## 1 Introduction  
Transportation is an essential factor in human lives, as it plays an important role in developing civilization. Therefore, recent work on both scientific and industrial sides has focused on constructing an intelligent transport system (ITS), in which autonomous vehicles are arguably the most attractive part [1; 2; 3]. It is partly due to the rapid development of artificial intelligent approaches that their contributions have been shown in several fields in recent years [4; 5; 6]. However, since the final target is completely replacing the traditional vehicles with the autonomous ones, there are still many challenges ahead that need to be resolved. For example, the on-road autonomous vehicles may need to estimate each other's positions to maintain safe distances and make urgent decisions when necessary. Thanks to that, we can avoid traffic accidents and congestion. Therefore, there is an increasing demand for an efficient vehicle-to-vehicle (V2V) positioning solution. Referring to previous studies, many drawbacks that affect the performances of the existing V2V positioning technologies, such as time difference of arrival (TDOA) and light detection and ranging (LiDAR), have been observed [7; 8]. In particular, with TDOA, an estimation result greatly depends on the time measurement, which causes difficulty in obtaining high accuracy in practice. Besides,LiDAR has to face some major limitations such as high cost, complicated installation, high sensitivity to signal interference, and jamming. Compared to these methods, the stereo vision system has some strong points as follows. First, the stereo vision system has an affordable price. Second, it is easily installed and maintained on the vehicle. Third, the stereo vision system can observe the appearance of the objects. Therefore, the stereo vision system can be considered as an alternative for the V2V positioning application. To estimate the world coordinates of the object relative to the camera using the stereo-vision-based approach, initially, this object has to be detected from the captured image. However, it is extremely difficult to directly detect a vehicle at nighttime, since the appearance of the vehicle may become hardly observable due to the inadequate lighting conditions. Instead, most papers focus on detecting the most prominent part of the vehicle at nighttime (vehicle lighting), which is often a taillight [8; 9; 10; 11]. In these papers, they use the stereo vision system, which includes two cameras, on the host vehicle to capture a real scene from two different views. Next, the world coordinates of the front vehicle's taillights can be determined based on the relation between their corresponding pixel coordinates on the two captured images. This helps in estimating the position of the corresponding front vehicle. However, as all of them were based on simulation experiments with a single in-front vehicle, they have not dealt with three serious problems that need to be addressed to locate multiple front vehicles in practice. First, in the urban traffic environment, the cameras would presumably capture several light sources in the front, which may lead to difficulties in identifying the real taillight. Second, with many taillights detected from each image, how can we determine which one in the left image corresponds to a certain one in the right image. The third problem is how to pair every two taillights that belong to the same vehicle so that the vehicle's presence can be confirmed. These three issues, which are respectively termed the detection problem, the stereo matching problem, and the pairing problem, are what we want to address in this paper. Initially, we briefly review what has been done in previous works to deal with each of the above problems as follows:  
(1) Detection problem: Due to the arbitrary shape and size of a vehicle's taillights, it is challenging based on these characteristics to detect the taillight regions from an image, especially in nighttime situations.