By radio position update I mean radio navaids updates IRS which in turn updates the FMC.
I do not know what is Kalman Filter. Could you explain how it works?
The 3 IRS has an algorithm which is a weighted computation to lessen the contribution of any IRS which drifts excessively. This algorithm results in a weighted average position of the IRS called the MIX IRS. Difference between this weighted centre n the GPIRS is the BIAS.
Therefore BIAS can be viewed as the difference between the IRS positions by itself n with updates.