Where did Macbeth kill Macdonwald?

The event occurs before the play, and descriptions are given of how Macbeth killed him but do we know WHERE it happened? From the information given, I've umed it was at Macdonwald's own palace or castle; but then, that idea's thrown off by the Sergeant's description of how Macbeth "fixed his head upon our battlements." OUR battlements, he says - so is it the battlements of another castle? (-keeping in mind that "battlements" refers to the portion of a caste's wall that protects archers) I can't find an answer anywhere, or even a theory of where it might be. Thanks ahead of time for your thoughts...