## 3 Experiments for Jason-3 Attitude Modes and Receiver PCVs Calibration
### Effect of Jason-3 Attitude Modes on Receiver PCO and POD
#### 3.1.1 Effect of Jason-3 Attitude Modes on PCO Estimation  
The orbital time series of all altimeter satellites are required to be consistent in their geophysical models, reference frame and measurement model corrections, for which the corresponding parameters between Jason-2 and Jason-3 should have this inheritance. Thus, we considered the receiver PCO vector of Jason-2 as the initial PCO of the Jason-3 satellite, which the z-offset of PCO is -521.7 mm for the SBS. Given the particular geometry of the orbit and its complex interaction with the attitude, we estimated the z-offset of PCO using one beta cycle of data without fixed-yaw data about more than 90 days, according to the thresholds of attitude transition. Due to data reasons used, the results based on the combined attitude and event file are consistent with each other, only the nominal mode, combined mode and quaternions were selected to test in this section. By POD experiments, we have determined that the z-direction of PCO estimation using quaternions based on an initial value of -521.7 mm is more accurate; thus, we considered the estimation results (-518.7 mm) as the reference value. The initial z-direction bias of receiver PCO with respect to the reference value are randomly increased to -24.4 mm and -100.2 mm; the z-offset of PCO in both cases were estimated based on three attitude modes. To compare the differences, the initial bias and \begin{table}
\begin{tabular}{c c} \hline
**Module/Parameter** & **Selection/Description** \\ \hline
**Force** & \\ \hline Gravity model & EIGEN-684 \\ N-body perturbation & JPL DE405 \\ Solid earth tide & TIDE2000 \\ Ocean tide & FES2004 \\ Solar radiation pressure & ECOM2 model [35] \\ Atmosphere drag & Pseudo-stochastic pulse \\ \hline
**Data parameter** & \\ \hline Data type & Code and phase observation of ionosphere-free combination \\ Data interval & 30 s \\ Cut-off elevation angle & 7\({}^{\circ}\) \\ Arc length & 24 h \\ Satellite ephemeris and clock & CODE precise products \\ Attitude & Attitude model/Quaternions \\ Receiver antenna PCO/PCV & Direct/Residuals approach \\ \hline
**Estimation parameter** & \\ \hline Initial state parameters & Six Keplerian osculating elements \\ Solar radiation pressure & ECOM2 parameters \\ Receiver clock error & One per epoch as process noise \\ Pseudo-stochastic pulse & One group per 6 min in the RTN directions \\ Ambiguities & Float solutions of ionosphere-free combination \\ \hline \end{tabular}
\end{table} 
Table 1: Module/Parameter for Jason-3 POD. estimated bias with respect to the reference value are listed in Table 2. The values in parenthesis indicate the percentage of the estimated PCO bias with respect to the initial bias. In both cases of Table 2, the estimated results with nominal attitude (36.2 and 124.8 mm) are the worst; results with the combined attitude (\(-18.8\) and \(-62.8\) mm) are relatively closer to the reference value. These results indicate that different attitude modes have different impacts on PCO estimation. In tests, the estimated receiver PCO bias based on the nominal attitude are about 148.4% and 124.6% with respect to initial bias, those with combined model are about 77.0% and 62.7%, and those with quaternions are 14.3% and 5.1%. The receiver PCO does not need to be updated in real time and only needs to be revised regularly. In POD, we should use more accurate attitude model firstly. If the PCO needs to be updated, it will be estimated; if not need, it will not be estimated. 1.2 Effect of Different Attitude Modes on PCO Correction (Modeling Analysis of the Combined Attitude)  
The PCO correction error can directly make the calibration of satellite mass center inaccurate. Supposing that receiver PCO provided from a ground or an in-flight estimation is accurate, the differences in PCO correction are calculated using different attitude modes. The difference analysis can be as the validation way and the defined method for the transition nodes of the combined attitude mode. The yaw angle is mainly controlled by the beta angle of the satellite.