Background: In order to help reduce rear-end collisions, a forward vehicle collision warning system has been developed and deployed. The effectiveness of the system largely depends on how early the warning can be given. However, we also need to consider that too early warning may cause a nuisance because the driver may not feel any avoidance maneuver is necessary at the timing. If the system can alert the driver by detecting the absence of braking at the normal timing based on his/her longitudinal risk estimate, the warning can be acceptable without nuisance. In order to achieve the goal, we aimed to develop an index of the driver's perceptual estimate of longitudinal risk.
Method: First, we hypothesized that a driver judges when to brake based on two kinds of perception: kinematic perception to approach a lead vehicle and dynamic perception when the lead vehicle decelerates. Each perception was derived from previous studies of human perception. Then, an index of the longitudinal risk estimate reflecting these kinds of perception was proposed. The index is formulated as "perceptual relative velocity" divided by "perceptual distance." Both elements are corrected from their physical value so as to reflect their perceptual magnitude. The perceptual distance is the exponent of the distance between the subject vehicle and the lead vehicle. The perceptual relative velocity is the velocity difference of these two vehicles that is corrected by the subject vehicle's velocity and their relative acceleration. The hypothesis was tested on test track using two actual vehicles with the combination of various relative velocities and accelerations.
Result: It was found that drivers' brake timings were well matched to the hypothesis; they braked when the proposed index reached a certain threshold. Thus, the index was confirmed to be able to measure driver's longitudinal risk estimate. We call the index Perceptual Risk Estimate (PRE). Since PRE can describe perceptual longitudinal risk, it is natural to consider that it also can predict the timing when a driver starts steering avoidance maneuver. The timing, i.e., the parameters of PRE, may be different from that of braking, though. We again tested with actual vehicles and found that PRE also matches to steering avoidance timing, and as we expected, the parameters were different from the ones for brakes. Finally, PRE was compared with other indices (TTC, THW, Risk Perception (RP), and KdB_c) and it was shown that the PRE is a comprehensive and enhanced model of those indices.