For the Lord your God hath driven out. So the Masora and the LXX. The Vulgate and the margin of our version translate by the future. So Luther also. The next verse is undeniably future. An appeal to their experience, which did not fail (see Joshua 24:31) to be effective as long as the memory of these things was fresh in their minds.
So in the Prayer Book of the Church of England we find the appeal, "O God, we have heard with our ears, and our fathers have declared unto us, the noble works that thou didst in their days, and in the old time before them."
And the passage (Psalms 44:1-3), from which the idea of this petition is taken, is an allusion to this speech of Joshua. And we often, in times of faintheartedness or sloth, need to be thus reminded of the moral and spiritual victories of the true Israel, under the true Joshua the Saviour, over the enemies with whom we are forbidden to make a compromise.