2.8 Automatic Insertion of Geodetic Segments

Phase referencing for weak source detection and astrometry depends on the ability to transfer interferometer phase from a calibrator to a target. The largest source of error in that transfer is the atmosphere. The ionospheric component of the atmosphere can be calibrated using multiple observing bands or modeled with the help of GPS based ionospheric models. The non-dispersive tropospheric component needs to be calibrated, either by measuring gradients using multiple calibrators near the target, or deriving the zenith delay from observations and using a mapping function to get the elevation dependence. The latter method is generally accomplished by inserting occasional clusters of observations of calibrators around the sky from which the clock offset and the zenith delay can be derived. AIPS task DELZN is typically used to make the solutions, although some users have their own programs for the purpose. These clusters of calibrator observations are called geodetic segments or DELZN segments.

Constructing a geodetic segment can be tedious given that one wants low elevation observations at all stations. The tropospheric effect scales roughly as secant(zenith angle) (hereafter SecZ). The elevations at each VLBI station are different and change rapidly with time. It is also best to have sources that are high at some stations and low at others to give robust SecZ fits. External programs have been written to construct geodetic segments for insertion into SCHED and libraries of segments are available, mostly from Mark Reid of CfA. But any schedule with such segments is tightly constrained in time — any time shift will cause what were low elevation scans to become either high elevation scans or scans where the source is down. Plus gathering the required segments can be tedious.

/schedb can build and insert geodetic segments automatically into schedules. This should drastically reduce the overhead in constructing such segments, and allows such segments to be made easily when the station list is not just the VLBA. Also the schedule can be time shifted easily, a possible benefit for dynamic scheduling. When there is a time shift, a different list of sources for each segment, optimized for the new time, will be built. It has also been found that this capability can be used to make short groups of scans that can be used for atmospheric opacity solutions by AIPS task APCAL.

To request that a geodetic segment be built, the user should specify a scan with the parameter GEOSEG given with an argument that is the total duration of the segment (typical values are 20 to 45 minutes). A list of sources from the normal SCHED catalogs to consider for the geodetic segments is given with the input parameter GEOSRCS. Other parameters to consider to influence the source selection are DWELL (the length of the individual scans within the segment), OPMINEL (the minimum elevation to consider — 10 degrees is a reasonable choice), OPMINANT (the minimum number of stations in a scan) and SETUP (the setup file — typically one with a wide spanned bandwidth and maybe not at the same band as the main observations). Be sure to set these parameters back to their desired values for the main observations (GEOSEG will revert to zero by default) or you may get unexpected behavior. In addition, for the scan that is being turned into a geodetic segment a source needs to be specified. It will be ignored in constructing the segments, but without it some of the SCHED checking that comes earlier will not be happy.

The parameter GEOPRT can be used to cause some details about each trial source sequence tested to be printed to sched.runlog. There are various levels of print possible.

The algorithm used to construct geo segments is described in more detail below. It involves constructing a number of trial segments and selecting the best. There are a number of control knobs sticking out that the user might want to play with although the defaults are reasonable. The parameter GEOTRIES controls the number of trial segments to test. Setting GEOTRIES large will likely produce a slightly better solution at the cost of high run times for SCHED. The algorithm for picking sources is reasonably good so the best of the early tested segments is likely to be nearly as good as anything found later. The source picking algorithm is based on fits for secZ, with a penalty for long slews. It is also capable of leaving an antenna out of a scan if it gets to source much later than other antennas. If that source would have been important for the slow antenna (low elevation), it is blocked so that it can be used in a later scan. The standard is that an antenna will be left out of the scan, or the source blocked, if that antenna gets to source more than GEOSLOW (default 40 seconds) later than the third to last antenna to get there. The choice of the third-to-last antenna for the reference was an effort to deal with various awkward scenarios that can arise when not all antennas are in all scans.

There is an example among the SCHED examples called egdelzn.key that shows how to construct a file with automatic geodetic segment insertion. The GEOSRCS in that example are the set provided by Mark Reid for his packaged geodetic segments, but with source names corresponding to those used in the normal SCHED catalog. Users are likely to just cut and paste that list into their schedules.

The example egdelzn.key includes three different source lists in GEOSRCS. One is Mark Reid’s original 60 sources. In testing, this list was found to be too sparse in some parts of the sky. The second list is the 295 defining sources of the ICRF2. This should be a good list, especially at frequencies not too far from the 2.3 and 8.4 GHz bands in which it was derived. The third list is based on the USNO 1cm survey and is should be the right one to use at 22 GHz and up. It also has over 200 sources.

The algorithm:

Note: There were minor changes to the algorithm when it got tested for 2 station observations. Those changes are not yet reflected in the description below.

As long as SCHED is producing good geodetic segments, the details of the algorithm shouldn’t matter too much to users. But some may wish to know, so it is described here. When starting to work on a segment, SCHED calculates the elevations at the middle of the segment for all of the specified sources. It assigns a priority for each source depending on how many stations see it at low (below GEOLOWEL) and high (above GEOHIEL) elevation. The best sources are low at at least two stations and high at at least two. The next priority sources have at least one low and three high stations or at least three low stations. The mix of low an high stations helps with the eventual least squares fit to SecZ terms. Higher priority numbers (worse sources) are assigned to less optimal sources. With the help of the calculated information and priorities, SCHED constructs a number ( GEOTRIES of trial geodetic segments. A quality measure for each segment is determined by setting up a least squares fit for SecZ and clock terms. The formal error on the fitted SecZ term for the station with the highest such error is the quality measure.

An algorithm is used to construct each tested segment that tries to come up with a source set that works reasonably well. This makes constructing each segment slow, but means that not many need to be tested. The algorithm starts by locating the 5 closest sources in the top two priority bins to the preceding source in the schedule. “Close” here means in terms of slew time for the array. For the first scan of the schedule, all qualified high priority sources are considered since the array will usually slew to the first source before the observations start. One of the chosen sources is picked at random. Then the next source is picked at random from the 5 closest sources that either add a high or a low observation to a number of stations that is the lesser of a third of the total or a third of the total number of low and high scans still needed. That scheme continues until there is at least one low and one high source for each station. That usually takes of order 6 scans.

For later scans in the segment, all sources given in GEOSRCS that are up at enough stations (set by OPMINANT) are tried, one at a time. A dummy least squares fit for SecZ and clock is tried with the sources in the segment so far, up to a maximum of the preceding GEOBACK sources. Restricting the number in the look-back seems to help some times when choosing long segments. The default is large (100) so there will be no effect and this should be good most of the time, but users might want to fiddle the value. Three quality measures are considered in the selection of the next source. The first is the improvement in the sigma for SecZ for the station that was worst with the already-selected sources, subject to a penalty for long slew times. If that is not sufficiently good, the source that gives the best improvement for the previously worst antenna without the slew penalty is selected, but with a requirement that the improvement be more significant than was required when the slew penalty was used. If even that is not sufficiently interesting, the source that gives the best RMS improvement in the SecZ sigmas across the array, subject to the slew penalty, is chosen. The deranged may wish to use GEOPRT to watch in detail , in sched.runlog, what is going on in the algorithm. Actually you can tell quite a bit from GEOPRT=0 but you will likely need to use the code to understand much of what is being spewed out, especially for a high value of GEOPRT such as 2.

Note that, in the fits, any SecZ of more than 4 (about an elevation of 15 degrees) is treated as 4. This will make the quality of the fits seem somewhat lower but will place less emphasis on scans that are so low that the risk of failures is great.

While selecting sources, normally no one source will be allowed to repeat. But sometimes there aren’t very many low elevation options and it may be desirable to allow repeats. Parameter GEOSREP sets the minimum number of scans that must go by before a source is allowed to repeat. This was a problem for the original 60 source list, but much less so for the ICRF2 or 1cm sources.

For each of the GEOTRIES trial segments, a quality measure is generated. SCHED picks the best segment according to the quality measure, and inserts that into the schedule. The quality measure is based on the expected errors of a fit for the zenith delay and clock for all stations. Standard errors of 100ps are set for all observations (the value doesn’t really matter here although a future enhancement would be to vary the number based on the source strength) and the highest reported sigma across the stations is used as the quality measure. This process is similar to what is done when the data are used and encourages both a high range of elevations at each site and a significant range of elevations across antennas for each scan.