It's mugwort. You have to dig down to get ALL the roots, as this beast will regrow from the smallest bit of root. It will take a while to get rid of all of it, but if you keep after it, and it's not coming into your yard from a neighbor, you can do it. I recommend using a garden fork rather than a spade or shovel, as it's less likely to break the roots. I did a lot of it on my hands and knees with a cultivator, too. Jeez, I hate this stuff.