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Yes, it's a ridiculously tight spec. Their "object" is likely going to be bigger than that. 10cm is not out of the bounds of professional surveying GPS units, but they are not cheap.
I assume the OP is US based so that means WAAS access which improves things. With averaging and a good antenna you should be able to get sub 1m repeatability with a
another posibility is to use x/y/z accelerometers to keep track of exact movement and subsequent offsett from some base/starting position
requires no external refernce point other than a know starting position
self contained rate of change and virtual location software might be tricky in a cost effective package though.
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