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

Abstract

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.