A320 EXPERIENCES GROSS NAV ERROR JUST PRIOR TO ENTERING MEX AIRSPACE.

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ENRTE FROM SFO TO MMAA (ACAPULCO); ACFT WAS FLYING AT FL370. ZLA CLRED ACFT TO DIRECT PDZ J93 JLI; FLT PLAN RTE. SHORTLY THEREAFTER; A FREQ CHANGE OCCURRED. UPON PASSING PDZ; CREW DID AN ACCURACY CHK VERIFYING FMGC POS VERSUS RAW DATA. ACCURACY WAS HIGH AND POS WAS CONFIRMED. AT XA38Z; ZLA ASKED US WHAT OUR LAST CLRNC WAS. WE RESPONDED WITH DIRECT JLI THEN J93. I THEN CORRECTED OURSELVES AND ADVISED THEM IT WAS DIRECT PDC J93 JLI. ATC GAVE US A HDG CHANGE FOR TFC. HE THEN CLRED US TO DIRECT JLI J93 ON COURSE. I ADVISED HIM THAT WE SHOWED OURSELVES PAST JLI ON J93 PASSING GWIRE (FIR BOUNDARY) AND APCHING ALTAR IN MEXICAN AIRSPACE. ATC ASKED OUR SQUAWK CODE AND TO IDENT. WE DID. HE ADVISED US THAT WE WERE 15 MI N OF JLI AT FL370. WE IMMEDIATELY CHKED OUR POS ON POS MONITOR PAGE AND THE FMGC INFO WAS CONSISTENT WITH MAP AND A CHK ON PROGRESS PAGE OF JLI SHOWED WE WERE 100 NM SE OF JLI. THE POS MONITOR SHOWED NO RADIO POS; AND IRS #1; #2 AND #3 TO BE IN ERROR OF 99.9+ NM AND LOW ACCURACY. (I BELIEVE THE FMGC ATTEMPTED TO AUTOTUNE VORS NEAR ITS CURRENT POS; WHICH WAS NOWHERE NEAR ITS REAL POS AND THAT IS WHY WE HAD NO RADIO POS DATA.) WE IMMEDIATELY SELECTED THE RMP AND HARD TUNED JLI AND USED THE DDRMI AND ROSE VOR TO NAV DIRECTLY TO JLI. UPON PASSING JLI; WE FROZE POS TO VERIFY ERROR. THE IRS'S WERE IN FACT CORRECT AND BOTH FMGC'S SHOWED ALMOST 2 DEGS LATITUDE ERROR; BUT ON THE CORRECT RTE. ATC TOLD US WE WERE NOT ON J93 AND TO TURN TO 080 DEG HDG TO INTERCEPT COURSE. I ADVISED HIM WE WERE IN FACT TURNING ON COURSE. I TOLD ATC WE HAD A GROSS LONG RANGE NAV ERROR. ATC ASKED IF WE WERE ABLE TO NAV TO MEXICAN AIRSPACE AND I ADVISED HIM TO CHANGE OUR CODE TO /A. I DETERMINED THAT A SINGLE FMGC RESET MIGHT NOT WORK BECAUSE THE REMAINING FMGC HELD BAD POS DATA. THEREFORE; I PERFORMED A DUAL LATCH RESET; REMOVING BOTH FMGC OFFLINE BY PULLING FMGC 1# AND FMGC #2 CIRCUIT BREAKERS. AFTER 2 MINS WE RESET CIRCUIT BREAKERS AND WHEN BOTH FMGC'S CAME ONLINE THE IRS'S CORRECTLY LOADED THE CORRECT MIX IRS POS. THE RTE INFO REMAINED IN THE BOX AND WE DID MULTIPLE RAW DATA XCHKS. THE POS DATA VERIFIED WITH FMGC. FMGC NAV WAS THEN COUPLED TO AUTOFLT. THE REMAINDER OF FLT WAS NORMAL WITH CONSTANT XCHKING OF RAW DATA AND POS MONITORING WITH ROSE VOR RAW DATA BACKING UP FMGC NAV. FMGC ERROR WAS ENTERED IN LOGBOOK ON ARR AND A BITE TEST WAS DONE ON IRS #1; IRS #2; IRS #3; FMGC #1; AND FMGC #2 WITH NO ERRORS SHOWN. RETURN FLT SHOWED NO ANOMALIES. IT IS MY BELIEF THAT SOMEWHERE BTWN PDZ AND JLI; AN 118 NM DUAL FMGC POS SHIFT OCCURRED. THE MAP CONFIRMED THIS AS WELL AS THE PROGRESS PAGE SHOWED US TO BE ON COURSE. THE IRS POS WAS ALWAYS CORRECT BUT NOT CONSISTENT WITH FMGC'S. OUR POS VERIFICATION OVER PDZ VERIFIED THAT WE WERE ON COURSE AT THAT TIME. NO ECAM WARNINGS OR FMS MESSAGES WERE EVER DISPLAYED. THE LACK OF FMGC MESSAGES WOULD BE CONSISTENT WITH POS; (THAT BEING THE FMGC POS WAS CORRECT IN ITS OWN POS CALCULATION). SINCE IRS'S #1; #2 AND #3 WERE CORRECT; WE RECEIVED NO IR FAULTS OR ERRORS. IT IS MY ESTIMATION THAT WHEN ATC NOTICED OUR POS; WE WERE LESS THAN 5 NM OFF COURSE AND AFTER PASSING JLI DURING ACCURACY CHK (WHICH REQUIRES FLT DIRECTLY OVER FIX PRIOR TO TURNING ON COURSE) WE HAD TRAVELED 12 NM (SLANT RANGE) FROM JLI BEFORE WE INTERCEPTED OUTBOUND COURSE. I DON'T BELIEVE WE CAUSED ANY TYPE OF CONFLICT SINCE ATC NEVER NOTIFIED US OF SUCH. MY RECOMMENDATION IS TO ELEVATE THIS TO MANUFACTURER LEVEL AND RECOMMEND THAT WHEN FMGC AND IRS POS DIFFERS; THAT AN FMGC MESSAGE ALERT CREW OF POS DIFFERENCE.