标题： 动态目标地理坐标识别：基于内在线性代数结构的无姿态和无参考框架 显示英文标题

标题： Dynamic Object Geographic Coordinate Recognition: An Attitude-Free and Reference-Free Framework via Intrinsic Linear Algebraic Structures

摘要： 地球作为一个瞬态复杂系统，正在见证对其坐标系统的研究方向发生转变，从传统的静态定位转向拥抱动态建模。 早期的定位主要集中在静态的自然地理特征上，随着地理信息系统的发展，对空间数据的需求不断增加，研究重点转向捕捉动态对象。 然而，以前的方法通常依赖于昂贵的设备或外部校准物体来进行姿态测量。 我们提出了一种应用数学模型，该模型利用时间序列和动态对象的本质来确定相对姿态，而不需要绝对姿态测量，然后使用基于SVD的方法进行三维坐标识别。 该模型在数值模拟中验证时表现出微小误差，这是计算机数值近似固有的特性。 接下来，为了评估我们的模型在工程场景中的表现，我们提出了一种框架，该框架集成了应用数学与人工智能，仅使用三台摄像机来捕捉无人机。 我们通过利用时间序列增强YOLOv8模型，以实现准确的二维坐标获取，这随后作为输入用于通过我们的数学模型进行二维到三维转换。 结果表明，该框架具有高精度，体现在低误差指标，包括均方根误差、平均绝对误差、最大误差以及较高的R平方值。 需要注意的是，数学方法本身是无误差的；任何观察到的不准确性完全是由外部硬件或基于AI的二维坐标获取过程引起的，这代表了当前最先进的改进版本。 我们的框架通过提供一种简化模型来丰富大地测量理论，用于非合作目标的三维定位，减少输入姿态参数，利用应用数学和人工智能。 显示英文摘要

摘要： The Earth, a temporal complex system, is witnessing a shift in research on its coordinate system, moving away from conventional static positioning toward embracing dynamic modeling. Early positioning concentrates on static natural geographic features, with the emergence of geographic information systems introducing a growing demand for spatial data, the focus turns to capturing dynamic objects. However, previous methods typically rely on expensive devices or external calibration objects for attitude measurement. We propose an applied mathematical model that utilizes time series, the nature of dynamic object, to determine relative attitudes without absolute attitude measurements, then employs SVD-based methods for 3D coordinate recognition. The model is validated with negligible error in a numerical simulation, which is inherent in computer numerical approximations. What in follows, to assess our model in the engineering scenario, we propose a framework featuring the integration of applied mathematics with AI, utilizing only three cameras to capture an UAV. We enhance the YOLOv8 model by leveraging time series for the accurate 2D coordinate acquisitions, which is then used as input for 2D-to-3D conversion via our mathematics model. As a result, the framework demonstrates high precision, as evidenced by low error metrics including root mean square error, mean absolute error, maximum error, and a strong R-squared value. It is important to note that the mathematical method itself is inherently error-free; any observed inaccuracies are due solely to external hardware or the AI-based 2D coordinate acquisition process, which represents an improved version of the current state-of-the-art. Our framework enriches geodetic theory by providing a streamlined model for the 3D positioning of non-cooperative targets, minimizing input attitude parameters, leveraging applied mathematics and AI.