# Multi-Tag Fusion Localization Method Based on Geometric Constraints
## 1 Introduction  
Localization is fundamental to vehicle planning, control, and subsequent tasks, essential for the integrity of vehicle functions [1; 2; 3]. The most common positioning technology is Global Navigation Satellite System (GNSS); however, not all scenarios offer ample and reliable signals, such as urban canyons, parking lots, tunnels, and indoor areas [4; 5]. Visual tag positioning technology has become increasingly prevalent across a spectrum of applications, including robotics [6; 7] and Unmanned Aerial Vehicles (UAVs) [8; 9], offering innovative solutions for the precise positioning of intelligent transport systems. By employing tags with predefined coordinate information, this technology achieves centimeter-level accuracy in positioning, which is crucial for various mobile platforms, including but not limited to automotive applications. Despite the low cost and capability for absolute positioning of visual tags [10; 11], they still face issues of inaccuracy and instability. During the localization process utilizing tags, the detection quality is significantly influenced by the distance and rotation angle between the camera and the tag [12]. The precision of the system is also impacted by the number and position of the tags within the image. Furthermore, lighting conditions can affect the accuracy of tag detection, particularly for tags like AprilTag [13]. It is crucial that the tag size is substantial enough to offer adequate information while remaining within the camera's field of view [14]. There are three main approaches to address these issues: improving the detection accuracy of individual tags, fusing individual tag data with other sensor information, and increasing the number of tag detections. To enhance positioning accuracy, some researchers have focused on improving marker detection accuracy. Two processing techniques were proposed by [15], including a method that can filter out very inaccurate detections resulting from partial border occlusion, and a new highly accurate method for edge refinement. Based on observations, ref. [16] proposedimprovements include trigonometric yaw angle correction for camera alignment, real-time tag center tracking via a custom yaw-axis gimbal, and a novel pose-indexed probabilistic sensor error model for AprilTag utilizing Gaussian Processes and validated by particle filter tracking. In the process of vehicle movement, ref. [17] found that the marker detection error ranged from 0.028 m to 0.13 m. To reduce pose jitter, they designed a strategy to constrain the inner and outer corner points of the markers, limiting the relative error between markers to within 0.05 m.  
Meanwhile, fusing marker information with other data can also improve positioning accuracy. Ref. [13] described an algorithm that improves the pose estimation accuracy of square fiducial markers in difficult scenes by fusing information from RGB and depth sensors. Ref. [18] utilized particle filtering techniques to fuse data from ArUco markers and sonar sensors, achieving effective integration of multi-source sensor information. Ref. [19] introduced a variational Bayesian estimator for mobile robot localization with unknown noise covariance, utilizing tags as landmarks and an onboard camera. By treating the unknown measurement noise covariance as a random matrix following an inverse Wishart distribution, the method simultaneously estimates the robot pose. Ref. [20] proposed an on-manifold extended Kalman filter for tag-based visual-inertial localization, addressing the topological structure of rotation and pose groups and associated uncertainty propagations. Ref. [21] combined the robustness of makers to environmental uncertainty with motion data to minimize the required number of tags. An Iterative Extended Kalman Filter (IEKF) is employed to fuse visual and motion information, and an area detection algorithm is introduced to accelerate AprilTag processing.