Uncertainty Adjustments: Selection, Implementation & Validation

A set of scans for which the quoted position uncertainties may not adequately reflect the actual errors over a portion of the scan has been selected by various means, most of which were described previously. A set of 179 "low density" problem scans were identified via large differences between the SFPOS and FPOS files. The half dozen cases (980310n095, 980501n053, 990526n014, 000112n155, 000130n045 & 001022s070) where the PosFrm reconstruction algorithm fell back to the USNOA as the reference catalog are in fact a subset of the "low density" problem list. A set of 29 scans with abnormal x-scan scale factors was selected as well. Also included were the qa_fix and qa_sig lists, of 10 and 270 scans respectively, generated during pipeline quality checking. All 311 scans crossing the north pole were selected due to an error spike of unknown cause very near the pole, inadequately reflected by the quoted uncertainties. At the time of the previous analysis it was expected the same would be true at the south pole. As it turned out, although the error spike can also be found at the south pole, the quoted uncertainties are adequate.

Since the previous report, the run generating scan-segment overlaps for the entire sky has completed, providing global scan-segment overlap chi-square data. As a result an additional 277 scans have been selected. The worst-case chi-squares were selected at the scan-segment level as well as the scan level. With a very few exceptions each scan-segment (12 segments per scan) has a minimum of two overlaps and frequently many more. In each case only the overlap with the minimum mean radial overlap difference was considered. This was done to reduce the chance of inadvertently including adjacent non-problem scans in the selection. The selection process was done first on scan-segments with the threshold set at a mean chi-square of 10. It was then repeated on whole scans with the threshold reduced to 5. It was decided to be more conservative at the scan level since the consequences are greater and the number of scans selected remained relatively small.

A few (30) additional scans with unusually large Tycho-2 differences were added as well. Combining all these scans and removing duplicates leaves the previously mentioned 987 scans. That constitutes about 1.65% of the scans, but since only portions of some scans are affected, the percentage of point sources with modified uncertainties drops to 0.56%.

II. Implementation of Uncertainty Adjustments:

Having eliminated manual adjustment of uncertainties as undesirable for a number of reasons, it was necessary to come up with an automated adjustment technique which could address the various types of problems encountered. Given the very small percentage of sources affected a rather conservative approach could be tolerated, however, an attempt was made not to be ridiculously so. Adjustments were made by first converting to x-scan and in-scan sigmas, making the changes there and then converting back to an error ellipse. Two specialized types of corrections were made for selected scans:

1) For scans from the "low density" problem list differences between the desired SFPOS positions and the achieved FPOS positions are known as a function of frame number. Thus the positions for these scans could have actually been corrected. Based on time cost and risk considerations the decision was made some time back to only adjust the uncertainties. A variance adjustment was made by adding the known position difference squared to the original quoted sigma squared. No other adjustments were made to these scans.

2) Scans from the list of abnormal x-scan scale factors were handled in a similiar fashion. An estimated x-scan position error (due to this problem only) for each point was determined by multiplying the distance off the x-scan center by the difference between the abnormal x-scan scale factor and the mean x-scan scale factor for all scans from that hemisphere. A variance adjustment was made by adding the square of the estimated x-scan error (as determined above) to the square of the original quoted sigma. The mean overlap chi-square adjustments as described below were also made to these scans. Thus the uncertainties for these scans may have ended up a bit more conservative than most.

All other adjustments were made by multiplying the original variance by the mean chi-square of the overlaps (as interpolated between scan-segment center points). For north pole scans, mean chi-square adjustments were made only within a degree of the pole unless the scan had been flagged as having an additional problem. In all cases (pole or not) this adjustment was made only if the interpolated mean chi-square value to be used as a multiplier was greater than one. In other words, it was never allowed to reduce the quoted sigma.

It should also be noted that no adjustment was made resulting in a new sigma greater than 1.0 asec. In the very rare event that the original quoted sigma was greater that 1.0 asec it was left untouched. In the event that the original value was less than 1.0 asec and the adjusted value would have become greater than 1.0, it was trimmed at that value.

III. Validation of Uncertainty Adjustments:

000119s014, 000308s050, 000925s138, 001022s070, 980109n166, 980202n117, 980310n095, 981121n069, 990429s008, 990429s009, 990527n018, 991015n021, 991016n035

Four of these scans had abnormal x-scan scale factors in addition to their other problems. For these scans the above plots are repeated, this time as a function of x-scan position. Only overlaps within the same Dec band are plotted. Otherwise scan ends, which are not characteristic of the overall scan, would dominate.

980109n166, 981121n069, 990429s009, 990527n018

These plots illustrate that the quoted uncertainties grow toward the edges, as expected, and that the overlap differences are consistent with those uncertainties.

In order to verify the adjusted position uncertainties were properly inserted into the database a join was made between the uncertainty update table and the database table (my thanks to Nian). All 3.1 million updated position uncertainties were compared and all matched.