TopoEKF: From State-Space Estimation to Topological Signatures for Enhanced Multi-Object Tracking and Anomaly Detection in UAVs
Rabia Kıratlı1, Hatice Ünlü Eroğlu2, Alperen Eroğlu1,*
1 Department of Computer Engineering, Necmettin Erbakan University, Konya, Türkiye
2 Department of Mathematics and Computer Science, Necmettin Erbakan University, Konya, Türkiye
* Corresponding Author: Alperen Eroğlu. Email: 
(This article belongs to the Special Issue: Innovative Applications of Fractional Modeling and AI for Real-World Problems)
Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.081411
Received 02 March 2026; Accepted 27 May 2026; Published online 18 June 2026
Abstract
Reliable multi-object detection and tracking play a critical role in Unmanned Aerial Vehicles-based aerial surveillance applications operating under challenging real-world conditions. This study presents a mathematically grounded, model-driven tracking framework named TopoEKF, which integrates an enhanced Adaptive Extended Kalman Filter with Topological Data Analysis to improve both tracking robustness and anomaly detection performance. Unlike prior approaches that primarily focus on refining object detection architectures, this work emphasizes the predictive power of iterative Bayesian filtering, optimal state estimation, and adaptive error minimization within a unified mathematical framework. The proposed system employs a carefully optimized YOLOv12 detector to provide accurate object location priors, followed by a formally defined discrete-time linear Gaussian tracking model. The Adaptive EKF is leveraged to handle nonlinearities arising from the projection of three-dimensional object motion onto the two-dimensional image plane through local linearization. To further enhance robustness under low resolution, large object-to-image distances, frequent occlusions, and environmental noise, TopoEKF introduces adaptive noise covariance modeling driven by measurement confidence, occlusion status, and topological feedback. Persistent homology is applied to EKF-filtered trajectories to extract topological signatures that characterize the global structure of object motion. These features are transformed into fixed-dimensional representations and processed by an unsupervised Isolation Forest classifier for trajectory-level anomaly detection. Experimental evaluations are conducted on a challenging hybrid dataset combining scenarios from COCO, VisDrone, UAVDT, Road_Anomaly_Dataset, and DoTA benchmarks. Quantitative results demonstrate that TopoEKF improves Multi-Object Tracking Accuracy from
72.8% to
76.3% and reduces identity switches by approximately
34% compared to a standard EKF baseline. The enhanced EKF achieves up to 20% higher robustness in highly noisy and indoor environments while maintaining real-time performance at 28.5 frames per second on resource-constrained embedded platforms. In the anomaly detection stage, the integration of persistent homology–based features improves the F1-score from
66% to
84%, with substantial gains in both precision and recall. Overall, the proposed approach highlights the effectiveness of interpretable, mathematically founded state estimation models as a reliable and efficient alternative to black-box deep learning systems in safety-critical UAV applications.
Keywords
Extended Kalman filter; UAV tracking; multi-object tracking; mathematical modeling; Bayesian estimation; YOLOv12; topological data analysis; persistent homology
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