## 5 Results
### TDRS Orbit Determination Results
#### 5.1.4 Arc Length Dependency  
The accuracy of an orbit determination and the quality of the solved-for parameters can be impacted by the length of the arc used for the determination. The arc length refers to the time interval during which measurements are taken. Longer arc lengths typically provide more data points and a more comprehensive trajectory picture, which can lead to more accurate orbit determination. However, several factors can affect orbit determination accuracy, even with a longer arc length. One of these factors is systematic measurement errors. If these errors are not correctly accounted for in the orbit determination process, they can result in errors in the solved-for parameters, regardless of the arc length.  
To investigate the impact of arc length on orbit determination accuracy, a study was conducted using the TDRS satellites. Figure 10 shows the histogram of orbit errors, compared to the operational solution, for different arc lengths ranging from two to five days. The solutions were computed using TT&C-only measurements when measurement bias covariances were fully unconstrained. The study indicates that longer arc lengths generally lead to more accurate orbit determinations. However, for smaller arc lengths, such as two to three days, the solutions sometimes diverged or led to orbit errors up to 38 km primarily due to the overestimation of the range bias.  
Another study was carried out to investigate how the length of an arc affects TDRS orbit accuracies when the solutions are constrained. These solutions did not include  
Figure 9: This figure is analogous to Figure 6, but it presents the results for the JPSS-2 DOWD pass events.  
estimates for TT&C measurement biases, and the bias values were set to zero meters. Figure 11 shows the histogram of these results. The results indicated that the estimated orbit errors were the same for all arc lengths tested. This suggests that if a TT&C measurement error is constant over time, then a solution with a smaller arc length is sufficient for determining the TDRS position and velocity accurately.  
However, when TT&C measurement biases are not considered, the maximum error in the TDRS orbit is the sum of any dynamic error and systematic error in the measurements. The relationship between measurement bias and orbit error can be complicated and depends  
Figure 11: The TT&C-only TDRS orbit error is based on the chosen arc length for constrained solutions. The observed discrepancies in the maximum error across the TDRS orbits provide insights into the inherent bias present in the TT&C measurements. As the magnitudes of measurement errors increase, the resulting orbital errors also increase. It is important to note that the TT&C bias was neither applied nor estimated in the constrained solutions.  
Figure 10: The TT&C-only TDRS orbit error based on the chosen arc length for unconstrained solutions.  
on factors such as the type of bias, the measurements used, and the orbit determination algorithm employed. It is, therefore, crucial to identify and correct any measurement biases in the TT&C data to obtain reliable and accurate orbit predictions.  
Nevertheless, not accounting for TT&C measurement biases is still a viable choice in these studies compared to overestimating biases. As shown in Figure 12, estimated TT&C biases were consistently below 50 m for five years except for TDRS-12, where bias consistently remained around 82 m since the late 2020s.