Here's a crazy idea which I might as well put on the blog.
Multipath is an important error source for GNSS reference stations. Monuments for antennas are nearly always placed close to the Earth's surface, so the ground will act as a reflector with a grazing geometry that generates short-delay multipath. Usually other objects contribute as well (nearby buildings or fences for example).
Many solutions exist for multipath mitigation, both at the antenna and correlator levels. Another possible system technique, though, would seem to be to move the antenna upwards, far enough away from local objects that any reflected signals have delays larger than the support of the autocorrelation function for any signal of interest.
Conceptually, an antenna could simply be placed at the top of a tall tower a few hundred meters in height. The tower would ideally be transparent to RF (perhaps of lightweight dielectric construction). Of course there are many practical problems with this, but the environment around the antenna would be nearly ideal.
Another possibility is to place the GNSS antenna on a UAV, which would keep station above the reference monument and several auxiliary sensors (whose location and stability are not critical). The UAV would simultaneously maintain links with visible GNSS satellites (aided by an on-board inertial system) and with sensors on the ground using any of a variety of accurate (~0.1 mm say) short-range ranging techniques. In this way the pristine airborne GNSS signal environment is transferred to the reference monument despite the relative movement.
The UAV could execute certain maneuvers to continuously calibrate its antenna, similar to robot absolute antenna calibrations on the ground. The craft could spin slowly around the vertical axis, or tilt slightly, or both. The attitude from the inertial system would become part of the observation stream to close the calibration loop. By contrast, there is great reluctance to move ground-based GNSS reference antennas to carry out any sort of ongoing calibration program on them. With flyers, continuous monitoring comes for free.
Small rotations and tilts on an airborne platform are impossible to completely avoid, and high-wind situations may force some loss of observing time. But for most of the time, the environment should permit an accurate tie from UAV track to ground network. Depending on the choice of flying craft, several may be needed, spelling each other for charging or refueling. Automatic fleet management will probably have many good solutions over the next few years.
It's hard to know whether there's a benefit without more detailed study, but the prevailing trends in GNSS system accuracy seem to be increasing the relative importance of multipath. If we assume progressively better satellite orbit and clock estimates and ionosphere and troposphere sensing, then multipath may well loom as the last remaining large, difficult, uncertain systematic error. (Perhaps a UAV could help with estimating the wet troposphere delay as part of normal operation, to the extent that measurements on the very bottom segment of the troposphere are predictive of the full path.)
Finally, I wonder whether UAVs could help with urban canyons or tree-canopy issues. A surveyor might deal with an awkward situation by tossing a UAV into the air and replacing a bad-GNSS-signal problem with a perhaps easier-to-solve UAV-to-ground-sensor problem using vastly stronger optical or RF links.