Sure, pegging it to GDP sounds like not a bad idea.

As the nation gets more productive, everyone's effective UBI goes up.

If the real value of the UBI gets to be too high and too many people stop working in balance with automated labor, then GDP starts to decline and people start getting worse off and increasingly incentivized to find some productive work to do.

Seems like it could end up being a self balancing system.

In fact instead of lending Fed inflation dollars to big banks, we could partially fund a UBI with those same dollars!