Given that a time-variant position uncertainty model has not yet been implemented in PosFrm, adjustments are needed to avoid under estimating uncertainties during problem (generally low ACT) periods of the Sample Release.
Until the time-variant uncertainty model can be installed, PosFrm is setting all frame position sigmas to 0.1 asec in the fpos files. Combined statistically with the extraction uncertainties, this results in overall position sigmas out of BandMerge of .12 asec for the best sources (clean and reasonably bright with magj<15). These sources are used since they give the best indication of position reconstruction errors. Analysis of chi-squares in the scan overlap regions reveals that for most time periods the sigmas described above are conservative estimates of the position uncertainties. There are, however, some intervals during which these sigmas are significantly too low. This generally occurs when there are not enough ACT's and can be compounded by a low density of the extraction sources needed to tie the frames together. A conservative approach which utilizes the overlap chi-squares to adjust the position uncertainties is described.
Each survey scan is broken down into a dozen 1/2 degree long segments. The in-scan and x-scan chi-squares are computed for each segment for the overlap on each side. Working with a contiguous set of surveys and a single segment number across the scans, variance factors are iteratively determined for each scan segment. The iteration attempts to drive the average of the chi-squares on the two sides of each scan segment to unity. In-scan and x-scan are handled independently.
On the final iteration, the variance factor for each scan segment is calculated to drive the larger (as opposed to the average) of the chi-squares on either side to one. Finally, any variance factor less than 1.0 is raised to 1.0 to insure that no uncertainties are reduced.
In order to prevent penalizing sources with large extraction uncertainties unfairly, the variance factors are applied as follows:
varx = varx +varmin*(vfacx-1)
vary = vary +varmin*(vfacy-1)
The parameters "vary" and "varx" are the in-scan and x-scan variances respectively, and "vfacy" and "vfacx" are the corresponding variance factors. The parameter "varmin" is the minimum variance value, which in this case is (.12 asec) squared.
After execution of the above procedure, the final set of in-scan variance factors for 971116n are tabulated in Table I. The corresponding x-scan variance factors can be seen in Table II. In both tables the minimum variance factors of "1.00" have been replaced by "----" to make it easier to spot the segments requiring adjustment.
The average in-scan sigmas for the best source extractions, after the variance factors are applied, are tabulated in Table III. The corresponding x-scan sigmas reside in Table IV. In both tables the minimum mean sigma values of "0.12" have been replaced by "----" to make it easier to spot the segments with larger mean sigmas.
The in-scan chi-squares (sum_chi2y/n), after the variance factors
have been applied, are tabulated in Table V.
The x-scan values can be found in Table VI.
Histograms of the in-scan chi-squares are plotted in
Figure 1, and the
x-scan chi-squares in Figure 2.
There histograms confirm that the final position uncertainties are
conservative.
