# Modified Uncertainty Error Aware Estimation Model for Tracking the Path of Unmanned Aerial Vehicles
## 4 Conclusions  
Tracking UAVs has become more important because they provide not only location-based services but also pose serious security threats and vulnerabilities. UAVs are inherently smaller, move at high speeds, and operate at low altitudes, so it is conceivable to track UAVs with fixed or mobile radars. This paper presents a model for tracking UAVs that is efficient considering the volatility of UAV trajectory in a highly dynamic and noisy environment. Previous methods used particle filters and Kalman filters with diffusion maps to track UAVs. We have generated 1000 samples of trajectories with an interval time of \(\Delta t=0.01\) and varied the signal-to-noise ratio (SNR) by changing the standard deviation of phi and the radius. Then, we applied KFUEA and the state-of-the-art PF and DMF simultaneously to measure and evaluate the tracking performance of the different models.  
In this paper, initially \(x_{l+1}\) and \(z_{l}\) are computed using a modified Kalman filter matrix, an environmental matrix, and a measurement matrix. Then phase prediction is performed. After phase prediction, the phase estimation is updated for the Kalman filter. Then tracking the path of the unmanned aerial vehicle using the computed \(x_{l+1}\) and \(z_{l}\), and the updated phase. The KFUEA employs regularized least squares (RLS) for minimizing measurement error and brings good tradeoffs among preceding estimate confidence and forthcoming measurement under a dynamic environment.  
However, under high uncertainties, the existing models performed very poorly. In the experiments, DMK is found to perform slightly better than PF at low noise levels. However, at higher noise levels, DMK performance deteriorates, and RMSE is slightly lower compared to PF-based UAV tracking methods. Therefore, DMK-based tracking cannot be used in high-uncertainty environments. In contrast, the KFUEA-based tracking model achieves very good RMSE compared to PF-based and DMK-based UAV tracking methods at lower and higher SNR values. Thus, the KFUEA is efficient enough to deal with the uncertain behavior of UAVs.  
The safety of drone tracking is not always guaranteed because different drones have different signatures, and some drones try to mimic the signatures of other drones to avoid tracking. Developing an effective mechanism for tracking and detecting drone signatures is critical to counter malicious drones.  
[PERSON] and [PERSON] contributed to the main idea and the methodology of the research. [PERSON], [PERSON], and [PERSON] designed the experiment, performed the simulations, and wrote the original manuscript. [PERSON], [PERSON], and [PERSON] contributed significantly to improving the technical and grammatical contents of the manuscript. [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] reviewed the manuscript and provided valuable suggestions to further refine the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (grant number: NRF-2016R1D1A1B01011908) and was a part of the project titled 'Marine digital AtoN information management and service system development (2/5) (20210650)', funded by the Ministry of Oceans and Fisheries, Korea. First author was supported in part by Weifang University of Science and Technology Doctoral Fund Project under grant (2021 KJBS13).  
Not applicable.  
The authors declare no conflict of interest.