From: OL_7.html#HEADING55

Pointing Calculations and Sources of Error

The methods used to calculate the pointing depend on the guiding mode in use. These are described in detail below. We emphasize that the pointing is referenced to the nominal aperture position, and the name and coordinates of that aperture are provided in the header. Offsets from this aperture reference position, e.g., POS TARGs, real-time maneuvers, are not taken into account by the observation log software.

The 3 methods used in the calculation of the RA, Dec, and roll are Two FGS Fine Lock Guiding, GYRO Control, and Single FGS Pitch and Yaw plus GYRO Roll Control.

Two FGS Fine Lock Guiding: This mode will produce the most accurate pointing. Absolute accuracy of the aperture RA and Dec in this mode can vary over time as calibrations improve, and geometries change, but can be expected 0.5 - 2 arcsec. Relative accuracy throughout an exposure will be ~1-50 milliarcsec. The inputs are the FGS star selector encoder positions, four Photomultiplier Tube Counts per FGS, the RA and Dec of the two guide stars (from the Mission Schedule and originally from the HST Guide Star Catalog), the spacecraft velocity, and the V2V3 coordinates of the aperture in use. The software first calculates the V2V3 coordinates of the guide stars using the current FGS alignment and distortion calibrations. These data are then fit to the RA and Dec of the guide stars. From the fit, the telescope attitude (V1 pointing) and the RA, Dec, and roll of the aperture reference position are derived.

GYRO Control: Pitch, yaw, and roll control is performed by the Rate Gyro Assembly. The pointing is calculated using the data from the gyros. These vectors, (quaternions), are corrected for the differential velocity aberration between the V1-axis (for which the vectors are reported in the telemetry) and the aperture reference position. Because of the gyro drift, this mode produces the least accurate absolute and relative pointing. Absolute accuracy of the aperture RA and Dec will be 2-100 arcsec and relative accuracy will be of order 1-5 milliarcsec per second of observation time (drift).

Single FGS Pitch and Yaw plus GYRO Roll Control: In this mode, a single FGS is used to control the pitch/yaw of the spacecraft and the roll control is handled by the gyros. The absolute pointing is calculated from the Rate Gyro Assembly output. The jitter information from the guide star in the FGS is added (in correct quadrature) to the absolute pointing. Finally, the combined pointing profile is determined at the position of the aperture (i.e., absolute and differential velocity aberration corrections are applied in all telemetry formats except FN). This guiding mode will produce less accurate pointing than the two FGS guiding mode because of gyro drift, in this case, a drift in roll about the single guide star. Because of the drift, relative pointing during an observation will be affected, but absolute pointing can also be impacted due to possible roll biases at the time of acquisition. Expect absolute accuracies 0.5 - 5 arcseconds. The error due to the roll drift during the observation (affecting relative accuracy) will be 1-5 milliarcsec/sec.

More on roll angle changes (roll drift) during an observation:

The roll will change when the RA and Dec change via spatial scans, offsets, moving targets, slews. All small angle maneuvers will change the direction of north with respect to the aperture reference position. The telescope itself does not adjust the roll during the observation, and the pointing calculations reflect the change in position.

Gyro drift will cause a change in the roll angle. The drift rates are up to 5 milliarcseconds of roll per second depending on the gyro bias update and slew activities prior to the observation (gyro and single Guide Star modes);

Thermal expansion or contraction and jitter (single and two FGS guiding modes). The peak-to-peak amplitude of the breathing in the direction of pitch and yaw is less than 15 milliarcsec. The effects on the roll are still to be determined.

Sources of Error:

There are several reasons why the observation log RA, Dec, and roll may be different from the commanded values. Some of these depend on the guiding mode used for the observation. The reasons for some discrepancies are summarized here:

If pre-planned or real-time offsets were commanded (all guiding modes);
The relative guide star positional error over scales comparable to HST field of view, 0.33" for northern hemisphere plates and 0.43" for southern hemisphere plates (two FGS guiding mode);
Mis-identified guide stars (two and single FGS guiding modes);
Inherent error of tenths of an arcsec in the telemetered gyro data (gyro and single FGS guiding modes);
Gyro drift which ranges from 1-5 milliarcsec/sec depending on the gyro bias update and slew activities prior to the observation (gyro and single FGS Guiding modes);
Thermal expansion, contraction and jitter. The peak-to-peak amplitude of the breathing in the direction of pitch and yaw is less than 15 milliarcsec. Jitter is on average about 2-8 milliarcsec RMS (single and two FGS guiding modes);
In TLMFORM=FN where the absolute and differential velocity aberration corrections are not applied. The absolute velocity variation is up to 20 arcsec and the differential aberration is up to 50 milliarcsec (all modes);
Slight differences in the method of calculation between the observation log software and the operations ground and onboard flight software systems (all modes).

The causes for the target missing the aperture reference position include the following:

Relative guide star position error (0.33-0.43 arcsec) and target coordinate error (single and two FGS guiding modes);
Misidentified guide stars or binary guide stars;
Focal Plane calibration errors including:
- FGS/FGS alignment (currently time dependent; has been as high as 0.3 arcsec, but after a recent calibration should be < 0.050);
- FGS/SI aperture calibration errors which can depend on the target acquisition method used and the relative errors between target acquisition aperture and science aperture, as well as other internal instrument calibrations. Values range from 0.1 arcsec to 0.5 arcsec;
- Calibration errors between the Fixed Head Star Trackers, Rate Gyro Assembly and FGSs
Gyro drift of 1-5 milliarcsec/sec (single FGS and gyro modes);
Thermal expansion and contraction, known as breathing (up to 15 milliarcsec).