Abstract
Early positioning concentrates on static natural geographic features, shifting focus to capturing dynamic objects with the emergence of geographic information systems and the growing demand for spatial data. However, previous methods typically rely on expensive devices or external calibration objects for attitude measurement. Here we propose a real-time hybrid framework with a dual-phase strategy that leverages the time-series nature of dynamic objects, combining AI detection with mathematical modeling to estimate relative attitudes via efficient singular value decomposition, thus enabling reference-free 3D coordinate recognition. In particular, we enhance the state-of-the-art You Only Look Once version 12 model by incorporating time-series analysis for rapid and precise 2D detection, which serves as input for 2D-to-3D conversion via our singular value decomposition-based solver. By leveraging data from only three off-the-shelf smartphone cameras, the system achieves accurate and reference-free 3D positioning of a flying UAV. Experimental results demonstrate high precision in terms of RMSE, MAE, and R-squared. Therefore, under sensor-resource constraints, this AI-mathematics fusion enables real-time 3D coordinate recognition without traditional attitude measurement.
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Data availability
The UAV dataset used in this study is publicly available at https://github.com/wordbomb/PoseFree-GeoLocator.
Code availability
The source code is publicly available at https://github.com/wordbomb/PoseFree-GeoLocator. The code was developed using Python with PyTorch v2.3.0 and CUDA 12.1. The benchmark YOLO detector is based on the Ultralytics framework (https://github.com/ultralytics/ultralytics).
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (61803047), and the Social Sciences Fund of Jiangsu Province 24XWB004. Ke-ke Shang is supported by Jiangsu Qing Lan Project and the NJU-China Mobile Joint Research Institute. Michael Small is supported by the Australian Research Council Discovery Grant (DP200102961). Michael Small also acknowledges the support of the Australian Research Council through the Center for Transforming Maintenance through Data Science (IC180100030).
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J.Y. (Co-first author) was responsible for experiment design, linear algebra analysis, coding, data analysis, and drafting the manuscript. K.-k.S. (Co-first author & Corresponding author) contributed to analysis, experiment, and simulation design, supervision, and manuscript writing. M.S. provided guidance and assisted in manuscript reviewing.
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Yi, J., Shang, Kk. & Small, M. Bridging mathematical modeling and AI for 3D coordinate recognition of moving objects without external reference and attitude measurement. Commun Eng (2026). https://doi.org/10.1038/s44172-026-00648-x
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DOI: https://doi.org/10.1038/s44172-026-00648-x
