In reply to Murko Fuzz:
That would depend on the beam profile of the antenna. Ideally (but unlikely in practice), the antenna will have zero response below its horizon, but then you have the issues of receiver attitude and the orientation of the antenna horizontal plane within the receiver (which is rarely documented). For these reasons, it's hard to be sure that a reflection from below you will not be picked up by the receiver, assuming there's a line of sight between the receiver and the reflecting surface.
If there's an obvious strong reflector, you may be able to shield the receiver from it by putting your body in the way; we're mostly water, and water is pretty good at stopping L-band signals... The downside of that is that your body and head are common shadowing objects for the receiver, especially if you hold it at your waist, and peer down at the thing...
PS reflections are also a problem in high-rise urban areas, causing the same drift of computed position, compounded by the 'urban canyon' which restricts sky visibility, blocking out the satellite constellation. That's why your smart phones fuses GNSS position with WiFi signal strength maps, etc, to come up with a composite solution to try to reduce the effect of reflections.
Post edited at 10:59