# Vehicle Lane Change Models--A Historical Review
## 2 Vehicle Lane Change Models
### Mixed Models of Lane Change  
The mixed lane change models can also improve the overall performance by combining the advantages of different models, and thereby obtain a more comprehensive lane change decision. By combining the results of multiple models, the driver's lane change process can be more accurately simulated. In order to improve the safety of vehicle lane change, [PERSON] et al. (2015) proposed a coevolutionary lane change trajectory-planning algorithm (CLTP), as shown in Figure 8. A GRU algorithm optimized by a recurrent neural network (RNN) collects vehicle movement information from adjacent lanes of lane change vehicles. The algorithm adds reset, update, and input modulation gates to the model to finetune the state flow and input flow of historical data. The GRU algorithm optimizes the problem of gradient disappearance and backpropagation in long-term memory. Compared to the LSTM algorithm, the GRU has a simpler training mode and better training model efficiency and performance. The hidden layer of the GRU includes reset and update gates. The reset gate mainly combines the newly entered information with the historical information, and the update gate mainly stores the previous historical information in the current step. The GRU predicts the vehicle track information of adjacent lanes, and the calculation process of each control gate is shown in Equations (9) to (10):  
\[r=\sigma\Big{(}x_{t+1}^{k}U^{t}+s_{t}^{k}W^{t}\Big{)} \tag{9}\]  
\[z=\sigma\Big{(}x_{t+1}^{k}U^{t}+s_{t}^{k}W^{t}\Big{)} \tag{10}\]  
\[h=\ \tan\ h(x_{t+1}^{k}U^{t}\ +s_{t}^{k}\otimes r)W^{h}) \tag{11}\]  
Figure 7: Three typical lane change strategies. Red indicates the target vehicle of the lane change, white vehicle indicates the vehicles around the red vehicle during the lane change process, gray dashed line indicates the path of the red lane change vehicle, and arrow indicates the direction of travel. The left picture indicates that the vehicle successfully completed the lane change, the middle picture indicates that the vehicle did not complete the lane change, and the right picture indicates that the vehicle successfully completed the lane change after waiting in the process of lane change ([PERSON] et al., 2016). In Equations (9) to (12), \(r\) represents the reset gate, \(z\) represents the update gate, and \(h\) represents the contents of the current memory. \(s_{t}^{k}\) represents the memory of the adjacent vehicles \(k\) with the current time step, \(\sigma\) represents the sigmoid activation function, \(x_{t}^{k}\) represents the coordinates \(\left(x_{ij}^{k},y_{ij}^{k}\right)\) of the adjacent vehicles \(k\) at time \(t\), \(U^{i}\) represents the update transfer matrix, \(W^{i}\) represents the weight matrix, \(i=r,z,h\), and the symbol \(\otimes\) represents the multiplication of vector elements. The experiment adopts the natural driving vehicle trajectory data contained in the HighD dataset [136], and the GRU algorithm collects the vehicle movement information of adjacent lanes of lane-changing vehicles in the HighD dataset. Using fault tree analysis [137; 138], as shown in Figure 9, a spatial-temporal risk recognition model of lane change events was established. Based on the overtaking rule of acceleration and deceleration and the ladder acceleration method, the longitudinal and lateral motion schemes during a lane change were planned, and the motion parameters were obtained by using the genetic algorithm. The experimental results effectively improved the safety of a lane change. Figure 8: Schematic diagram of CLTP model [135]. Figure 9: FTA analyzes safe cross-lane change behavior [135]. Vehicles can cause turbulence in the traffic flow when performing dangerous lane changes, and even cause traffic accidents during dangerous lane changes [1; 2]. Therefore, the effective prediction of lane change risk can improve the safety of drivers when making lane changes. [PERSON] et al.