# Modified Uncertainty Error Aware Estimation Model for Tracking the Path of Unmanned Aerial Vehicles
## 3 Simulation Analysis and Result
### Nonlinear UAV Tracking Environment
From experiment it is seen that DMK clean achieves much better performance when compared with PF. However, with the presence of noise in the measurement model, the DMK noise performs badly when  
Figure 5: The estimations of the clean measurement for different algorithms with an SNR value of 1. (**a**) shows the measurement of \(\tau_{n}\). (**b**) shows the measurement of \(\varnothing_{n}\). compared with PF. Thus, it shows the DMK model is affected due by the presence of noise. On the other side, the KFUEA achieves much better \(nRMSE\) when compared with DMK noise and PF; further, achieve much better performance when compared with DMK without the presence of noise in the measurement model. This proves the robustness of KFUEA for tracking UAV in uncertainty, dynamic, and noisy environments. Figures 7 and 8 show the mean asymptotic RMSE (\(aRMSE\)), which is measured using the following equations  
\[aRMSE=\sqrt{\frac{1}{M}\sum_{k=1}^{M}\|\varepsilon_{n}^{(k)}-\zeta_{n}^{(k)}\| ^{2}} \tag{46}\]  
where \(M\) defines the number of noisy samples considered, \(\hat{\varepsilon}_{n}^{(k)}\) the estimates measured with the filter, and \(\zeta_{n}^{(k)}\) the clean measurement in the instance \(n\) of sample \(k\). Figure 7 shows the results of KFUEA (in red), DMK noisy (in blue), DMK clean (in cyan), and PF (in gray), considering two different SNR levels. Figure 7a shows the \(aRMSE\) outcomes for measurement coordinate \(\varnothing_{n}\) and Figure 7b shows the \(aRMSE\) outcomes for measurement coordinate \(r_{n}\). From the results obtained, it can be interpreted that the convergence rate of KFUEA is not significantly affected due to noise. KFUEA achieves a much better convergence rate compared to PF and DMK when different SNR levels are considered. Figure 8 shows the \(aRMSE\) outcome achieved by KFUEA (in red), DMK (in blue), and PF (in gray) considering two different SNR levels. Figure 8a,c were obtained at an SNR level of 0.67, and Figure 8b,d were obtained at an SNR level of 0.18. From the results, it can be concluded that KFUEA achieves a better convergence rate compared with PF and DMK at different SNR levels. Figure 6: Standard deviation and Mean of \(nRMSE\) of clean measurement estimates; \(nRMSE\) result were averaged over 50 samples of process and noise trajectories. A \(nRMSE\) comparison among KFUEA (in red) with DMK clean (in cyan), DMK noisy (in blue), and PF (in gray). \[\Delta\theta_{n+1}^{(1)}=-\frac{1}{2}\Big{(}\theta_{n}^{(1)}-1\Big{)}^{3}+ \Big{(}\theta_{n}^{(1)}-1\Big{)}+\sqrt{2}u_{n}^{(1)} \tag{42}\]0 Asymptotic Root Mean Square Error (\(aRMSE\)), averaged considering 50 samples of the measurement’s estimations for different algorithm DMK noisy (in blue), DMK clean (in cyan), PF (in gray), and KFUEA (in red). (**a**) shows the \(aRMSE\) outcomes for measurement coordinate \(\varnothing_{n}\). (**b**) shows the \(aRMSE\) outcomes for measurement coordinate \(r_{n}\)  
\[\Delta\theta_{n+1}^{(1)}=-\frac{1}{2}\Big{(}\theta_{n}^{(1)}-1\Big{)}^{3}+ \Big{(}\theta_{n}^{(1)}-1\Big{)}+\sqrt{2}u_{n}^{(1)} \tag{42}\]1 _Cont._  
\[\Delta\theta_{n+1}^{(1)}=-\frac{1}{2}\Big{(}\theta_{n}^{(1)}-1\Big{)}^{3}+ \Big{(}\theta_{n}^{(1)}-1\Big{)}+\sqrt{2}u_{n}^{(1)} \tag{42}\]2 \(aRMSE\), averaged considering 50 samples of the measurement’s estimations for a different algorithm such as DMK (in blue), the PF (in grey), and KFUEA (in red). The SNR level is fixed at 0.67 for cases (**a**,**c**), and the SNR level is fixed at 0.18 for cases (**b**,**d**). The plots (**a**,**b**) show the outcome of \(aRMSE\) achieved for measuring coordinates \(\varnothing_{n}\) and the plots (**c**,**d**) show the outcome of \(aRMSE\) achieved for measuring coordinates \(r_{n}\).