Abstract
The paper proposes a rear-end collision warning system for drivers, where how to learn the risk of collision is critical. In the proposed system, the time-to-collision (TTC) assuming a constant relative acceleration is employed as a subjective index of risk, which is justified from both the mechanical and psychological viewpoints. This is referred to as the second-order TTC (TTC2) since Newtonian mechanics in a constant acceleration leads to a quadratic equation.
In our studies based on the originally collected data in an unconstrained drive, it is found that a driver uses the brake pedal of the vehicle before the index of risk reaches a threshold. In other words, when the index exceeds the threshold, the situation is dangerous and hence the system should produce an alert.
In fact, however, the threshold varies from driver to driver and from situation to situation. Moreover, the value slightly depends on other factors such as the velocity of the vehicle and the relative distance from the preceding one. Hence, the system has to adapt the threshold to the driver's characteristics, that is, it detects anomaly of the TTC2 as well as learns the threshold from the data. One method to realize it is the one-class support vector machine (OCSVM), that produces a small support of density function for a given probability. Since the OCSVM learns data in batch mode, we combine it with an online learning technique, so that the system continuously adapts to any driver and/or any situation.
In implementing the online system, the anomalies in the dataset must be removed, or the sensitivity of the system is getting worse. Hence, we propose to a data selection system. The system models the brake sequences in the training data with hidden Markov models and evaluates the likelihood of a new sequence. When the sequence has a high likelihood, it is used for training. Otherwise, it is thrown away. To confirm the effectiveness of our system, we carried out some computer simulations. The results show that the system improves the robustness of the warning system.
Keywords: collision warning system, time-to-collision, data selection, support vector machine