Get hold of the FMC guide. There are 2 of them and either will do. Transair have them or you could borrow and read up the opening chapters. It's one of the best no nonsense guides to IRS and will answer most of your questions.. .I had a mate who passed Nav/Instruments and never understood what the gyros(real ones as in tristar vintage) actually did. He thought that the gyros calculated some kind of position fix and had answered all his questions on that basis. the gyros(INS) or ring laser gyros(IRS) simply keep the platform level so that the accelerometers can faithfully determine which way it moved and how much for how long. the INS system had an actual dinner plate affair with gimbals and christ knows what. the IRS does it mathematically. So, having adjusted the output of the accelerometers mathematically to simulate being a stable platform, the system number crunches all that wonderful sin/cos/lat stuff that you spent hours plotting on a distorted photocopy of an Icelandic chart, and comes up a version of your position.