# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
## 5 Conclusions  
In this work, we have demonstrated that the measured range used in altimeter calibration with a transponder is not correctly referred to the satellite CoG because of attitude changes. We propose an improved calibration procedure, where measured and geometric ranges are referred to the same and specific reference point. In our case, this reference point is chosen to be the APC. The estimation of the new geometric range between the transponder and the APC requires the APC coordinates in the EFRS. These are determined using the three-dimensional baseline vector between CoG and APC and satellite attitude. The evaluation of the differences between the conventional and improved calibration procedure allows the examination of attitude effects on range and datation biases. We study these effects for Jason-3, which was the reference mission for approximately six years (2016-2022). At first the Jason-3 attitude angles (i.e., roll, pitch and yaw) are determined over the CDN1 and GVD1 transponder sites. A spectral analysis revealed periodic constituents with periods of 117, 39 and 23 days in all attitude angles. The same periodic constituents are also evident in the time series of range bias of the CDN1 transponder. This can serve as a first evidence indicating that satellite attitude affects the transponder Cal/Val results. Jason-3 attitude effects on range and datation biases show a fluctuation from \(-2\) mm to \(+1\) mm and \(\pm 110\)\(\upmu\)s, respectively. The magnitude of attitude effects on datation bias corresponds to about 30% of its total value per cycle. These results indicate that non-ideal attitude has a strong impact on datation bias. The minimum and maximum values of attitude effects on datation bias emerge for a yaw angle of \(\theta_{y}=180^{\circ}\) (\(-110\)\(\upmu\)s) and \(\theta_{y}=0^{\circ}\) (\(+110\)\(\upmu\)s), respectively. This is due to the relative position and orientation of APC and CoG points in space as they pass over the transponder (i.e., which point precedes with respect to an observer at the transponder). The attitude effect is minimized when the satellite is flying with a yaw angle \(\theta_{y}=90^{\circ}\) because both APC and CoG points pass over the transponder at the same time. The attitude effects on datation bias can be predicted to a large extent using an analytical expression that is a function of the yaw angle and the x-axis distance between APC and CoG in the SAT system. An additional analysis was conducted at the Jason-3/Sentinel-6 MF crossover point over the GVD1 transponder to assess the proposed calibration procedure. The agreement of range bias between the ascending (A109) and descending (D018) pass using the new calibration procedure showed an improvement of 12% for Jason-3 and 14% for Sentinel-6A MF compared to the conventional procedure. We note that the Sentinel-6A MF results are preliminary and may change when updated quaternions become available. The level of improvement for Jason-3 is comparable with previous studies Blossfeld et al. [18], Li et al. [19], where similar crossover analyses were performed in the context of SLR orbit determination and POD to assess the use of observation-based attitude realization. The proposed calibration procedure is comprehensive and can be applied to every past, current and future mission with available attitude measurements. Thus, it offers  
Figure 13: Sentinel-6A MF crossover bias determined by the GVD1 transponder using the conventional (red) and new (blue) calibration procedure. the capability for a more accurate and objective comparison of transponder calibration results from different altimetry missions by removing the influence of systematic effects that depend on both physical characteristics (e.g., internal geometric structure) and attitude realization of each satellite. The new calibration procedure is not computationally demanding and can be easily implemented by any Cal/Val team.