Comparison of Time to Collision and Enhanced Time to Collision at Brake Application during Normal Driving

The effectiveness of Forward Collision Warning (FCW) or similar crash warning/mitigation systems is highly dependent on driver acceptance. If a FCW system delivers the warning too early, it may distract or annoy the driver and cause them to deactivate the system. In order to design a system activation threshold that more closely matches driver expectations, system designers must understand when drivers would normally apply the brake. One of the most widely used metrics to establish FCW threshold is Time to Collision (TTC). One limitation of TTC is that it assumes constant vehicle velocity. Enhanced Time to Collision (ETTC) is potentially a more accurate metric of perceived collision risk due to its consideration of vehicle acceleration. This paper compares and contrasts the distribution of ETTC and TTC at brake onset in normal car-following situations, and presents probability models of TTC and ETTC values at braking across a range of vehicle speeds. The data source of this study was the 100-Car Naturalistic Driving Study (NDS). The study is based on a total of 72,380 trips, resulting in over 870,000 braking events with a closing lead vehicle. The resultant models provide the probability of occurrence across a range of continuous ETTC and TTC. Compared to TTC, ETTC distributions were shown to have lower variance between drivers across all vehicle speed ranges. The current study is the first large scale naturalistic data analysis to characterize probability of brake application in normal driving, and will provide valuable data on driver braking behavior to improve future forward collision warning/mitigation systems.