# Modified Uncertainty Error Aware Estimation Model for Tracking the Path of Unmanned Aerial Vehicles
###### Abstract  
Recently, with the advancement of technology, unmanned aerial vehicles (UAVs) have had a significant impact on our daily lives. UAVs have gained critical importance due to their potential threat. In this study, the problem of UAV tracks were investigated. The first study deals with a particle filter (PF) and a diffusion map with a Kalman filter (DMK). From the experimental analysis, it is found that both PF and DMK are very suitable for drone tracking because the trajectories of drones are highly uncertain in highly dynamic and noisy environments. To address this problem, we introduce a Kalman filter (KFUEA) for drone tracking based on uncertainty and error. The KFUEA uses regularized least squares (RLS) to minimize measurement errors and provides an appropriate balance between confidence in previous estimates and future measurements. The experiment was conducted to evaluate the performance of KFUEA compared to PF and DMK, taking into account the high uncertainty and noisy UAV tracking environment. The KFUEA algorithm achieved an excellent result in the root mean square error (RMSE) compared to the non-parametric filtering algorithms PF and DMK. drones; tracking; UAVs detection; radar; RLS +
Footnote †: journal: Applied  
drones. As indicated in [12], drones are much more difficult to detect than manned aircraft; therefore, governments and law enforcement agencies are developing new strategies to detect and track drones. Remote control [13], computer vision [14], and radar detection [15] are usually used to detect drones. Figure 1 shows how UAVs/Drones communicate with the ground control system. Radar-programmed target identification is a common application in radar organizations. A stationary radar is usually used to detect objects. In contrast, there are various mobile radars, such as ship-born and airborne. Space-borne and vehicle-borne radars are used to track objects. The load-carrying capability of the drone makes it possible to detect objects using onboard radars. Synthetic-aperture radar (SAR) and pulse Doppler radars are commonly used in drones. Equipped with onboard radar, these UAVs can be used for surveillance, search, interception, and tracking of ground objects, etc. However, the existing methodologies [16; 17; 18] focused on the detection and identification of UAVs; but did not take into account the continuous tracking of drones or their trajectories. Continuuous tracking and measurement of the trajectory is a state estimation problem. The Kalman filter (KF) is a widely used radar-based stochastic linear measurement model [19]. However, in most application scenarios, a nonlinear environment is very common. References [20; 21] employed KF and modeled an unscented Kalman filter (UKF) and an extended Kalman filter (EKF), respectively. These models used different linearization methods for linearizing the nonlinear functions using KF. References [22; 23] presented unbiased converted measurement Kalman filter (UCMKF) and converted measurement Kalman filter (CMKF) for modeling random errors considering dynamic motions. In [24], covariance matrix errors are dynamically optimized, taking fixed speeds into account. With this method, an ideal estimation condition with minimal convergence time and low computational costs is achieved, taking different signal-to-noise ratios (SNR) into account. One way to reduce computational costs is to use two operators, namely the Perron-Frobenius operator and the Koopmans operator. The Perron-Frobenius operator defines the evolution of the probability density, and the Koopmans operator defines the temporal evolution of observables that describe a functional space of infinite dimensions [25; 26]. In [27], a nonparametric KF was constructed by approximating the Koopmans operator using extended  
Figure 1: UAVs/Drones communication. dynamic mode decomposition (EDMD) [28,29]. However, this model requires multiple trajectories of the environment to update the measurements.