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Next: Tracking over joints Up: The experiments Previous: Azimuth Pointing Errors

`No-track' pointing and tracking

Also in May, but repeated in September, we have tracked bright sources with a TEL configuration that did not include the track model. The resulting pointing errors ought then to be comparable with what we would expect from our preferred track model. The differences between the two might reveal deficiencies in our assumptions and algorithms. Tracking of planets was performed without a track model as follows :

   Date   Source         HST               az,el          seeing   adopted
 950518   Mars      17:30 - 23:00     143,83 - 276,28   1" - 0.4"    1"
 950913   Mars      16:20 - 18:20     210,52 - 240,30   2" - 1"     1.5"
 950913  Uranus     18:30 - 19:20     139,37 - 152,44   2" - 1"     1.5"
 950914   Mars      16:20 - 18:30     219,48 - 241,29   4" - 2"  not analysed
 950914  Jupiter    18:40 - 20:20     208,44 - 230,28    < 0.5"     0.5"
The first dataset was taken with a track model of resolution 1 and the others with the latest mixed-resolution model, with greatest resolution around the track joints of 0.2. The azimuths of the logged pointing measurements are corrected for the effect of the delay in logging,

az az - 0.5*(az-az),

and the observed data are compared with those predicted by the appropriate track model :

daz = f1 * F1*cos(el) + f2 * F2*sin(el) , del = f3 * F3

where F1, F2, F3 are the columns of the current model1, and f1, f2, f3 are coefficents with nominal values -1, +1, -1, respectively.

Data like this tests how well the track model predicts the observed pointing errors. If T, O, & P represent the track, the observed errors and the predicted errors as functions of azimuth, and if I and S are the distributions of inclinometry and seeing errors with azimuth then without a track model

O = T + S
P = n * T + I

where n is the efficiency with which the inclinometry predicts the track errors. These relationships may be solved for n in two ways. First, the observed pointing and predicted pointing errors are plotted against each other. The error on the observed pointing (0.5 to 1) is typically larger than that of predicted corrections (0.35) so the predicted corrections may be considered the independent variable in the relationship. Thus we solve for m in O = m * P + const where m = 1/n. Secondly an analysis of the variances is made :

n = (VAR(P) - VAR(I)) / (VAR(O) - VAR(S))

The data are also divided into two subsets for those data within <1 of a joint (j) and those not (nj). All rms's are all w.r.t. the nj means. The results are presented below.
Str line fits :              -------  daz  ------       -------  del  ------
                       N     m     +-    s.d.   n       m     +-    s.d.   n
 950518   Mars   all 176    0.91  0.03   1.2   1.10    1.19  0.03   1.0   0.84
                  nj 106    1.05  0.04   0.9   0.95    1.20  0.04   0.8   0.83
                   j  70    0.84  0.05   1.4   1.18    1.22  0.04   1.1   0.82
 950913   Mars   all  61    1.09  0.12   1.2   0.92    0.80  0.04   0.9   1.25
                  nj  44    1.10  0.22   1.3   0.91    0.78  0.05   0.9   1.28
                   j  21    1.05  0.16   1.0   0.95    0.78  0.06   0.7   1.28
 950913  Uranus  all  30    1.03  0.09   1.8   0.97    1.01  0.10   1.4   0.99
                  nj  14    1.12  0.09   1.0   0.89    1.17  0.10   0.9   0.85
                   j  16    1.00  0.14   2.3   1.00    0.87  0.16   1.6   1.15
 950914  Jupiter all  61    0.90  0.08   1.2   1.11    1.14  0.14   0.8   0.88
                  nj  40    0.80  0.11   1.1   1.25    1.23  0.04   0.8   0.81
                   j  21    0.94  0.12   1.4   1.06    0.99  0.05   0.7   1.01

Weighted Means : all        0.93               1.03    1.05               0.99
                  nj        1.04               1.00    1.11               0.94
                   j        0.88               1.05    1.05               1.07
         typical +-          .04                .10     .10                .18

VARIANCE analysis  

             data    N          daz                      del
                           rms(O)  rms(P)   n      rms(O)  rms(P)    n
 950518       all  176      2.61    2.57   1.06     3.11    2.49    0.84
  Mars         nj  106      2.25    1.97   0.97     2.54    2.00    0.85
                j   70      3.08    3.27   1.12     3.84    3.15    0.85

 950913       all   61      1.91    1.34   1.10     2.41    2.80    1.48
  Mars         nj   44      1.60    0.89   1.50     2.26    2.66    1.56
                j   17      2.60    2.12   0.99     2.87    3.17    1.29

 950913       all   30      4.19    3.67   0.93     2.86    2.50    1.02
 Uranus        nj   14      3.59    3.08   0.94     3.02    2.47    0.94
                j   16      4.69    4.24   0.95     2.70    2.74    1.21

 950914       all   61      2.15    1.96   0.93     3.58    3.06    0.86
 Jupiter       nj   40      1.63    1.51   0.95     3.71    2.95    0.80
                j   21      2.94    2.62   0.90     3.39    3.31    0.98

              all                          1.01 +- 0.09             1.05 +- 0.30
  Means        nj                          1.09 +- 0.27             1.04 +- 0.35
                j                          0.99 +- 0.09             1.08 +- 0.20
In summary, there is no compelling evidence to suggest that m, and hence n, which = 1/m, is systematically different from 1.0 for az or el, joints or non-joints. The agreement between the two methods for each night, and the internal errors for each night, are better than the deviations between nights, indicating that the validity of the track model varies, perhaps with elevation, temperature, azimuth range, or perhaps with a general evolution of the track. Recent experience following a central bearing adjustment was that the track model derived from inclinometry had become inapplicable after maybe as little as a week.

The efficiency, n, is thus a variable, with a possible variation of 0.1 or 0.2 about an average value of 1.0.



next up previous contents
Next: Tracking over joints Up: The experiments Previous: Azimuth Pointing Errors



Iain Coulson
Wed Mar 12 15:06:27 HST 1997