DC10 CREW MISSED A POS ESTIMATED BY 5 MINS ON THE HAWAIIAN TRACKS FROM THE MAINLAND.

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WHEN MAKING OUR DUETS POS RPT WHILE FLYING WBOUND ON THE DELTA TRACK BTWN LOS ANGELES AND HONOLULU; WE ESTIMATED DOPPS (THE NEXT REQUIRED POS RPT) AT XA02Z BASED ON THE DISPLAYED DATA OF OUR #1 GPS SYS. FOR A PERIOD OF ABOUT A HALF HR IN THE VICINITY OF DONER (THE NEXT WAYPOINT AFTER DUETS) WE ENCOUNTERED MODERATE CLR AIR TURB ACCOMPANIED BY RAPID INCREASES AND DECREASES IN MACH SPD; WHICH REQUIRED SEVERAL PWR ADJUSTMENTS. JUST PRIOR TO REACHING AND RPTING DOPPS WE NOTICED THAT THE #1 GPS WAS NOW ESTIMATING DOPPS AT XA07Z; A VARIANCE OF 5 MINS. UPON CHKING WE REALIZED THAT THE #1 GPS; WHICH WAS BEING USED FOR POS RPTING; HAD EITHER DROPPED OR HAD NEVER PROPERLY RECEIVED; THE FORECAST WINDS ALOFT DATA WHICH HAD BEEN INPUTTED INTO THE #2 GPS AND XMITTED TO THE #1. APPARENTLY THE #1 GPS HAD BEEN ESTIMATING FIXES USING ITS OWN SPOT WIND CALCULATIONS INSTEAD OF FORECAST WINDS. THIS COMBINED WITH THE LOSS OF AIRSPD DURING ENCOUNTERS OF TURB PROBABLY CAUSED THE INACCURATE ESTIMATE. CLOSER XCHKING BTWN GPS SYS AND BETTER AWARENESS OF THE EFFECT OF AIRSPD DEVS ON PROJECTED TIME ESTIMATES MAY HAVE AVOIDED THIS PROB.