# Modified Uncertainty Error Aware Estimation Model for Tracking the Path of Unmanned Aerial Vehicles
###### Abstract
Recently, geometry and manifold learning have been used for nonparametric state estimations considering the stochastic environment [30]. References [30,31] probability-based methods were used by constructing a diffusion map (DM) [32] along the coordinates; here, the probability density function is used for state estimation without prior knowledge of the environment. In [33], modeled ensemble KF for the dynamic estimation [34] is modeled; here, the time delay is measured using nearest neighbors. In [25], the relation between DM and the Koopmans operator [35] is discussed. In [36], a state estimation mechanism for stochastic environments was modeled, namely diffusion-KF (DMK). The model uses DM [32] and KF, considering minimal environmental knowledge. The model considered a series of noise measurements using an unknown nonlinear stochastic function and showed that the linear state model of an unknown environment could also be measured in a highly nonlinear environment. Here, DM is used to construct virtual state coordinates and their inherent dynamics [37]. The KF is modeled with the recovered model; the measurement model is efficient for multidimensional systems due to the nonlinear dimensionality reduction achieved by the diffusion map. However, the DMK fails immensely when the noise in the environment increases. Therefore, in [38,39], the regularized least square (RLS), together with the KF, is used with good results to create an invariant noise filter. However, these models optimize the measurement considering worst-case scenarios in a high-uncertainty environment, which significantly affects the measurement update. In order to obtain efficient measurements in multidimensional, nonlinear, stochastic, and dynamic environments, this paper presents an improved Kalman filter measurement model using a regularized least-squares problem, namely, KFUEA. The KFUEA estimation model is robust in a highly dynamic, noisy environment. The main significance of this work is as follows. The KFUEA algorithm for tracking UAV reduces the measurement error in nonlinear, stochastic, and uncertain noisy environments. The standard filtering method generally upper bounds the subsequent estimate under the Gaussian hypothesis; however, in certain circumstances, the ideal estimate is the prior rather than the subsequent. However, the KFUEA-based tracking method aims to achieve a good trade-off between the upcoming measurements and the previous estimates in dynamic, uncertain, and noisy environments. The behavioral pattern is incorporated into the measurement model through stochastically controlled noise, with absolute parameters that account for the dynamics of the estimate; the resulting filter is nonlinear and robust. To our knowledge, no work has yet addressed such a robust filtering mechanism. The manuscript is organized as follows. Section 2 presents UAV tracking with the KFUEA algorithm in a noisy and unknown environment. In Section 3, an experiment is conducted to account for uncertainties and noisy trajectory patterns, and the RMSE results of KFUEA, PF, and DMK are discussed. In Section 4, conclusions and future opportunities to improve the UAV tracking model are discussed.