I'm sorry for the double post but I've been sitting thinking about this and it's a little trickier than I initially thought.
I live in Texas. I own the mineral rights on my property. A landman once told me that as such I not only own the surface rights, I own the rights to any minerals below the surface, all the way to the center of the earth. Not only that but I own the air above my property all the way to wherever. I remember that he said it was all the way from heaven to hell.
Now, the sky is regarded as a public thoroughfare so I can't sue airlines or the military for flying through "my" airspace at altitude but exactly where my airspace ends and public airspace begins has never been defined as far as I know. I'm willing to bet though that it's over the 400 feet that these drones are supposed to be limited to. Either way, I'm willing to take the chance by arguing in court that they were trespassing on my property and airspace and I was legally entitled to shoot it down.
Now my head hurts and I'm going to bed.