# Radar-Based Target Tracking Using Deep Learning Approaches with Unscented Kalman Filter
## 3 Simulation Analysis and Results
### Results of DL
For evaluating the performance of the system, which incorporates DL models with UKF, five different scenarios were designed. Table 4 shows the values for those scenarios. The fifth scenario from Table 4 is chosen to display the simulation result. The Monte Carlo method was used to model the nonlinearities in the target motion and measurement models, which allows for more accurate predictions of the target's state. The following graphs present the results of this study. Figure 12(a) displays the true path of both the target and observer, as well as the estimated path of the target achieved through the utilization of the UKF algorithm. The standard deviations implemented in the UKF algorithm are determined based solely on human intuition and experience, with an assumption of being within the range of 0 to 3 degrees. The UKF algorithm alone has demonstrated efficaciousness in estimating the unknown states of the target as expected. Where xo, yo, and zo are the observers' x, y, and z coordinates. xt, yt, and zt are the target's x, y, and z coordinates. prxt, pryt, and przt are the estimated x, y, and z coordinates. Figure 12(b)-e depict the true path of both the target and observer, as well as the estimated target path achieved through the integration of GRU, LSTM, MLP, and CNN, respectively, into UKF. For comparative purposes, the accompanying graphs depict a combination of the mean square error for range, bearing, elevation, course, and speed of all model predictions. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{_scar_} & \multirow{2}{*}{\(\delta_{mg}\) **(m)**} & \multirow{2}{*}{\(\delta_{mg}\) **(deg)**} & \multirow{2}{*}{\(\delta_{dev}\) **(deg)**} & \multirow{2}{*}{_rng_ **(m)**} & \multirow{2}{*}{\(\mathbf{brg}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{V_{t}}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{V_{u}}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{cdev}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} & \multirow{2}{*}{\(\mathbf{tcr}\) **(deg)**} \\ \hline
1 & 11.4183 & 0.0576 & 0.073 & 49,076 & 44 & 319 & 41 & 68 & 89.90 & 120 & 119 & 116.4 \\ \hline
2 & 13.2466 & 0.0424 & 0.041 & 45,972 & 268 & 507 & 33 & 54 & 269.9 & 100 & 239 & 115.5 \\ \hline
3 & 12.4102 & 0.0617 & 0.071 & 56,902 & 330 & 213 & 38 & 76 & 270.0 & 60 & 300 & 55.5 \\ \hline
4 & 9.8108 & 0.0448 & 0.085 & 47,861 & 137 & 651 & 31 & 43 & 90.00 & 53 & 60 & 56.4 \\ \hline
5 & 11.6255 & 0.0821 & 0.076 & 57,338 & 351 & 287 & 37 & 58 & 270.0 & 65 & 300 & 63.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scenario parameters and initial conditions for DL-UKF. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{4}{c}{**MSE**} \\ \cline{2-5}  & **MLP** & **CNN** & **LSTM** & **GRU** \\ \hline \(\delta_{mg}\) (in m) & 1.81981 & 1.45124 & 0.54328 & 0.3335 \\ \(\delta_{\text{brg}}\) (in deg) & 1.59 \(\times\) 10\({}^{-08}\) & 1.32 \(\times\) 10\({}^{-08}\) & 4.84807 \(\times\) 10\({}^{-09}\) & 3.2981\(\times\)10\({}^{-09}\) \\ \(\delta_{\text{elev}}\) (in deg) & 1.61 \(\times\) 10\({}^{-08}\) & 1.37 \(\times\) 10\({}^{-08}\) & 5.46733 \(\times\) 10\({}^{-09}\) & 4.0326\(\times\)10\({}^{-09}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of LSTM, GRU, CNN, and MLP Models during training. Figure 14 showcases a comparative model performance analysis integrated into the UKF algorithm. The predictions made by the UKF algorithm were used as the benchmark to establish a reference for analysis.