# Multi-Tag Fusion Localization Method Based on Geometric Constraints
## 1 Introduction
While single-tag localization techniques have seen significant advancements, they encounter challenges when marker observation is obstructed or incomplete during vehicle movement [22]. This highlights the necessity for a method that can integrate information from multiple markers, especially in environments with partial occlusions or dynamics. Ref. [23] designed an integrated vision and LIDAR robot localization method using two AprilTag tags for pose estimation, proving the stability of the proposed method over single-tag approaches. The third category of methods, which we focus on, involves detecting multiple tags simultaneously and fusing their data. For example, Ref. [24] averages observations from multiple markers and applies a constant velocity motion model for Kalman Filtering (KF) but does not adequately account for variability among different markers. Ref. [17] integrates markers into SLAM and applies the 3\(\sigma\) principle to filter outliers, which may be insufficient with fewer than ten markers as it defaults to ranking pose estimates and selecting the median, potentially not reflecting true poses if the observation distribution is skewed. Ref. [25] fuses IMU data with multiple markers using Extended Kalman Filtering (EKF), which can negatively impact localization accuracy when kinematic predictions significantly deviate from actual conditions. The optimization algorithm presented in [26], fusing multiple ArUco marker data based on the Mahalanobis distance, shares conceptual similarities with our approach but also reports trajectory discontinuities due to marker detection errors, especially when markers are distant or partially occluded. In the aforementioned filtering methods, observation noise is often determined by trial and error. However, ref. [27] discovered that the observation noise of pose from planar fiducial markers varies across the measurement range, a fact that must be considered during sensor fusion for a reliable estimate. They present experimental measurements of fiducial markers in real and simulation scenarios for 2D pose estimation and propose analytical functions that approximate the variances of pose estimates. This paper proposes a multi-tag fusion localization method based on geometric constraints. The approach begins with detecting visual markers to acquire relative pose information between the target and the markers. Following coordinate transformations, the global pose of the target in the world coordinate system is computed. To ensure data accuracy and reliability, geometric constraints are constructed for all observations, effectively eliminating outliers. Subsequently, the filtered and reliable observations are incorporated into a multi-observation fusion framework utilizing a modified KF. This integration facilitates the effective fusion of multiple observations, ultimately leading to precise positioning information. Our main contributions are as follows:  
1. A linear fusion method using only a camera: This method is simple, low-cost, and avoids complexities and potential inaccuracies associated with motion model-dependent predictions. 2. Introducing an outlier factor based on geometric constraints: The outlier factor quantifies the variability among different tags, excluding outliers before fusion and dynamically adjusting observation noise during the fusion process, reducing the likelihood of initial noise settings being unreasonable. The paper consists of several parts. Section 2 introduces common visual tags and provides a detailed description of the AprilTag's detection process. Section 3 describes the outlier handling method before data fusion, focusing on the construction of geometric constraints. Section 4 outlines the fusion approach, utilizing a modified KF for integrating data from multiple tags. Section 5 summarizes the experimental setup and presents the results and analysis. The final section concludes this paper with a summary of the key findings.