## 3 Proposed Method  
### Driving Intention Estimation  
It can be assumed that all drivers simply have two intentions: lane-keeping and lane-changing. When a driver is satisfied with a current driving condition, he/she may keep a current lane and only focus on maintaining a safe distance from the preceding and following vehicles. However, if the driver is in a state of dissatisfaction with the current driving condition, he or she may try to change a lane. For the trajectory prediction, this paper defines the driving intentions more specifically as shown in Figure 4.  
When a driver has an intention of keeping, the driver control the speed for maintaining a safe distance from the preceding vehicles. By contrast, changing expresses an intention to start changing a lane until crossing the lane marking. The intention of arrival represents a step until the vehicle reaches the center of the target lane, after it is over the lane marking. When a driver has an intention of adjustment, drivers start to adjust the speed with respect to vehicles on the target lane.  
The proposed method defines each intention as a class and treats the estimation of driving intentions as a multiclass problem using the SVM. Two features representing the lateral movement of the target vehicle are extracted: the distance from the centerline and the lateral speed. In addition, one feature is extracted to describe the driving condition around the target vehicle. Details on how to extract the features are described in our previous work [26]. The feature vector at time \(t\) can be represented as follows.  
\[\mathbf{x}_{t}^{(k)}=\left[\mathbf{d}_{t}^{(k)}\ \ \mathbf{\dot{d}}_{t}^{(k)}\ \ \mathbf{p}_{t}^{(k)}\right]^{\mathrm{T}}, \tag{1}\]  
\[\mathbf{d}_{t}^{(k)}=\left[d_{t-(W-1)}^{(k)}\...\ d_{t-1}^{(k)}\ \ d_{t}^{(k)} \right], \tag{2}\]  
\[\mathbf{\dot{d}}_{t}^{(k)}=\left[d_{t-(W-1)}^{(k)}\...\ \dot{d}_{t-1}^{(k)}\ \ \dot{d}_{t}^{(k)} \right], \tag{3}\]  
Figure 4: Definition of driving intentions: driving intentions may correspond to four classes: keeping, changing, arrival, and adjustment.  
\[\mathbf{p}_{i}^{(k)}=\left[p_{t-(W-1)}^{(k)}\...\ \ p_{t-1}^{(k)}\ \ p_{t}^{(k)} \right], \tag{4}\]  
where \(k\) is the index that denotes the lane marking. Both left and right lane-changing can be adapted. Depending on the lane-changing side, all features are extracted by the specified side. Moreover, a moving window is set, as the lane-changing is a continuous process. \(W\) denotes the size of moving window in Equations (2)-(4), and it is a parameter to determine the sequence memory for the continuous process. For instance, the distance from the centerline, \(\mathbf{d}_{t}^{(k)}\), is a sequence that consists of the \(W\) data until the time \(t\).  
The SVM kernel converts features from a low-dimensional space into a high-dimensional space to handle the complexity of driving intentions, which may lie in a high-dimensional feature space. The proposed method uses the radial basis function known to provide the best performance. A one-versus-one strategy is implemented in the proposed method for the multiclass classification. Finally, the intention at the current time step of each adjacent driver is the output in this part.