Analysis of tracking experiments performed in February 1998

The datasets
As in 1995 (see the report MTPPN05 - specifically the Section titled `No-track pointing and tracking' ), tracking was done with the track model disabled, and a comparison made of observed and predicted pointing errors. SCUBA was not available so RxA2 tuned to its mid-range was used. Bright sources were essential to enable rapid pointing determinations and hence good azimuth resolution. In the absence of planets at this time, the quasars 3c273, 3c279 were used. 3c273 was followed over a large azimuth range that includes 16 wheel/joint interactions , and 3c279 was followed over the last 4 of these.

   Source         HST            azimuth       elevation 
    3c273    01:18 - 04:01      133 - 234       65 - 61
    3c279    04:06 - 05:05      215 - 234       59 - 49

The seeing was erratic early on but stabilized for the latter part of the experiment :

   HST       01:00   02:00    02:30   04:00   05:00  HST
   seeing     1.0     1.7      0.5     0.4     0.3    "

Pointing errors are predicted from the track model, and plots of the observed and predicted errors, their differences and ratios can be seen by selecting the entries in the table below :

The azimuths of the track joints are shown by the green vertical lines.

The observed azimuth errors in the azimuth range 215 to 234 are very repeatable (read `systematic'). For instance, for both the 3c273 data and the 3c279 data, plots of (daz_obs - daz_pre) -vs- azimuth (the green traces in the above plots) show a positive `hump' at about azimuth 220, followed by a negative spike at azimuth 223. The larger 3c273 dataset also shows difference spikes of amplitude ~5", particularly at azimuths 142 and 174, that are associated with wheel/joint interactions .

In contrast, the behaviour in elevation errors appear to be quite random, except perhaps for a 2" or 3" glitch at azimuth 155, which is unassociated with a joint .

One measure of the goodness of fit of the track model is the scatter in the difference plots (the green lines) :

   Source   az range     N    ------------- rms scatter --------------
                              (daz_obs - daz_pre)   (del_obs - del_pre)
    3c273   133 - 234   73            1.8                   1.2
    3c273   215 - 234   20            1.3                   0.9
    3c279   215 - 234   27            1.3                   0.6

Straight line fits were made to the plots of Observed-Errors -vs- Predicted-Errors for each of daz and del, and are shown in the plots accessible from the above table. The straight line fits are of the form

           O_daz  =  m_daz * P_daz  +  const_daz
           O_del  =  m_del * P_del  +  const_del

   Source  azimuths    N    m_daz   +-    rms     m_del   +-    rms
    3c273  133 - 234  73    1.22   0.05   1.6      0.99  0.04   1.2
    3c273  215 - 234  20    1.01   0.12   1.4      0.94  0.06   0.9
    3c279  215 - 234  27    1.06   0.10   1.3      0.98  0.04   0.6

Note that the rms's of the observed data about these lines are still sufficiently larger than the expected accuracy of the predictions (0.35 arcseconds) that the predicted data may be regarded as the independent variable in this relationship.

The derived values of m_daz and m_del are, in their general range, not unlike those seen in 1995 . The efficiency of the track model in representing the motion of the telescope is again essentially 100%, with uncertainties between 5% and 20%. In the shorter (20 degree) azimuth ranges covered twice in these experiments, the efficiency, in both coordinates, is typically 5%. Only the azimuth performance over the 100 degrees or so of the 3c273 data implies an efficiency unlike 100%. Poor-ish azimuth pointing performance has been noted in the course of routine examination of the nightly pointing data.

The pointing glitches at 223 and 155.
Examination of the track model and the inclinometry data that created it shows that azimuth 223 is between joints and there is no reason, a priori, to expect trouble here. Any feature at this azimuth not detected by the inclinometry at the current resolution is in the middle of a track segment. The same may be said for the glitch at 155. The appearance of mid-segment defects would be a worrying development, and if more widespread would require increasing the inclinometry resolution to the 0.2 degree level to ensure detection of all such flaws. This would increase the time needed to take inclinometry data from the current 3 hours to about 9 hours - a rather impractical proposition.

Yaw
I have also worried for a long time over the factor of 0.83 that we use in constructing the yaw part of the track model. Currently

               yaw = 0.83 * (LY - RY)

               yaw = fL*LY  +  fR*RY

   Source   az range     N    ------------- rms scatter --------------
                              (daz_obs - daz_pre)   (del_obs - del_pre)
    3c273   133 - 234   73            1.6                   1.2
    3c273   215 - 234   20            1.5                   0.9
    3c279   215 - 234   27            1.4                   0.6

An alternative suggested by the dissociation of the left A-frame tilt from the calculation of pitch is that fL = 0. Varying fR to achieve m_daz = 1.00 from the 3c273 data suggests that fR = -1.6, but this also increases the scatter to 2.2". Using this value of fR on the smaller (3c273 and 3c279) datasets gives m_daz = 0.73 +- 0.21 and 0.52 +- 0.19, respectively, with similarly large scatters, so the entire exercise does not support this option.

The effect of fL = -fR = 1.21 on allsky pointing data
It's always difficult to go backwards from observed pointing data to corrections to the track model, partly because the data are logged at the end of the pointing experiment rather than in the middle, which gives a more representative `azimuth', but mainly because any corrections that could be applied would be only to those azimuths at which observations were made - and this is a very small subset of the azimuths forming the track model. The best that can be hoped for is that a prospective track model be tested against a pointing dataset, to see if the overall residuals are reduced (improved).

The 32 RxA2 data of Feb 24th and the 69 SCUBA data of the 25th and 26th were analysed. Their basic statistics are shown below, together with the azimuth performance that would be expected if a model based on fL = - fR = 1.21 had been used instead of that based on fL = -fR = 0.83 :

           dataset   FE    N    fL   rms daz      rms del
           980224    A2   32   0.83    2.2          2.0
                               1.21    3.2
           980225-26  S   69   0.83    1.5          1.9
                               1.21    2.3          

This part of the analysis does not support changing fL from 0.83 to 1.21.

Conclusions
If the 980410 experiments do not lead to a much improved pointing performance, the data above must be used, as is, to determine the extent of any increase in efficiency following the Azimuth Track Improvements Project. The results from the 1995 work were that the track model was efficient at the 100% mark +- 10-20% , whereas the above data suggest that this has improved, typically to the 5-10% level.

It may be that the structure of these experiments, with their supporting inclinometry from the previous night, allows better results, and it may be that the 980410 results will provide an even better track model. But, with the exception of unexplained, unexpected glitches , often with amplitudes of 5", it seems reasonable to claim that the inclinometry and track model provide a description of the track irregularities accurate to 5-10% : a factor of ~2 better than the performance reported in 1995 .