## 1 Introduction
However, the IMU error will continue to accumulate in the case of long distances, so the localization error is still increasing in such cases. To solve this problem, IMU and lidar are generally coupled via a tight coupling method that usually offers improved accuracy. A tightly coupled lidar inertial odometry and mapping framework (LIO-Mapping) is introduced in the literature [26]. It comprises the state optimization for the odometry and the refinement with rotational constraints. Results showed that this method outperformed the state-of-the-art lidar-only and loosely coupled methods. Since LIO-Mapping is designed to process all sensor measurements, real-time performance is not achieved. The authors of [27] proposed a tightly coupled Lidar Inertial Odometry via Smoothing and Mapping (LIO-SAM) based on LeGO-LOAM. LIO-SAM performs highly accurate, real-time mobile vehicle trajectory estimation and map building, suitable for multi-sensor fusion and global optimization. Although the tight coupling of lidar and IMU can improve the localization accuracy, lidar sensors have certain drawbacks. Conventional lidar can only be used to scan the environment in a narrow range of vertical angles and the point cloud feature information obtained is limited. For example, in an indoor corridor or staircase environment, lidar can receive the point cloud information of the sidewall, but only a tiny part of the point cloud information is obtained from the floor and ceiling. In such cases, the matched lidar features can easily cause ill-constrained pose estimation and incomplete mapping. Aiming to broaden the FOV of lidar, lidars can be actuated in a number of ways. The periodic nodding and continuous rotation can be adopted and the resulting configurations can potentially enlarge the FOV. While the implementation of this method depends on a complex mechanical structure, the localization accuracy is relatively low [28; 29]. More recently, a new design for a 3D sensor system was introduced [30], involving construction from a 2D range scanner coupled with a passive linkage mechanism, such as a spring. However, the system requires reasonably continual excitation to induce motion of the sensor head. Therefore, the system is not considered appropriate for electric ground vehicles operating with infrequent accelerations on smooth terrain. In order to solve the above problems, some researchers have started investigating the use of multiple 3D lidars for better coverage of the environment. In [31], a high-precision lidar odometry system was proposed to achieve robust and real-time operation under challenging perceptual conditions. In this system, the two lidars are mounted at 180 degrees to each other to make up for the self-similar areas with low lidar observability. The authors of [32] proposed a system to achieve robust and simultaneous extrinsic calibration, odometry, and mapping for multiple lidars, while [33] proposed a scheme to combine multiple lidars with complementary FOV for feature-based lidar-inertia odometry and mapping. While the above methods can work well in single-scene applications, their adaptability to different environments was not considered, especially the environments that need to perceive height information. This paper proposes a high-precision SLAM framework based on tight coupling of dual lidar inertial to overcome the above problems. In this framework, the horizontal lidar and the vertical lidar are integrated to broaden the FOV. Then the dual lidar and IMU are tightly coupled to improve the localization accuracy. In the outdoor environment, this paper introduces GPS measurements to further improve positioning accuracy. The main contributions of this paper include:  
1. A general high-precision SLAM framework is provided by fusing different sensors. It can adapt to multi-scene applications, such as a corridor with fewer features, stairs with height, and complex outdoor environments. 2.