## 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
To better analyze the correlation between beta angles and differences in PCO correction, we selected related data which the beta angles encompass the threshold of attitude transition. Considering the limitation of length of the paper, we presented the analysis results related to 20 days of data: days of year (DOY) 189-208 in 2016. The related beta angles were calculated and linearly vary from \(-35^{\circ}\) to \(20^{\circ}\) in Figure 2. The tests didn't selected one beta cycle of data because the transition threshold of the combined attitude has characteristics with short-term change with time, which is better for getting the transition threshold and POD. Figure 3a-f shows that the Jason-3 beta angles are nearly the transition threshold (\(\pm 14.6^{\circ}\) and \(1.06^{\circ}\) are obtained from test analysis in this section) of the combined attitude in DOY190-191 (Figure 3a,b), DOY195-196 (Figure 3c,d) and DOY201-202 (Figure 3e,f). In Figures 4-6, the units of the \(x\)-axis are epoch of day. The left and right sides of Figures 4-6 reflect the differences in receiver PCO correction in the inertial system using different attitude modes in DOY190-191, DOY195-196, and DOY201-202, respectively. From top to bottom are the differences in PCO correction between nominal attitude and quaternions, between nominal and combined attitude, and between combined attitude and quaternions. The Jason-3 beta angles are nearly \(+14.6^{\circ}\) in DOY190-191, nearly \(1.06^{\circ}\) in DOY195-196 and nearly \(-14.6^{\circ}\) in DOY201-202 (see Figure 3). In Figures 4-6, the differences in PCO correction between nominal attitude and other attitude modes reached a maximum of 2 m in DOY190, DOY196 and DOY201-202. In DOY191 and DOY195, the differences between three attitude modes are almost 0, which indicates that three attitude modes are available in these cases. In DOY190-191, DOY196, DOY201-202, the results using combined attitude are almost consistent with quaternions; it shows that the combined attitude and the other attitude modes are not available in these cases. Figure 4: Differences in PCO correction using different attitude modes near \(+14.6^{\circ}\). Figure 3: Variation of Jason-3 beta angles near \(\pm 14.6^{\circ}\) and \(1.06^{\circ}\) (the transition threshold of the combined attitude) in DOY190-191 (**a**,**b**), DOY195-196 (**c**,**d**) and DOY201-202 (**e**,**f**). attitude and quaternions can be employed in PCO correction. At the end of DOY195, some abnormal values are shown in Figure 5; we searched for the attitude event information and discovered a process about yaw flip of 10 min at 21 o'clock on that day. And all attitude models have the modeling error that caused the poor results. In Figures 4-6, the nominal attitude is not feasible and can cause the meter-level correction error. The results of PCO correction using the combined attitude are almost consistent with those using quaternions. In fact, the difference analysis in PCO correction between quaternions and nominal mode are also the basis of the combined attitude modeling in this section. Figure 5: Differences in PCO correction using different attitude modes near \(1.06^{\circ}\). Figure 6: Differences in PCO correction using different attitude modes near \(-14.6^{\circ}\).