical framework for surrogate safety measures

This paper presents a generic analytical framework tailored for surrogate safety measures (SSMs) that is versatile across various highway geometries, capable of encompassing vehicle dynamics of differing dimensionality and fidelity, and suitable for dynamic, real-world environments. The framework incorporates a generic vehicle movement model, accommodating a spectrum of scenarios with varying degrees of complexity and dimensionality, facilitating the estimation of future vehicle trajectory evolution. It establishes a generic mathematical criterion to denote potential collisions, characterized by the spatial overlap between a vehicle and any other entity. A collision risk is present if the collision criterion is met at any non-negative estimated future time point, with the minimum threshold representing the remaining time to collision. The framework's proficiency spans from conventional one-dimensional (1D) SSMs to extended multi-dimensional, high-fidelity SSMs. Its validity is corroborated through simulation experiments that assess the precision of the framework when linearization is performed on the vehicle movement model. The outcomes showcase remarkable accuracy in estimating vehicle trajectory evolution and the time remaining before potential collisions occur, comparing to high-accuracy numerical integration solutions. The necessity of higher-dimensional and higher-fidelity SSMs is highlighted through a comparison of conventional 1D SSMs and extended three-dimensional (3D) SSMs. The results showed that using 1D SSMs over 3D SSMs could be off by 300% for Time-to-Collision (TTC) values larger than 1.5 s and about 20% for TTC values below 1.5 s. In other words, conventional 1D SSMs can yield highly inaccurate and unreliable results when assessing collision proximity and substantially misjudge the count of conflicts with predefined threshold (e.g., below 1.5s). Furthermore, the framework's practical application is demonstrated through a case study that actively evaluates all potential conflicts, underscoring its effectiveness in dynamic, real-world traffic situations.