RPTR IN G-3 GRUMMAN GULFSTREAM GETS OFF COURSE GOING FROM NAGOYA TO MAUI AND MISSES THE HAWAIIAN ISLANDS.

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WHILE XING THE INTL DATELINE; ACFT MADE SCHEDULED TURN ON COURSE OF APPROX 15 DEGS R. SHORTLY THEREAFTER; ACFT MADE A 10 DEG L CORRECTION. POS WAS CHKED AND PLOTTED ON CHART. POS WAS ON FLT PLAN COURSE LINE. TRIP CONTINUED AND THE FOLLOWING COURSE FIXES WERE PLOTTED AT THE APPROPRIATE TIMES. ALL FIXES WERE ON PROJECTED COURSE LINE. WHEN WE PASSED DANNO INTXN I WAS NOT ABLE TO IDENT THIS FIX BY VHF NAVAIDS. I CONTINUED TO FOLLOW PLANNED COURSE AND MADE RADIO CONTACT (VHF) WITH ZHN. HF RADIO CONTACT WAS ALWAYS MAINTAINED. AFTER APPROX 45 MINS WE DECLARED AN EMER BASED ON UNKNOWN ACFT POS. AT THIS TIME; THERE WAS APPROX 2 PLUS 05 HRS OF FUEL REMAINING. COMMERCIAL RADIO WAS DOING EVERYTHING POSSIBLE TO LOCATE US. WE TALKED WITH SEVERAL AIRLINERS ON 127.5 AND 128.9. THEY GAVE US THEIR LOCATION. WE TRIED TO IDENT SOMEONE; BUT TO NO AVAIL. COMMERCIAL RADIO ASKED US TO MAKE A TURN FROM 155 MAGNETIC TO 230 MAGNETIC. AFTER A SHORT PERIOD; AN AM RADIO STATION (BEACON) 870 ON HONOLULU WAS RECEIVED; BUT VERY WEAK. WE CONTINUED ON THIS HDG (230 DEGS) UNTIL WE HAD A BETTER SIGNAL ON THE AM STATION AND PROCEEDED TOWARDS THIS STATION. AT APPROX 230 NM NE OF MOLOKAI; WE RECEIVED A VOR SIGNAL AND DME LOCK. ABOUT THIS TIME WE WERE NOTIFIED WE WERE IN RADAR CONTACT BY ZHN. WE CONTINUED TOWARDS MAUI (PHOG-OUR DEST). ONCE WE HAD LAND IN SIGHT; WE WERE APPROX 90 MI FROM THE ARPT. WE STARTED OUR DSCNT FROM FL450 FOR LNDG. WE LANDED ON RWY 20; STRAIGHT IN AND CLRED THE ACTIVE WITH 1400 LBS OF FUEL REMAINING AFTER PARKING. A CHK OF OUR POS WAS PERFORMED AND THE GLOBAL FMS INDICATED THE ACFT TO BE 1.2 MI FROM THE ARPT. THE ACFT WAS SECURED FOR THE EVENING. THE NECESSARY PAPERWORK WAS COMPLETED. THE FMS'S WERE OF NO USE TO US AFTER THE LAST WAYPOINT (PHOG) WAS SUPPOSEDLY CROSSED. THE ACFT POS DISPLAYED IN THE FMS'S AND THE LOC OF THE ACFT WERE NEVER IN AGREEMENT AS WE WERE TOLD LATER. WE HAD NO WAY OF KNOWING OUR EXACT LOC UNTIL WE WERE IN RADAR CONTACT. AT SOME POINT SHORTLY AFTER XING THE INTL DATELINE; BOTH FLT MGMNT SYS INDICATED DRIFT ON THE VLF/OMEGA AND THE 3 INDEPENDENT LASER SYS OF MAX DRIFT; 99.9. WE HAD NO CHOICE BUT TO CONTINUE TOWARD OUR DEST AS WE FELT OUR POS TO STILL BE ACCURATE BASED ON PLOTTING THE DISPLAYED LAT/LONG ON OUR CHARTS. NOT UNTIL WE REACHED WHAT WAS SUPPOSED TO BE DANNO INTXN DID WE REALIZE WE HAD A GROSS NAV PROB. WE USED EVERYTHING AVAILABLE TO US TO DETERMINE OUR POS AS WELL AS ESTABLISH VHF RADIO CONTACT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED HE WAS FLYING A G-3 GRUMMAN GULFSTREAM FROM NAGOYA TO MAUI. THE OMEGA DICTATES TO THE 3 INERTIAL REFERENCE UNITS THE POS THEY ARE SUPPOSED TO COINCIDE WITH. SO THE OMEGA DROVE AN ERROR INTO THE GLOBAL NAV SYS. 1400 LBS OF FUEL EQUATES TO ABOUT 30 MINS OF FUEL AT CRUISE ALT AND AIRSPD OF .80 MACH. THE RPTR STATED WE COULD HAVE NURSED ABOUT 50 MINS OF TIME OUT OF 1400 LBS OF FUEL AT CRUISE AND AIRSPD OF .65 MACH WHICH IS WHAT HE WAS DOING AFTER DECLARING AN EMER. THE RPTR STATED HE; IN THE FUTURE; WOULD DEACTIVATE THE OMEGA ABILITY TO UPDATE THE IRS UNIT IF HE HAD ONLY THE NAV TOOLS HE HAD THEN. NOW HE HAS 2 GPS RECEIVERS TO PROVIDE THE BACKUP INFO FOR PLOTTING. THE FAA EXAMINED THE RPTR'S NAV PROCS AND DETERMINED HE WAS USING APPROPRIATE APPROVED NAV PROCS. THE GLOBAL NAV SYS WAS FLAWED.