Gate coordinates in the FMC, ARP coordinates in the FMC?
Why would the FMC need either one of these?
That is what GPS is not localizing. An Inertial Reference with an ARP as a last IRS POS might the best for a specific SID at the airport. For pre-GPS days, it would be always the VORs or NDBs nearby, but at that days, most aircraft also did not have a FMS.