Ground planes are utterly useless unless you're running a 1/2 wavelength antenna -- that'd be a whip 17 feet high. 1/4 wave antennas, or indeed anything other than 1/2 (including 5/8, which is frankly useless) the ground plane actually degrades the signal.
Furthermore, the so-called groundplane kits sold in truck stops etc are actually connected to the antenna feed, not to ground as you'd need for a real groundplane. Also, a groundplane has to be relatively large -- about as big as the vertical part of the antenna -- to do anything useful whatsoever.
Dan KG6OHK