# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
## 3 Satellite Attitude and Transponder Calibration
### Calibration Accounting for Satellite Attitude
This is because the selection of a transponder site is limited by (a) the terrain topography and site accessibility based on existing road infrastructure, (b) the need to support the simultaneous calibration of multiple missions, and (c) the quality of the signal clutter in the area. Even if a transponder is installed at the nadir of a satellite based on its nominal orbit, the repeat ground track  
Figure 4: Altimetric measurement acquisition over sea surface for (**a**) ideal and (**b**) non-ideal satellite orientation. The axes of the SAT system (satellite body system) are also presented. location of a specific satellite pass can vary several hundreds of meters on the ground even for consecutive cycles. The case of a satellite with ideal attitude passing over a transponder is given in Figure 4(a). The CoG correction denoted by the equidistant line segments \(\mid\) APC;B\({}_{0}\mid\) and \(\mid\) APC;B\(\mid\) is again applied to the measured range \(\mid\) APC;A\(\mid\) and accounts for the coordinate difference between APC and CoG in the \(z_{B}\) direction. As a result, the measured range is referred to the apparent CoG, which corresponds to point B. The same also applies for non-ideal satellite attitude, as demonstrated in Figure 4(b). It is evident in both cases that the corrected measured range \(\mid\) A;B\(\mid\) is not equal to the line segment \(\mid\) A;GoC\(\mid\); therefore, the measured range \(r(t)\) is not accurately referred to the satellite CoG. From the discussion provided so far, it can be concluded that the conventional implementation of CoG correction is proper only when both of the following requirements are met: (a) ideal satellite attitude (i.e., zero attitude angles) and (b) targets located along the altimeter nadir. For satellites passing over transponders, none of these requirements are met. It is therefore reasonable to argue that during satellite calibration, the measured range \(r(t)\) is not correctly referred to the CoG. On the contrary, the geometric distance \(r_{0}(t)\) is rigorously referred to CoG, since the estimated CoG coordinates provided in the GDR products already account for attitude effects. This inconsistency has a direct impact on the evaluation of range bias using Equation (8). In addition, the different reference of the measured and geometric range can affect the TCA and introduce errors in the estimation of datation bias using Equation (11). The datation errors due to non-ideal attitude mostly depend on the relative position between B and CoG. It is evident that attitude effects have an influence on transponder results and need to be further examined. An improved calibration procedure that accounts for these effects using attitude information is also required. A revisited calibration procedure is discussed in the rest of this section. Attitude effects on transponder results can be corrected by rigorously referring the measured and geometric ranges to the same reference point using information regarding the instantaneous orientation of the spacecraft. In this work, we have chosen the APC as the reference point for all parameters related to the calculation of range and datation biases. The new range bias, denoted as \(\vec{B}(t)\), is defined as:  
Figure 5: Altimetric measurement acquisition over a transponder for (**a**) ideal and (**b**) non-ideal satellite orientation (when pitch is introduced). The vector with origin at the satellite’s CoG and end at the APC is presented. The “CoG correction” is the distance added to the measured range (i.e., A, APC) to account for the APC offset. The axes of the satellite body reference system are also presented. \[\widetilde{B}(t)=R(t)-R_{0}(t), \tag{12}\]  
where \(R(t)\) and \(R_{0}(t)\) are the corrected measured and corrected geometric ranges between transponder and APC. The calculation of \(R(t)\) is performed using Equation (9) and only requires the subtraction of the constant CoG correction from the corrected altimeter range used in the conventional calibration procedure.