# Driving Behavior Modeling Based on Consistent Variable Selection in a PWARX Model
## 1 Introduction
Therefore, through the application of hybrid system modeling, the decision-making and motion-control facets can be simultaneously synthesized, leading to higher-level understanding of human driving behavior. The piecewise affine autoregressive exogenous (PWARX) model is commonly used as the mathematical model to identify hybrid systems. Numerous algorithms have been proposed for the PWARX model identification [38; 39; 40; 41; 42; 43]. However, the issue of estimating or selecting the optimal number of sub-models (modes) is still persistent [44; 45; 46]. Considering driving behavior modeling in particular, recent works have demonstrated the effectiveness of using mode segmentation [47; 48; 49]. In [47], a hierarchical PWARX model was used to model driving behavior, [48] exploited the PWARX model for the design of an assist system for the driver and [49] used a stochastic ARX (SS-ARX) to model the human driving behavior. The assumption in these works is that the explanatory variables are consistent across all modes (i.e., the explanatory variables do not change from one ARX region to another). The drawback of this assumption is that the flexibility of the model is reduced, hence increasing the likelihood of the model performance being restricted. In addition, if the explanatory variables are allowed to vary from one mode to another, by introducing, for example, statistical variable selection [50], the motion-control facet could be analyzed and understood at a higher level. Therefore, the resulting model is simpler and facilitates online application because of the reduced computational cost. In addition, personalized driver preferences could easily be identified and embedded for ADAS design. The results shown in [47; 48; 49] are questionable to apply in the real world since driving simulator data, instead of real-road driving data, were used in these works. Lastly, the issue of how to decide the optimal number of modes was not addressed, and the number of modes was chosen manually. In [51], [PERSON] et al. demonstrated the usefulness of allowing flexibility in form of statistical variable selection within the hybrid system modeling when modeling driving behavior. In particular, driving behavior in the motion facets could be understood at a higher level with results showing that the variables influencing the dynamics in each region change from one region to another. However, the mode segmentation was carried out manually based on the range band. This gives little insight into understanding the driver's decision making and model structure (transition between modes) in general. In addition, the robustness of the model to change in data was not considered. Giving that driving behavior changes over time depending on surrounding environment, driving time, driver's mood, etc., developing a model which is consistent in the sense that the model should be robust to a slight change in the training data should be addressed for automated driving and designing driver's assistance systems. In this paper, a hybrid system identified by a PWARX model for modeling human driving behavior is proposed, wherein the mode segmentation is carried out automatically, and the optimal number of modes is decided by a novel methodology based on consistent variable selection (Section 2.4). In addition, model flexibility was added within the ARX partitions in the form of statistical variable selection. The resulting model is an optimal basal model that is not affected by a slight change in the training data, where the explanatory variables are allowed to vary within each ARX region. In the proposed model, the driving data used were collected on a real road which is one of the important points of this work. Information that expresses the relationship between the ego vehicle and surrounding traffic agents such as distance to the leading vehicle, time to collision (TTC), range rate, etc. are collected using 3D LiDAR and camera sensors.