WPF treeview: how to implement keyboard navigation like in Explorer?

I am using the WPF treeview for the first time and am astonished of all the basic things it does not do. One of those is keyboard navigation, implemented in any self-respecting treeview, e.g. in Windows Explorer or Regedit.

This is how it should work:

If the treeview has the focus and I type (letters/numbers) the selection should move to the first visible (aka expanded) item below the currently selected item that matches the string I typed and bring that into view. If not match is found below the current item the search should continue from the top. If no match is found, the selected item should not change.

As long as I continue typing, the search string grows and the search is refined. If I stop typing for a certain time (2-5 seconds), the search string is emptied.

I am prepared to program this "by hand" from scratch, but since this is so very basic I thought surely someone has already done exactly this.