THE FLC OF AN ACR B757 EXPERIENCED A MAP SHIFT DURING AN APCH TO LGA. THE ATCT LCL CTLR DIRECTED THE FLC TO GAR AND THEY SUCCESSFULLY COMPLETED A RAW DATA APCH LATER. THE EFIS MAP DISPLAY WAS 2 PT 5 NM OFF TO THE W AFTER THE FLT WAS IN THE GATE. THE RPTR ADMITTED THAT THEY WERE NOT MONITORING THE RAW DATA DURING THEIR INITIAL APCH.

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CLRED THE LGA VOR/DME-G RWY 22 TURNED ON 4 MI OUTSIDE FAF. NOTICED A SLIGHT MOVEMENT ON HSI MAP; WHICH WE HAD ENTERED THE VOR APCH IN EARLIER. FLYING THE LNAV COURSE ON THE HSI; NO ASSOCIATED MESSAGES FROM EICAS OR FMS; NO FLAGS ON ANY INSTS. WHEN WE FINALLY SAW RWY 22 WE WERE 2 MI N AND APCH CTL DIRECTED A MISSED APCH TO 3000 FT AND VECTORED FOR ANOTHER APCH VOR DME-G TO RWY 22; WHICH WAS UNEVENTFUL. AFTER LNDG; THE HSI MAP HAD DRIFTED 2.5 MI AWAY FROM THE ACTUAL RWY. THIS WAS A VERY INSIDIOUS EVENT DURING THE BUSY TIME OF APCH AT THE FAF. SOME NOTIFICATION OF OUR PRIMARY NAV BEING BOLDLY DISPLAYED WHEN IT IS OUT OF TOLERANCE; WOULD BE HELPFUL IN PREVENTING THIS PROB IN THE FUTURE. SUPPLEMENTAL INFO FROM ACN 372125: IN THE BASE TURN FROM NORMAL DSCNT; AND SUDDEN 2 1/2 MI MAP SHIFT OCCURRED IN FMS; WITH NO ASSOCIATED MESSAGES/FLAGS. COMPUTER/AUTOPLT FLEW APPROX 2 MI L OF RWY; AND LGA TWR DIRECTED MISSED APCH; HDOF TO TRACON. WE RE-FLEW SAME APCH ON RAW DATA. AFTER LNDG; MAP WAS SHIFTED 2 1/2 MI W. THIS IS INSIDIOUS; PARTICULARLY WHEN IT OCCURS DURING A BUSY PERIOD; AS TRANSITIONING TO FINAL. CALLBACK CONVERSATION WITH RPTR ACN #372128 REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT HE WAS FLYING A B757-200 EQUIPPED WITH HONEYWELL FMCS WHEN THE MAP SHIFT OCCURRED. HE SAID THAT THIS WAS THE FIRST MAP SHIFT THAT HE HAS EXPERIENCED IN THE SEVERAL YRS THAT HE HAS FLOWN THE ACFT. HE DID HAVE THE RAW DATA TUNED; BUT NOT DISPLAYED AND HE ADMITTED THAT THE FO AS THE PNF SHOULD HAVE HAD THE ILS DISPLAYED ON HIS HSI IN ACCORDANCE WITH COMPANY PROC. AFTER LNDG THE EFIS MAP WAS IN ERROR BY 2 1/2 NM TO THE W. HE ENTERED THE PROB IN THE LOGBOOK AND FURTHER DISCUSSED IT WITH MAINT TECHNICIANS. THEY COULD NOT PINPOINT THE CAUSE OF THE ERROR SO MAINT PERSONNEL CHANGED THE FMCS AND SOME RELATED EQUIP. THE RPTR TALKED TO HIS CHIEF PLT ABOUT THE PROB ALSO. HE HAS NOT BEEN TOLD OF THE CAUSE AS YET. HE HAS DECIDED TO CAREFULLY BACK UP HIS APCH DISPLAYS WITH RAW DATA IN THE FUTURE; HE SAID. HE SAID THAT THIS EPISODE WAS DEEPLY DISTURBING TO HIM AND HIS FO.