determination and control
4.4 Characteristics of the inter-satellite pointing variations
The inter-satellite pointing variations can be expressed in terms of roll, pitch and yaw rotation angles, derived from the RKF→LOS matrix. Figure 4.5 shows the RPY angles for 2 orbital periods as well as for a period of 18 d along the groundtrack. The RPY angles in Figure 4.5 were computed onboard the satellite and were recovered from the THAD data product. The characteristics of the pointing variations of GRACE-A and GRACE-B are the same, thus the following description is valid for both satellites.
It is very obvious that based on the available input data, the AOCS successfully keeps the pointing variations within the specified deadband which is different for roll, pitch and yaw.
This means the requirements on the mission operation and the inter-satellite ranging are met successfully.
The pointing variations are dominated by several systematic effects which depend on the characteristics of the onboard attitude determination sensors and actuators rather then by satellite dynamics due to the disturbing environmental torques. Focusing on the pitch variations, the very prominent systematics is the oscillation at frequency about ∼3.3 mHz which results in very regular horizontal stripes apparent in Figure 4.5(d). Clearly, such systematics cannot be related to any geophysical phenomena. It is the dominant frequency of the magnetic torquer operation (cf. Section 3.4.1) that causes this systematics. This is proved also by the fact that the frequency of pitch variations suddenly changed in February 2004 on GRACE-A and January 2005 on GRACE-B when the settings of magnetic torquers were changed. As pitch is almost entirely controlled by MTQs, this dominant frequency becomes particularly amplified.
Further, pitch variations reveal stronger and rather irregular variations at specific geographical regions. They are not random, but very steady in space and time. The regions are different for ascending and descending orbit. For GRACE-A ascending orbit and GRACE-B descending orbit this region is located at 75◦W-100◦E, 50◦N-90◦S and for GRACE-A descending orbit and GRACE-B ascending orbit at 160◦E-50◦W, 50◦N-90◦S. In these regions, the y-component of the Earth’s magnetic flux density vectorB has strongly negative values, compare Figure 3.4(b) and 4.5(d). The By values differ for ascending and descending orbit (cf. Section 3.2.2) and therefore the geographical regions of irregular pitch variations are orbit dependent as well.
Obviously, the magnetic torquers do not manage to control the spacecraft in these regions as smoothly as in the other parts of the orbit. One possible explanation for that could be a particular constraint of the attitude control algorithms.
These two features are not so prominent in roll and yaw variations because the efficiency of MTQ attitude control is much lower due to the rather unfavorable orientation of the magnetic torquer rods with respect to the magnetic field lines. Hence the attitude deviations drift
rapidly and attitude thrusters need to be activated to maintain the desired attitude. The attitude control with thrusters is not as smooth as with magnetic torquers. Moreover, the thrusters are activated when needed in contrast to torquers which operate continuously at 1 Hz sampling rate. As discussed in Section 3.4.1, the MTQs sufficiently control roll over the geomagnetic poles and yaw along the geomagnetic equator. In all other regions the thrusters need to support the MTQs and pointing variations become larger. This is very well reflected in the roll and yaw pointing variations (cf. Figure 4.5(b) and 4.5(f)).
The inter-satellite pointing variations are mainly influenced by the characteristics of the attitude determination sensors and actuators as just discussed. At the same time, however, pointing variations provide valuable information about the performance of the AOCS, and about some events carried out onboard when no other information is available. Especially the long time series reveal interesting phenomena. Figure 4.6 shows the pitch variations along the orbit for 2 years, 2007 and 2008. Along with the already discussed features, another eminent systematics was revealed and that is the one with characteristic duration of 161 days. Within one 161 d epoch the variations are stronger and within the next 161 d epoch the variations are milder. These epochs alternate regularly. This feature is the consequence of using attitude data from only one star camera for the in-flight maintenance of inter-satellite pointing. As the measurement accuracy of the two star cameras is not the same (see Section 3.3.4), such systematics is inevitable. This feature has crucial consequences on the attitude control and the gas consumption and it is further discussed in Chapter 6.
After zooming in, specific pitch variations are typical for different kind of events. Figure 4.7 shows the pitch variations along the orbit for approximately 4.5 months. Events such as CoM calibration maneuver, disabling of supplemental heater lines, Moon intrusion into SCA FoV, primary camera switches and switches to back-up science mode are obvious at first sight. This information is valuable to obtain indirect information about the satellite motion and to detect any irregular performance within the onboard laboratory in case of the absence of other data sources.
Although, the inter-satellite pointing variations are kept well within the deadband, the KBR inter-satellite ranging observations still need to be corrected for the imperfect pointing. This is done by applying so called antenna offset correction which is defined in the following section.
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Figure 4.5: The inter-satellite pointing variations expressed in terms of roll, pitch and yaw angles as time series plotted for two orbital periods together with the deadband (left column) and plotted with respect to the groundtrack for ascending orbit for a time span of 18 days (right column), recovered from the Level-0 data
(THAD) for Dec 1st-18th,2008, GRACE-A
Figure 4.6:Variations of pitch inter-satellite pointing angle of GRACE-A in 2007 and 2008 plotted along the orbit, recovered from the THAD data
Figure 4.7:Long time series of pointing angles reflect well some events in the satellite operation. Here, the inter-satellite pointing pitch variations of GRACE-B in 2007 (April-August) are shown. Legend: 1 - Center of mass calibration maneuver, 2 - back-up science mode (the attitude was determined using SCA and IMU), 3 - simultaneous blinding of both SCA heads by the Sun and the Moon, followed by stronger attitude variations due to the residual stray light, 4 - short term primary camera switches due to blinding of the primary camera by the Moon, 5 - scheduled primary camera switch (β’=0), 6 - systematics due to the disabling of supplemental
heater lines