GROSS NAV ERROR OCCURS WHEN THE FLC OF A NIGHT FREIGHTER FAILS TO INSURE PROPER ALIGNMENT OF THEIR 3 INERTIAL NAV SYS DURING PREFLT PROCS. ACFT WAS MOVED PREMATURELY BY TUG. WX FACTORS CONTRIBUTED TO RUSHED DEP.

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THE FLT PUSHED BACK ON SCHEDULE; TAXIED TO THE RWY; AND WAS CLRED FOR TKOF. AS THE ACFT ENTERED THE RWY; THE #5 AND #6 ANNUNCIATORS ILLUMINATED ON THE FE'S ANTI-SKID PANEL; ACCOMPANIED BY THE ANTI-SKID INOP LIGHT ON THE PLT'S PANEL. THE ACFT WAS TAXIED CLR OF THE RWY AND THE ALL CHKLISTS WERE ACCOMPLISHED. CIRCUIT BREAKERS WERE CHKED AND RESET WITH NO RELIEF OF THE PROB AND THE ACFT WAS TAXIED BACK TO ITS ORIGIN; GATE X. THE ANTI-SKID 'PIG TAILS' ON EACH TRUCK WERE SPRAYED WITH CONTACT CLEANER AND THE ANTI-SKID SYS WAS TESTED FOR FAULT ILLUMINATION. THE SYS TESTED NORMALLY; AND THE GND CREW WAS ALERTED FOR AN IMMEDIATE PUSHBACK. A B747 WAS APPROX 15 MINS FROM SCHEDULED DEP; AND THE ARPT'S ONE AVAILABLE TUG HAD BEEN POSITIONED ON THAT ACFT FOR THEIR PUSHBACK. A SIGNIFICANT CUMULO NIMBUS CLOUD WAS APCHING THE DEP END OF THE RWY. I BRIEFED THE CREW THAT WE WERE NEAR MAX GROSS WT FOR THE RWY; THE OUTBOARD REVERSERS WERE NOT AVAILABLE AND WE HAD THE POSSIBILITY OF FUTURE ANTI-SKID MALFUNCTIONS. THESE ITEMS; COUPLED WITH A WET RWY; CREATED AN URGENCY TO DEPART PRIOR TO THE STORMS ARR ONTO THE RWY AREA. THE GND CREW WAS URGED FOR AN IMMEDIATE PUSHBACK. THE TUG WAS REMOVED FROM THE OTHER ACFT AND HASTILY REPOSITIONED TO OUR ACFT. AS THE CREW WAS ACCOMPLISHING THE BEFORE START CHKLIST; THE TUG WAS CONNECTED TO OUR NOSEGEAR AND THE ACFT WAS ACCIDENTALLY MOVED. IMMEDIATELY; THE 3 RED WARNING LIGHTS ILLUMINATED ON THE INS MODE PANELS. FROM REACTION; I MOVED ALL 3 MODE SELECTORS TO THE NAV POS AND THE RED LIGHTS EXTINGUISHED. ALL INS DATA SELECTORS WERE PLACED TO THE DSRTK/STS POS AND THE TEST BUTTONS WERE PUSHED UNTIL ALL FAULTS WERE CLRED. HAD THE WARNING LIGHTS REMAINED ILLUMINATED; OR ANY FAULTS REMAINED IN THE SYS; THEN NORMAL RE-INITIALIZATION WOULD HAVE BEEN PERFORMED. HOWEVER; ALL FAULTS WERE CLRED FROM THE INU. ALL MILEAGE AND OTHER INDICATIONS APPEARED NORMAL. PRIOR EXPERIENCE WITH INS SYS THAT WERE MOVED PRIOR TO SELECTING NAV; HAD ALWAYS RESULTED IN UNUSABLE SYS THAT REQUIRED COMPLETE RE-INITIALIZATION. THIS SYS; WHICH IS DIFFERENT AND MORE SOPHISTICATED THAN OTHER ACFT IN OUR FLEET; CLRED ALL FAULTS AND APPEARED COMPLETELY NORMAL. BECAUSE OF THE RAPIDLY APCHING WX; THE PERCEIVED ACFT ABNORMALITIES; AND WHAT APPEARED TO BE A NORMAL NAV SYS; THE ACFT WAS LAUNCHED. DURING DEP THE NAV SYS WAS MONITORED CONTINUOUSLY AND ALL INDICATIONS APPEARED NORMAL. GROSS NAV ERROR CHKS WERE PLOTTED AT 'KEBAR;' WHICH IS 107 MI FROM THE DEP ARPT. SYS #1 WAS 1.5 MI; SYS #2 WAS 2 MI; AND SYS #3; 2 MI; TOTAL ERROR. PERHAPS SLIGHTLY MORE 'ERROR' THAN USUAL; BUT NOT OUT OF TOLERANCE. FURTHER PLOTS WERE PERFORMED; HOWEVER THE ACFT WAS CONSTANTLY MANEUVERING DUE TO HVY WX ACTIVITY ALONG THE TRACK. PERMISSION WAS RECEIVED FROM NAN CTL FOR DEVS UP TO 20 MI AND THIS MANEUVERING CONTRIBUTED TO THE DIFFICULTY OF PRECISE PLOTTING FROM THE TWO AVAILABLE (1 NDB AND 1 VOR) LAND NAVAIDS; THUS ELIMINATING A PROPER POS UPDATE DURING THE 1 HR AFTER LAUNCH. DURING CRUISE; THE INS SYS WERE CONTINUOUSLY EVALUATED. AFTER MORE THAN 4 HRS OF FLT (PAST THE ETP); SYS #3 HAD ACQUIRED SEVERAL FAULTS THAT WOULD NOT CLR AND DIFFERED IN MILEAGE BY 15 MI; HOWEVER TRACK CTRLINE WAS CONSISTENT WITH #1 AND #2. SYS #1 WAS PARALLELING SYS #2 BUT THEIR CTRLINES WAS APPROX 14 MI APART. SYS #1 LED SYS #2 BY 10 MI. CONTINGENT NAV WAS MAINTAINED VIA COMPUTER FLT PLAN MAGNETIC HEADINGS; ETC. PRIOR TO ANTICIPATED VOR CAPTURE AT HNL; THE DME CAPTURED WITHOUT AZIMUTH AND ZHN WAS CALLED AND NOTIFIED OF AN APPARENT INS DISCREPANCY. THE FLT WAS RADAR IDENTED AND RECOVERED NORMALLY. WE WERE ADVISED BY ZHN THAT WE WERE APPROX 20 MI OFF COURSE. RECOMMENDATIONS: FURTHER TRAINING SHOULD BE PROVIDED ALL CREWS CONCERNING THE SPECIFIC INS INSTALLATION ABOARD THIS ACFT. EMPHASIS SHOULD BE MADE THAT RE-INITIALIZATION IS ALWAYS REQUIRED AFTER AN ACFT MOVEMENT PRIOR TO NAV SELECTION; REGARDLESS OF SYS INDICATIONS.