• Eugenia Yu. Felagereva, Kuban state university (Krasnodar, Russia)
• Nelly R. Rudoman, Kuban state university (Krasnodar, Russia)
• Alexander D. Novikov, Kuban state university (Krasnodar, Russia)

This paper considers the problem of robust tracking of aerial objects in a video stream, with an emphasis on predicting their trajectories in the presence of measurement noise and short-term detection losses. The aim of the study is to develop a hybrid tracking method combining a classical Kalman filter and a GRU-type recurrent neural network to improve the accuracy and robustness of object motion prediction. The proposed approach is based on the use of a Kalman filter to estimate the current state of an object, specified by the coordinate vector of the YOLO bounding box and the velocities [сх,су, w, h, vx, vy],, and a GRU-type neural network model, which is trained to predict the change in velocity Δvx,Δvy based on a sequence of previous states. Unlike traditional methods, where the motion model is specified a priori, in this paper the motion dynamics are partially extracted from the data. GRU predictions are integrated into the Kalman filter model through an adaptive smoothing mechanism with a coefficient α, which allows for flexible adjustment of the contribution of the neural network prediction to the final state estimate. The main content of the paper includes a description of the hybrid model architecture, a methodology for preparing a training dataset, and an algorithm for integrating neural network predictions into the filtering process. Particular attention is paid to the problem of long-term forecasting—up to 30 frames ahead—which is critical for active tracking and control systems. The scientific novelty of the paper lies in the proposed method for combining GRU and a Kalman filter through adaptive smoothing of the control action, which allows for the consideration of nonlinear and nonstationary characteristics of object motion without sacrificing the interpretability of the classical model. Unlike existing solutions, the proposed method ensures more stable operation under noisy measurements and missed detections. Experiments demonstrated that the proposed approach improves trajectory prediction accuracy and reduces error accumulation during multi-step forecasting compared to the classical Kalman filter and basic neural network models. As a result of the experiments, it was shown that the proposed approach increases the accuracy of trajectory prediction by 16.57% and reduces the accumulation of errors in multi-step forecasting by 21% compared to the classical Kalman filter and basic neural network models. The developed method can be applied to unmanned aerial vehicle detection and tracking, video surveillance systems, and autonomous navigation.

Kalman filter, GRU, UAV, positioning

2026-09-03