GPS/Inertial Navigation
A friend of mine solved this down to the sub 1M range for the seismic/surveying industry using inertial navigation married to GPS. Very simplistically, after the first 'good' GPS fix, all movement after that is relative, until the next 'good' fix etc.
Since you know 'exactly' where the garden shed is, as a starting point, GAGA could mow for x minutes (or to a pre-defined loaction) inertially, pause to acquire a 5, 7, 9, whatever satellite 'fix' , update its location if necessary and repeat as/if necessary until the job is done.
Size does matter, but since GAGA is a ride-on contraption, a designer backpack rig should not be a concern for the prototype.
I am not comfortable posting someone elses e-mail addy in a public forum, but if you wish to pursue, let me know and I will be happy to share with the SPB.
DP.