## 5 Results
### TDRS Orbit Determination Results
#### 5.1.3 Scenario #3
This analysis was performed for each user spacecraft that used a constellation of the TDRS satellites to acquire DOWD measurements (see Section 4.3). In these figures, the TDRS orbit error is shown as a solid line with circle markers, and the estimated TT&C bias is shown as a dotted line with diamond markers. The analysis underscores the critical role of obtaining precise a priori covariance values in achieving accurate orbit determination. A zero meters covariance value implies that the TT&C bias was not accounted for in the model, resulting in a constrained solution. On the other hand, an infinite covariance value represents an unconstrained solution, marked as a red star in the figure. Figure 6: The figure shows the relationship between TDRS positional uncertainties (solid line, circles) and estimated TT&C biases (dotted lines, diamonds) during IXPE DOWD pass events, analyzed against the a priori covariance of TT&C measurement bias. Sometimes, the unconstrained solution can lead to the overestimation of the TT&C bias. This issue is most pronounced when using the BLS estimator due to its iterative nature. The BLS estimator's output is very sensitive to the initial conditions, and this can cause it to become trapped in local minima. This behavior can lead to the overestimation of the TT&C bias, which in turn results in an inaccurate orbit determination. In this investigation, it was observed that all unconstrained solutions led to overestimated TT&C bias values, with a maximum value of approximately 2.4 km. As a result, the TDRS orbits were affected, with the maximum errors of about 17.5 km. In contrast, all constrained solutions were found to be in better agreement with the operational solution. Initially, as the a priori covariance increased, TDRS orbit errors increased rapidly. However, the errors stabilized after reaching a certain threshold. With further increases in a priori covariance, there were slight changes in the TDRS orbit and estimated TT&C bias. Figure 8: This figure is analogous to Figure 6, but it presents the results for the LANDSAT-8 DWWD pass events. Figure 7: This figure is analogous to Figure 6, but it presents the results for the LANDSAT-9 DWWD pass events. This indicates that the solution's dependence on the a priori TT&C bias covariance can be resolved to a large extent with a very high value but at the cost of poor orbit accuracy. In the context of TDRS orbit determination, the unconstrained solution yielded the highest TDRS orbit error, hence being regarded as the worst-case scenario. In contrast, constrained solutions were more accurate with insufficient a priori knowledge of the TT&C bias and its covariance since they were in better agreement with the operational solution. As such, the employment of a constrained solutions approach is advised in this circumstance. Monte-Carlo runs conducted in this scenario generated a broad spectrum of TDRS orbit solutions. The consequences of these solutions on the orbit of the user spacecraft were analyzed in detail to assess the changes in the user spacecraft's trajectory due to TDRS orbit uncertainties. Section 5.2 summarizes the results of this analysis.