# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
###### Abstract
The altimetry community has now acknowledged that satellite attitude needs to be taken into account in altimetry data processing. The Ocean Surface Topography Science Team (OSTST) Meeting in 2019 [17], recommends to include attitude information in Geophysical Data Record (GDR) products, and for the older altimeters. Up to now, effects arising from satellite attitude have been routinely considered in precise orbit determination (POD). Satellite attitude is realized in POD by either a priori attitude models (called \"nominal\" attitude), or by on-board measurements realized by star tracker cameras. Recent results [18] show that the use of observation-based attitude improves orbit determination with Satellite Laser Ranging (SLR) for the Jason series. An improvement of about 4.5-8.3% in the orbit RMS is reported in [18] when using the observation-based attitude instead of the nominal model. In addition, when POD results for Jason-3 are determined using the observation-based attitude, it leads to an average RMS of 3.29 cm instead of 4.13 cm with the nominal attitude model [19]. Besides orbit determination, non-ideal attitude has an additional effect on altimetric measurements and ocean products. In [20; 21], a correction was proposed for the measured ocean range of Geosat and TOPEX/Poseidon altimeters, respectively. This correction accounted for instrument biases due to significant wave height and attitude (off-nadir) angle, estimated from the averaged return waveform using the Brown model. A degradation of the Jason-1 star tracker system was observed in April 2002, which led to abnormally large attitude angles and a reduced accuracy of altimetric products derived by conventional retracking algorithms. To account for these large attitude angles, a second-order analytical model for the altimeter echo and a four-parameter maximum likelihood estimator was proposed in [22]. Their method resulted in a reduction in the bias of the geophysical parameters estimated by the averaged return waveforms. In [23], the attitude angle was identified as a potential indicator for detecting anomalies in the significant wave heights estimated from SARAL/AltiKa altimetric waveforms. Non-ideal attitude is also known to cause distortions on the measurements of altimeters operating in synthetic aperture radar (SAR) mode. More specifically, a pitch angle can result in asymmetries in the echo power distribution of forward- and backward-looking beams. This effect has been studied by [24] to independently estimate the pitch angle of CryoSat-2. Finally, attitude-dependent corrections have been implemented in [25] to account for non-uniform heating of the microwave radiometer and improve the estimation of wet troposphere delays. A systematic review of the literature on satellite altimeter calibration using a transponder indicates that attitude effects have neither been examined nor taken into account in this context [26; 27; 28; 29; 30; 31]. The non-ideal satellite attitude has been recognized in [32] as a potential source of uncertainty affecting the altimeter antenna gain, which should always be evaluated in the altimeter-to-transponder line-of-sight direction. Following the advancements and recommendations in recent altimetry studies, the standard procedure of calibration using a transponder should be revised accordingly to account for satellite attitude effects. In this work, we propose and test a methodology for incorporating attitude information into the calibration procedure. Our main objective is to improve the estimation of range and datation biases by mitigating systematic errors coming from the nominal offset between the altimeter phase center (APC) and the satellite center of gravity (CoG). We therefore design an analytical method for the rigorous calculation of the offset between the APC and CoG based on the instantaneous orientation of the satellite in three-dimensional space. We then use this offset to refer all measurements used in the calibration to APC.