I worked on the problem of least-square fitting with a
soft relationship between data and model; in particular the situation in which you are trying to get the best possible astrometric WCS for an image in the face of severe uncertainty about which source in the image ought to be identified with each astrometric standard star. Right now our WCS tweak code does a hard assignment and then updates it on each iteration, but I think there are better, continuous solutions.
I also worked on the problem of getting ultra-precise relative astrometry for, say, HST/ACS images of the COSMOS field, which is a slightly different problem from getting as-precise-as-possible absolute astrometry for each image using USNO-B1.0. It must be possible to align the HST images in a relative sense to much, much better than 0.05 arcsec, but we can't put things on the USNO-B1.0 system to better than about 1 arcsec (and the USNO-B1.0 system is not even this good, globally).