# Geolocation and Tracking by TDOA Measurements Based on Space-Air-Ground Integrated Network
## 4 Discussion
The random errors of TDOA measurements are 500 ns, which represents the TDOA covariance matrix \(\mathbf{Q}_{t_{j,k}}=diag\bigg{\{}\Big{(}\frac{500\text{ ns}}{10^{9}}\Big{)}^{2}, \dots,\Big{(}\frac{500\text{ ns}}{10^{9}}\Big{)}^{2}\bigg{\}}\). Other errors are assumed nonexistent. The emitter location is fixed on \((101^{\circ},3^{\circ},0\text{ km})\). The effect of observer position bias is clearly shown in Figure 6. The localization performance of the proposed ML estimator agree with the theoretical accuracy very well. Scenario 3: The sensor network contains the LEO satellite, airplane and ground station. Simulation results are shown in Figures 7-12. The random errors of satellite positions are \((100,100,100)\) m which represents the covariance matrix \(\mathbf{Q}_{s_{jk}}=diag\Big{\{}(100\text{ m})^{2},(100\text{ m})^{2},(100 \text{ m})^{2}\Big{\}}\). The target is moving on the surface of the Earth with a constant speed of \(300\) m/s. The course angle of the target is \(30^{\circ}\). The height of the target is \(10\) km. The detection number \(K\) is 50. The Monte Carlo number of the ML estimation is 1000. Figure 2.0 GDOPs of position estimation for the scenario of using LEO satellite, airplane and ground station. Figure 2.1 GDOPs of velocity estimation for the scenario of using LEO satellite, airplane and ground station. Figure 2.2 Localization accuracy comparison using LEO satellite, airplane and ground station by varying TDOA measurement noise. Figure 2.3 Localization accuracy comparison using LEO satellite, airplane and ground station by varying the target elevation bias. Figure 2.4 Comparison of velocity estimation using LEO satellite, airplane and ground station by varying TDOA measurement noise. The random errors of TDOA measurement are 500 ns in Figures 7 and 8, which represent the TDOA covariance matrix \(\mathbf{Q}_{t_{jk}}=diag\bigg{\{}\left(\frac{500\text{ ns}}{10^{9}}\right)^{2}, \ldots,\left(\frac{500\text{ ns}}{10^{9}}\right)^{2}\bigg{\}}\). Figures 7 and 8 show the GDOPs of position estimation and velocity estimation, respectively. Figure 7a presents the GDOP of position estimation with 1 us bias of clock synchronization. Figure 7b shows the GDOP of position estimation with observers' position bias of (2000, 2000, 2000) m. Figure 7c gives the GDOP of position estimation with 2000 m elevation bias of the target. Figure 7d shows the GDOP of position estimation when the non-horizontal velocity of the target is 20 m/s. From the simulation results in Figure 7, we can make the following conclusions: (1) The ambiguous location area is around the line between the sub-LEO point and the sub-airplane point. (2) The effects of different system errors are also diverse. We can observe that elevation bias of the target is the most influential factor for this scenario. The position bias of the observers is the second influential factor. The effects of clock synchronization bias and non-horizontal velocity of the target are not serious. Figure 8a presents the GDOP of velocity estimation with 1 us bias of clock synchronization. Figure 8b shows the GDOP of velocity estimation with observers' position bias of (2000, 2000, 2000) m. Figure 8c gives the GDOP of velocity estimation with 2000 m elevation bias of the target. Figure 8d shows the GDOP of velocity estimation when the non-horizontal velocity of the target is 20 m/s. From the simulation results in Figure 8, we can make the following conclusions: (1) The ambiguous area of velocity estimation is around the line between the sub-LEO point and the sub-airplane point. (2) The effects of different system errors are also diverse. We can observe that non-horizontal velocity of the target is the most influential factor for this scenario. This is different from the conclusion in Figure 7 where non-horizontal velocity is the lowest influential factor. The differences in clock synchronization bias and position bias are difficult to distinguish from Figure 8a,b.