## 1 Introduction
[PERSON] et al., proposed a close coupling method of inertial navigation and radar to carry out real-time positioning for vehicles [16]. The positioning accuracy can reach centimeter-level, but ordinary radar will weaken or even lose signals in long subsea tunnels. Therefore, this method may not be applicable to such scenarios. [PERSON] uses image sequences and wheel-inertial ego-motion results to build a local environment map and matches it with the electronic map to locate the vehicle [17]. [PERSON] et al., proposed a multi-sensor fusion slam method for vehicle location [18]. [PERSON] proposed a vehicle autonomous positioning method based on terrain relative navigation [19]. This method matches the terrain data collected by the vehicle during driving with the pre-established topographic map, so as to estimate the position of the vehicle on the topographic map and realize the position of the vehicle on the structured road. References [17; 18; 19] all proposed the use of electronic maps to accurately locate vehicles. Although this method has high accuracy (including high-precision lateral positioning), however, the establishment of electronic maps or topographic maps requires some real vehicle experiments to obtain topographic data first, which is a huge work and requires a lot of time, and once there is construction in a certain section, the previously established map data may not match with the actual situation. In this paper, a vehicle lateral positioning algorithm based on heading angle calculated by inertial navigation is proposed to provide high accuracy for vehicle lateral positioning when the GPS signal is locked for a long time. Strapdown inertial navigation uses the quaternion method to update attitude and provide heading angle information. The lane change can be determined by the difference in heading angle in adjacent time. The monocular camera is used to identify and fit the lane lines and calculate the slope and \(x\)-axis intersection of the fitted lane lines in the image to assist in determining whether the lane change occurs. A lane change can be identified only when the monocular camera and the heading angle difference simultaneously judge the lane change. The odometer provides information on the distance the vehicle passes in the process of lane change. The lateral displacement of the vehicle can be calculated by combining the difference between the heading angle at the end of a lane change and the beginning of a lane change with odometer data, which has high accuracy. A binocular camera is used to measure the distance between the vehicle and the lane line and the lane width to provide the initial input for the algorithm. The system proposed in this paper has the following improvements: (1) Most of the traditional inertial navigation and positioning technologies are aimed at the longitudinal positioning of vehicles, and because of the cumulative nature of inertial navigation errors, the positioning error of vehicles will increase with the accumulation of time. The system proposed in this paper is only for the vehicle lane change and overtaking process. The vehicle lane change and overtaking process time is very short, and inertial navigation can provide high accuracy in a short time. The lateral displacement of the vehicle can be calculated by calculating the heading angle of the vehicle through inertial navigation, calculating the difference in heading angle of the vehicle after changing lanes or overtaking, and then combining it with the odometer to calculate the distance information of the vehicle during the driving process. The algorithm has good accuracy and fast computation speed. (2) While many researchers use monocular cameras to calculate the lateral distance of vehicles, this paper proposes to measure the distance of vehicles from the lane line using binocular cameras, the main implementation of which is to mount the binocular camera under the rearview mirror of the vehicle to take a top view of the lane line.