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 assumed 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? Thanks ahead of time for your thoughts...

We are not told in the play. Holinshead would seem to indicate that it occurred at MacDonald's castle. Surely there were too many battles between the Norse and the Scots during Duncan's reign and no precise battle can be named. I'd be pleased to be wrong on that last point however. Shakespeare does seem to be putting Scotland on the defensive with that comment though, doesn't he?