I'd be surprised if IRS position was updated in flight. In general the IRS position is an input to the FMS (together with GPS (or not), DME, and VOR in some cases). The FMS determines its position taking all data and known errors into account using the ubiquitous Kalman filter but doesn't at any point change or update the raw IRS position.
The one inertial system that I am aware of that could be position updated in flight was the Carousel INS. I remember the start of the technique was to select position and hold over a known position like a VOR overhead, memory fades beyond that point.