This section deals with the pointing performance of the Herschel spacecraft. The spacecraft Attitude Control and Measurement System (ACMS) consisted of several components, as depicted in Figure 2.10. The main constituents of the ACMS were the attitude control computer (ACC), gyroscopes (GYR), star trackers (STR), reaction control system (RCS), reaction wheel assembly (RWA), Sun acquisition sensors (SAS), coarse rate sensors (CRS) and attitude anomaly detectors (AAS).
In normal operation, the spacecraft attitude was commanded by means of the reaction wheel system. It comprised of four 8.6 kg wheels in a skewed configuration, each with a momentum storage capacity of 30 Nms and a maximum delivered reaction torque of 0.215 Nm in either the positive or the negative direction.In the baseline configuration, all four whels are powered and used for actuation, providing optimum slew performance and momentum storage. Nevertheless, the ACMS was also capable of operating with only three reaction wheels powered. In the nominal configuration, the maximum slew speed was 0.00204 rad/sec, i.e. ∼ 7 arcmin/sec.
In normal science operation, the spacecraft attitude was controlled by means of two components: the star trackers (STR) and gyroscopes (GYR). The STR comprised of two cold-redundant units, nominally aligned with the -X axis. The STR hardware included:
From a functional point of view, the STR can be seen as a video camera plus an image processing unit that, starting from an image of the sky, extracted the attitude information measured with respect to the J2000 inertial reference system and delivered it to the ACC. A CPU (ERC32 microprocessor) controled the CCD sensor and also carried the image processing task.
The main characteristics of the Herschel's STR were:
The ability to determine the inertial position from "lost in space".
FoV: 16.4 × 16.4 deg².
An onboard catalogue, based on Hipparcos, of some 3000 bright stars.
A minimum of 3 stars, 9 was the maximum due to H/W limitations.
The STR bias was the largest contributor to the absolute pointing error and is pixel-dependent (some 0.8" × √2)
The STR was provided with an enhanced performance mode the so-called "interlaced mode", only applicable if there were ≥ 15 stars in the FoV. The STR sampled at twice the nominal frequency (4 Hz), measuring 9 stars at a time.
In order to get the maximum accuracy it was necessary for the ACC to provide an accurate value of the S/C angular rate as input to the STR (the maximum performance was achieved with rate errors below 0.2 arcsec/sec).
Gyroscopes (GYR) are devices that use a rapidly spinning mass to sense and respond to changes in the inertial orientation of it spin axis. Rate/rate-integrating gyros provided high-precision measures of the the spacecraft angular rate. The Herschel's ACMS was provided with four gyroscopes mounted in a tetrahedral configuration. The gyroscopes were hot-redundant, and each of the four could replace any of the others. The fourth gyroscope was not used for control, but served to detect an inconsistency in the output of the other three.
The STRs provided an absolute reference, but with limited accuracy. In contrast, the GYRs were very accurate, but only on short temporal (bias drift, 0.0016 deg/hour) and spatial (variation in the scale factor should be taken into account for distances larger than 4 deg) scales. Therefore, the GYR attitude must be recalibrated using the STR information. As a result, in normal operation the spacecraft attitude was computed by combining the STR and GYR measurements in the ACC using a linear Kalman filter. The so-called "filtered attitude" was sampled and downloaded with a frequency of 4Hz.
The Startracker used a catalogue of 3599 stars measured by Hipparcos, corrected for proper motion to the mid-date of the mission. Of these, 203 stars were blends of two stars, resolved by Hipparcos, but not by the Herschel Startracker. This required a barycentre to be calculated of the two Hipparcos components to give the Herschel position, taking into account the Herschel instrumental magnitudes. Finally, in analysis of tracking performance, 72 stars were found to give systematic residuals in pointing and were suppressed from the fine attitude guidance catalogue from OD-1032 [RD12].
Herschel pointing modes were based either on either stare pointings (fine pointing mode), or moving pointings at constant rate (line scan mode). These come in multiple flavours:
The formal definitions of the spacecraft pointing accuracy parameters are provided in this section. Five different measures of pointing accuracy are commonly used and are each defined below.
The term 'pointing', when applied to a single axis (e.g. the telescope boresight), refers to the unambiguous definition of the orientation of this axis in a given reference frame. When characterising the pointing performance of the telescope, it is possible to provide a figure of the absolute attitude accuracy provided by the ACMS (absolute pointing error), or how accurate the 'a posteriori' knowledge of the absolute attitude (the absolute measurement error) can be, or how stable the pointing is (the relative pointing error). Furthermore, the pointing performance can be also characterised in terms of the relative accuracy of a set of attitude measurements (the spatial relative pointing error). The latter measurement is important to characterise the accuracy of the relative astrometry in a map comprising several pointings (e.g. from a raster pointing).
Herschel pointing accuracy definitions, presented below, are based on the prescriptions given in the ESA Pointing Error Handbook (ESA-NCR-502):
Absolute Pointing Error (APE): the angular separation between the desired direction and the actual instantaneous direction.
Absolute Measurement Error (AME): the angular separation between the actual and the estimated pointing direction (a posteriori knowledge).
Pointing Drift Error (PDE): the angular separation between the average pointing direction over some interval and a similar average at a later time.
Relative Pointing error (RPE) or pointing stability: the angular separation between the instantaneous pointing direction and the short-time average pointing direction during a given time period (in this case 60 sec).
Spatial Relative Pointing Error (SRPE): angular separation between the average orientation of the satellite fixed axis and a pointing reference axis, which is defined to an initial reference direction.
The main pointing error contributors within the Herschel spacecraft were:
To AME and APE:
Position-dependent bias within STR. It is also the main contributor to SRPE.
Residuals from calibration
Thermo-elastic stability of the structural path between STR and FPU
Instrument LoS calibration accuracy w.r.t. ACA frame (best for PACS)
To PDE: Thermo-elastic stability
To RPE: The main contributor is the noise in the control loop, comprising STR+Gyro noise attenuated by a linear Kalman filtering.
Table 2.4 summarises the pointing performance of the Herschel spacecraft.
Table 2.4. Herschel pointing requirements (from SRS v3.2) compared with predictions and measured performance. Goal conditions assume that 18 stars were available for guidance within the STR field, allowing interlacing to be performed.
|Baseline (arcsec)||Goals (arcsec)|
*There could be a marginal non-compliance in the SRPE as this figure was measured in very small raster maps and was quite uncertain.
There was a considerable improvement in the pointing performance during the mission as the Startracker system was better understood and characterised. This was attained in a series of stages, with the impact of each one being carefully assessed before the next step was taken. This was a result of the considerable efforts of many people at MOC, HSC and in industry[RD12].
In the very earliest mission phases after launch, before the cryocover was opened, it was found in initial tests that the heaters for the gyros were causing magnetic fields that created an oscillation in the pointing. This was cured by turning off the heaters, which could be done without the gyros cooling beyond acceptable temperatures. Similarly, the Startracker CCD performance was significantly improved by lowering its operating temperature, on OD-320, from the initial +20oC to -10oC to reduce the number of bad pixels and, in combination with regular characterisation and update of the on-board bad pixel table, this eliminated the so-called "speed bumps" where false detections of stars in the Startracker field caused jumps in scans.
An important factor in the first year of the mission was to characterise the SIAM (Spacecraft Instrument Alignment Matrix) file. This matrix told the spacecraft where the instrument apertures were in relation to the centre of the field of view. The first SIAM was used on OD-38, using Sneak Preview data (see (Section 1.1.2), applying PACS 70 micron data to provide an initial correction to the pre-launch SIAM. Further updates were made as individual instruments obtained and analysed observations that allowed them to characterise the different instruments. These initial determinations were applied by PACS on OD-53, HIFI on OD-55 and SPIRE on OD-68. Further refinements were applied on OD-78, OD-82, OD-98 and OD-122, as additional observations allowed the initial estimates to be improved. The OD-122 update was the one used for most of the first year of operations. As the amount of observational data increased, with massive scheduling of science data, first in SDP and then in routine phase, it was recognised that a further, small adjustment was required to the SIAM. This was applied on OD-341 and was the last update required during the mission.
A few observations in certain sky directions were found to show systematic pointing offsets that were found, on investigation, to be due to a strong asymmetry in the distribution of the guide stars, with all, or almost all, being on the same side of the CCD field. These offsets could be understood as due to small distortions in the focal plane of the Startracker. These focal plane distortions were corrected in three stages.
The first stage was to introduce a focal length correction. This was performed on OD-762 and led to an improvement in the APE from 2.5 arcseconds to 1.45 arcseconds.
Further analysis showed that the introduction of a one-dimensional distortion correction would give rise to a further substantial improvement in the pointing. This was applied on OD-866 and led to a further improvement of the APE to 0.95 arcseconds; considerably less than the pre-launch goal for pointing.
With further study, it was realised that second and higher order polynomial distortions were still present. It was thus decided to attempt a further, more ambitious two-stage refinement of the pointing: the first stage was to apply a n-dimensional distortion correction; the second to apply a clean-up of the guide star catalogue, removing those stars that were found to give systematically larger residuals (this was the suppression for use in fine pointing of 2% of the stars in the catalogue, which were found to be consistent outliers). To complete the first part, it was necessary to determine 16 coefficients. This was done from five independent data sets, each constructed from twenty ODs of tracking data, which gave consistent solutions for the coefficients.
The first part was implemented on OD-1005 and, on being verified as being correctly implemented, was made definitive on OD-1011. The second part, the catalogue clean-up, was applied on OD-1031, was the final fine tuning. The effects of these improvements were checked with telescope pointing tests on OD-1005, OD-1028 and OD-1034 that verified further substantial improvements in pointing performance to the final values seen in see Table 2.4; the final, measured APE after both corrections had been applied was 0.81 arcseconds. These improvements also showed that the SIAM that had been applied on OD-341 required no further adjustments.