IRS drift
superpilot
How long was the flight. I bet you had a large IRS drift.
You know when you park and you see a residual GS or 7 kts or whatever?
In approach, a few knots of drift at right angles with the LOC will give a drift of say 1º or maybe more, so each time you center the bird, you deviate. So what you do, is when you see that the LOC is being maintained well with the bird 1º to the right, that is your target. It is like correcting the shooting with a rifle...