# Radar-Based Target Tracking Using Deep Learning Approaches with Unscented Kalman Filter
## 2 Materials and Methods  
This section presents the methods utilized for radar-based target tracking using UKF and DL techniques. A detailed block diagram in Figure 2 outlines the various stages of UKF processing. Additionally, it serves as a visual representation of the procedures carried out during this process. The UKF algorithm, a nonlinear estimate method used in target tracking, is depicted in the diagram. Its goal is to determine a system's state from noisy observations. Figure 2 shows that initial estimates are set for the system's state mean (x) and covariance matrix (P). These figures may be predicated on default assumptions or past knowledge. Radar is the source of the present measurement data (z). There is uncertainty and noise in this data. Weights for the sigma points are calculated (Wm and Wc). These weights evaluate the significance of every sigma point in the estimating process. Sigma points are produced around estimating the present state (x). These points represent the system's possible states.  
To anticipate the system's future states, the sigma points are transmitted through the nonlinear state equation (f). The predicted state mean (x') and error covariance matrix (P') are computed using the converted sigma points as a base. This step estimates the system's status at the following time step. The predicted sigma points are translated using the measurement equation (h) to produce expected measurements. The anticipated measurement (z') is computed using the altered sigma points as a base. The predicted mean and covariance values are used to update the sigma points. The cross-covariance matrix (Pxy) and output estimate (y) are computed. The output covariance (Pyy) and the expected error covariance (P') are used to calculate the Kalman gain (K). The Kalman gain determines the impact of the measurement update on state estimation. The difference between the expected measurement (z') and the actual measurement (z) is used to updatethe state estimate (x) along with the Kalman gain. The output covariance (Pxy) and the Kalman gain are used to update the error covariance matrix (P). Acceptance criteria are compared with the modified state and covariance values. The procedure ends if they satisfy the requirements. If not, step 2 of the algorithm is repeated.  
Figure 3 provides descriptive insight into steps undertaken to train and test the DL models, where the proposed system, a simulator, was developed to produce a dataset for training and testing. Range (_r_), bearing (_g_), and elevation (_e_) measurements were used as input to the neural network, which forecasted the standard deviations of those measurements. At each epoch, the predicted output of the neural network was compared to the actual output using a mean squared error as a loss function. The error was calculated and backpropagated in the network to adjust weights. Over time, once the error was reduced to a minimum, models were exported to be integrated into UKF. In this study, 300 possible scenarios are carefully designed. Each of these scenarios is used to simulate the target-observer movement dataset according to Figure 3.  
In Table 1, _scur_, _sdrg_, _bbrg_, _gelev_, _rng_, _brg_, _V1_, _Vo_, _elev_, _tcr_, _tp_, _ocrs_, _op_ stands for scenario number, the standard deviation in range, is standard deviation in bearing, standard deviation in elevation, initial range, initial bearing, target speed, observer speed, target course, target pitch, observer initial course, and observer pitch, respectively. This provides a comprehensive description of the mathematical model used for 3D target tracking and implements a clear explanation of the UKF algorithm. In this study, the observer and target are again assumed to move with constant velocities and course, as specified in Table 1.  
Figure 2: UKF block diagram for target tracking.