# Radar-Based Target Tracking Using Deep Learning Approaches with Unscented Kalman Filter
## 3 Simulation Analysis and Results
### Results of DL  
When training DL models, the true value (label) refers to the actual value of the output variable for input in the dataset. On the other hand, the predicted value refers to the output value predicted by the deep learning model for the same input. The true values were typically known during training because they were included in the labeled dataset used to train the model. The predicted values are obtained by feeding the input data into the model and observing its output. Figures 9-12 show the performance of MLP, CNN, LSTM, and GRU models during training by comparing the true unseen data to predicted data. Only 100 data points were plotted to have a clear view. (a) Shows True against predicted standard deviation in bearing, (b) True against predicted standard deviation in elevation, and (c) True against predicted standard deviation in range. After training, each model was tested and evaluated using mean squared error as evaluation metrics according to Equation (10). \[\text{MSE}=\frac{1}{n}{\sum_{i=1}^{n}}(yi\ -\ \hat{y}i)^{2} \tag{10}\]  
where \(n\) is the total number of samples, \(y_{i}\) and \(\hat{y}_{i}\) be the true and predicted value of the \(i^{th}\) sample, respectively. Figure 9: ML models evaluation metrics—MLP. Figure 11: ML model’s evaluation metrics—LSTM. Figure 10: ML models evaluation metrics—CNN. A comparative analysis of the actual and predicted values of standard deviations for specific parameters in a system is presented in Figure 9a-c. These parameters appear to be associated with bearing, elevation, and range values, potentially in the context of object tracking or localization. The model's ability to predict bearing values' variability (standard deviation) is contrasted with the actual variability observed in the data in Figure 9a. The model's capacity for predicting the variability of elevation values is illustrated in Figure 9b. The model's ability to predict the variability of range values is evaluated in Figure 9c. The parameters of bearing, elevation, and range are the primary focus of each subplot in Figure 10a-c. It represents the sequence of data points, denoted by the sample number, as well as the standard deviation's magnitude for the specific parameter along with the anticipated standard deviation for the given range, elevation, or bearing with the genuine or true standard deviation for range, elevation, or bearing, respectively. The model's ability to predict each parameter's variability (standard deviation) compared to the actual variability observed in the data is illustrated in Figures 11 and 12. The plots demonstrate that the actual standard deviations (orange lines) do not precisely align with the predicted standard deviations (blue lines) for any of the parameters. This implies that the model may not effectively represent the actual variability in the data. The sample range is characterized by fluctuations in the standard deviations, both predicted and actual. This implies that the data's variability is not constant. The model used to generate the predictions may have limitations in accurately estimating the standard deviations for these parameters, as evidenced by the discrepancies between the predicted and actual values. Table 3 below provides an overview of the models' performance. After testing, the new dataset shows each model's overall mean squared error. Figure 12: ML models evaluation metrics—GRU. Hybrid (DL-UKF)  
The average distance to a traceable target is about 65,000 m, and the average velocity of moving aircraft is 130 m/s. These measurements are used to compute the initial target's state vector, and they are assumed to follow Gaussian distribution with zero mean; therefore, the following expression is derived. \[X_{s}(0)= \begin{bmatrix}130\\ 130\\ 130\\ 65,000*\sin\beta*\sin\varepsilon\\ 65,000*\sin\beta*\sin\varepsilon\\ 65,000*\sin\varepsilon\end{bmatrix} ^{T} \tag{11}\]  
Moreover, from Equation (11), the initial covariance matrix \(P\left(\frac{0}{0}\right)=diagonal\)\(\left[4*\frac{X_{s}(k)^{2}}{12}\right]\).