# Geolocation and Tracking by TDOA Measurements Based on Space-Air-Ground Integrated Network
## 4 Discussion
Figure 2.5 Comparison of velocity estimation using LEO satellite, airplane and ground station by varying non-horizontal velocity bias. In Figures 9 and 10, the random errors of TDOA measurements are variable as \(\sigma_{t}\) ns which means the TDOA covariance matrix is \(\mathbf{Q}_{l_{jk}}=diag\bigg{\{}\Big{(}\frac{\sigma_{t}}{10^{9}}\Big{)}^{2}, \ldots,\Big{(}\frac{\sigma_{t}}{10^{9}}\Big{)}^{2}\bigg{\}}\). The emitter initial position is \((101^{\circ},3^{\circ},10\) km). \"Theoretical accuracy without system error\" is generated by (25), \"Theoretical accuracy with clock synchronization error\" is generated by (50), \"Theoretical accuracy with observer position bias\" is generated by (52), \"Theoretical accuracy with target elevation bias\" is generated by (54), \"Theoretical accuracy with target non-horizontal velocity bias\" is generated by (55) and \"ML localization accuracy without system error\" is generated by (58). Figure 9 presents the theoretical performances of geolocation with different system errors. We can observe from Figure 9 that elevation bias of the target is the most influential factor. After that are position bias of observers and clock synchronization bias. Due to the negligible effect, the target's non-horizontal velocity can be ignored for geolocation. The localization accuracy of the proposed ML estimator is also provided in Figure 9 for the case of no system error. It can be seen from Figure 9 that localization accuracy of the proposed ML estimator agrees with the CRLB very well when TDOA noise \(\sigma_{t}\) is less than 0.9 us. Figure 10 shows the theoretic performances of velocity estimation with different system errors. We can observe from Figure 10 that the target's non-horizontal velocity is the most influential factor, which is different from the conclusion in Figure 2.6 After that are clock synchronization bias, observers' position bias and target's elevation bias, respectively. The velocity estimation accuracy of the proposed ML estimator is also provided in Figure 10 for the case of no system error. It can be seen from Figure 10 that velocity estimation accuracy of the proposed ML estimator agrees with the CRLB very well when TDOA noise \(\sigma_{t}\) is less than 0.7 us. In Figures 11 and 12, the random errors of TDOA measurements are 500 ns, which represent the TDOA covariance matrix \(\mathbf{Q}_{l_{jk}}=diag\bigg{\{}\Big{(}\frac{500\text{ ns}}{10^{9}}\Big{)}^{2}, \ldots,\Big{(}\frac{500\text{ ns}}{10^{9}}\Big{)}^{2}\bigg{\}}\). The emitter initial position is \((101^{\circ},3^{\circ},10\text{ km})\). Figure 11 compares localization accuracy by varying the target elevation bias. Only TDOA measurement error and target elevation bias are present. The effect of target elevation bias is clearly shown in Figure 2.7 The localization performance of the proposed ML estimator agrees with the theoretical accuracy very well. Figure 12 compares localization accuracy by varying the non-horizontal velocity bias of the target. Only TDOA measurement error and non-horizontal velocity bias are present. The effect of non-horizontal velocity bias is clearly shown in Figure 2.8 The localization performance of the proposed ML estimator agrees with the theoretical accuracy very well.