# Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios
## 5 Simulation Results  
The localization and tracking scheme was first validated with synthetic data. A simulated radar scenario was generated considering the variant geometry and signal characteristics of the GPS constellation. The PR receiver is considered at the center of the local Cartesian space where the simulation is performed. The PR receiver antennas were considered at 2 m from the ground level where the movement of the targets was performed following the trajectories represented in Figure 7. A GPS satellite was selected as the illumination source. Real satellite ephemerides were used to include the motion of the space platform in the simulated geometry. The initial location of the satellite was placed at an elevation of 35.54\({}^{\circ}\) and an azimuth of 237.3\({}^{\circ}\) from true North.  
Six different targets with random initial positions around the PR location were simulated. A model with a quasi-constant modulus acceleration vector with independent components in X and Y coordinates was selected as the dynamic model of the targets. Initial velocities and accelerations were randomly selected from typical ground vehicle values.  
The position and dynamics of the IoO and targets were recalculated every 250 ms, simulating the PR refresh rate. Bistatic range, Doppler shift, and azimuth measurements were calculated from each instantaneous radar geometry. Additive white Gaussian noise with standard deviations of \(\sigma_{m}=7.79\) m, \(\sigma_{p}=1.39\) Hz and \(\sigma_{\phi}=1.87^{\circ}\) for each respective measurement was selected to simulate the expected performance of GPS-based PR in real operation. A total of 160 time steps were simulated, resulting in a 40 s simulation. The simulated radar scenario geometry and target trajectories are depicted in Figure 7.  
The localization and tracking results in the measurement and the tracking spaces for the simulated scenario are depicted in Figure 8. According to the RDM tracking results, a good trajectory estimation is obtained with reduced measurement errors. When the results are translated to the Cartesian plane, correct system performance is shown for most of the simulated trajectories, with higher localization errors after tight turns. However, the inclusion of new detections results in the convergence of the trajectory to the actual target location. Moreover, the longer distance to the PR location results in higher errors, being more relevant in the final part of the trajectory of the second target. Finally, a loss of tracking occurs at the beginning of the trajectory of target 5 due to the mixture of detections of different targets at nearby locations resulting in an unexpected track movement and thus the way out of the target from the detection gate. However, a new track is automatically generated and the remaining trajectory is correctly estimated.  
Figure 7: PR receiver location and targets’ trajectories in the simulated scenario.  
The localization error was also calculated as the Euclidean distance between the estimated track and the actual target location. Figure 9 shows the estimated localization error over the simulation time for the six targets. As expected from Figure 8, the localization error remains low along most of the tracked trajectories, with larger localization errors appearing at tight turns of the targets and when the distance between the target and the PR increases. However, despite the localization error can be as higher as 50 m at target 2, the average localization error of each simulated target remains low: 4.44 m, 10.76 m, 6.65 m, 2.96 m, 3.09 m, and 11.19 m, respectively.