## 1 Introduction  
The problem of localization and map-building for mobile robots, which is the basis for achieving autonomous navigation, has become a hot research topic. To solve the indoor and outdoor localization problems and achieve accurate autonomous navigation, the robot map-building process--a single sensor--cannot complete complex map-building. In simultaneous localization and map-building (SLAM), fusing multiple sensors for map-building has become a popular research topic [1, 2]. Traditional SLAM algorithms usually rely on a single sensor, such as LiDAR or a camera. Still, using a single sensor has some limitations [3]: vision sensors are susceptible to lighting conditions, while object reflections and occlusions limit LiDAR. To overcome these limitations, researchers have started to fuse multiple sensors to improve the accuracy and robustness of map-building [4]. Standard sensors include LiDAR, cameras, inertial measurement units (IMU), GPS, and more. LiDAR provides accurate distance and depth information. IMU can give information about robot attitude and acceleration, and vision sensors can provide visual information about the environment [5, 6, 7]. The choice of fused sensors depends on the specific application scenario and requirements [8]. The map-building algorithm for fusingmultiple sensors involves techniques for calibrating sensor data, data correlation, and state estimation. [PERSON] et al. [9] proposed a USV LiDAR-slam-assisted fusion localization method that combines GNSS/INS localization with LiDAR-slam, which uses different sensor-fusion information and data-feedback correction to achieve the effect in different situations, and obtains data with more stability and observability. [PERSON] et al. [10] proposed an improved Hector-SLAM algorithm by finding that the Hector-SLAM algorithm has the problem of map drift and overlap when constructing maps, which first eliminates invalid laser data and then uses Inertial Measurement Unit (IMU) for compensation, and the method effectively improves the accuracy of the maps and the efficiency of the robot. [PERSON] et al. [11] proposed a map-matching method based on the combination of LiDAR, IMU, and an odometer for point-cloud data, which matches the point-cloud information collected by LiDAR with the known point-cloud data, introduces the point-to-point iterative closest-point algorithm (PP-ICP), and at the same time, the starting point of the autopilot car is set to be the initial coordinates of the point-cloud map data, and then establishes a predictive-state equation composed of the autopilot car's gas-pedal control and steering wheel control of the self-driving car, then selects the predictive-state equations consisting of the throttle control and steering wheel control of the self-driving car. Finally, it utilizes the extended Kalman filter to fuse the information data from the three sensors, to update and correct the localization. Its robustness and localization accuracy meet engineering requirements, but on the other hand, it also increases the computational volume and difficulty of the algorithm. IMU-based fusion methods pose significant challenges in solving time synchronization and measurement delay problems. Researchers have been optimizing the Kalman filter update process to address this issue. [PERSON] et al. [12] proposed an algorithm for estimating the sideslip angle of self-driving cars based on the synthesis of consensus and vehicle kinematics/dynamics. Based on the measurement of the velocity error between the Reduced-Delay Inertial Navigation System (R-INS) and the Global Navigation Satellite System (GNSS), the velocity-based Kalman filter is formalized to estimate the R-INS velocity error, attitude error, and gyro bias error. [PERSON] and [PERSON] et al. [13] fused the information from the Inertial Measurement Unit (IMU) and the Global Navigation Satellite System (GNSS) to align the heading of the GNSS and proposed a method for estimating the sideslip angle based on the vehicle kinematics model. [PERSON] et al.