## 5 Case Study Example
Using Equation (3), its value at the acquisition starting time for each \(5\times 5\) m\({}^{2}\) cell of the defined coverage area was calculated (Figure 22a). Due to the small variation of the bistatic angle during the acquisition time, the variation of the bistatic range resolution in the \(1.5\) s has not been represented. Because of the satellite movement, the bistatic time delay and the associated bistatic range are also a function of time (\(R_{T}+R_{R}-L\), in Figure 6). This makes the estimated target location a time-dependent variable. In Figure 22b, the total variation of the bistatic range during the whole acquisition time is represented for each \(5\times 5\) m\({}^{2}\) cell of the defined area of coverage. In this case, variations of \(50\) m are calculated. The variation of the bistatic range with time for a stationary target (_i.e._, corner reflector) located at the center of a \(5\times 5\) m\({}^{2}\) cell gives rise to the virtual movement of the stationary target. In Figure 23, the virtual trajectory of a stationary target located at the upper right corner cell of Figure 22b is depicted. During the acquisition time, an average speed of \(38\) m/s and a total variation of the bistatic range of around \(55\) m were estimated. Figure 23: Virtual displacement for a fixed point inside the area of interest. Figure 22: Bistatic range resolution and bistatic range: (**a**) initial bistatic range resolution at each \(5\times 5\) m\({}^{2}\) cell of the coverage area; (**b**) total variation of the bistatic range during the acquisition time. This virtual movement is completely defined by the system geometry, so it can be predicted and, therefore, compensated. To complete the study, two examples of different system geometries are presented:  
* Virtual movement analysis for a bistatic radar scenario using the same satellite, but assuming a different acquisition date: The new date and time parameters are: 3 June 2015, 17:34:15. Figure 24 shows the total variation of the bistatic range and the virtual movement of the same stationary target as in the previous study, during the same acquisition time. In this case, the maximum magnitude of the bistatic range variation is approximately 35 m, lower than the approximated 55 m obtained in the previous study. * Virtual movement analysis for a bistatic radar scenario using a GPS satellite: A new study case is considered exploiting the signal transmitted by Navstart 59 (USA 192). This is a medium-orbit satellite. The date and time parameters are: 25 May 2015, 12:20:00. The characteristics of the orbit and the transmitted signal parameters used in the study are summarized in Tables 5 and 6, respectively. Results are presented in Figure 25. In this case, the stationary target is assumed to be located on the upper left corner of Figure 25a, in order to perform the analysis for a case characterized by a big variation of the considered parameters. For the same acquisition time used in previous examples, the obtained virtual displacement is significantly lower, less than 1 m.  
These results validate the proposal of a PAZ-based PR for PAZ calibration and maintenance purposes and for surveillance of critical areas where the increase of monitoring time and/or target speed estimation could be important added values. Figure 24: System geometry analysis assuming different TerraSAR-X orbital parameters (3 June 2015, 17:34:15): (**a**) total variation of the bistatic range during the acquisition time; (**b**) virtual displacement associated with satellite movement.