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I have noticed this many times across my company's fleet of A320's that is even after a full IRS alignment has been completed many a times there is still a drift value present between the FMGC position and the IRS position. Could any help explain as to how this happens ?

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From my understanding the FMGC position is a mix from GPS, IRS and radio navigation signals and maybe even other values, e.g. re-calibration to the runway database position as you apply takeoff thrust "on the runway". (I think I read this somewhere, not sure if it is true).

And as far as I know the IRS is aligned only with the GPS position, which could explain a discrepancy between the two values even right after an alignment.

Because the IRS on its own has a constant drift over time the FMGC computes a correction vector for each GPIRS. Maybe these drift corrections are not reset during the alignment (assumed installation error) or they are reset and take a bit of time to be re-evaluated after alignment. They could be an integrator type correction that accumulates the error of the GPS and IRS positions over time to "trim away" the IRS position error. The IRS could drift during the alignment which might only corrected for after the alignment is completed. This would take several minutes before the drift is compensated for.

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