E140 FLT CREW EXPERIENCES REPEATING UNRELIABILITY OF LOC-VOR COURSE AT DEST AND ALTERNATE. EXERCISE EMER AUTH TO FLY VOR APCH VIA FMS MAP DISPLAY WITHOUT RAW DATA INFO.

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WHILE CONDUCTING A FLT; WE HAD TO DIVERT AND USE CAPT'S EMER AUTH TO LAND. WE FLEW TO ZZZ WITHOUT ANY IRREGULARITIES DURING THE ENRTE PHASE. WE SHOT A LOC APCH TO RWY. WE INITIALLY SAW THE RWY AND PROCEEDED TO LAND. THE RWY BECAME OBSCURED BY CLOUDS AND WE EXECUTED A MISSED APCH. WE REQUESTED AN ILS TO RWY TO OBTAIN A LOWER DECISION ALT. WHILE EXECUTING THE ILS APCH AND THE LOC DISPLAY STARTED TO DEV L AND R OF CTR. THE ACFT WAS COUPLED WITH THE AUTOPLT ENGAGED. THE ACFT STARTED A SERIES OF GRADUALLY INCREASING TURNS L AND R TRYING TO OBTAIN APPROPRIATE COURSE GUIDANCE. I DISENGAGED THE AUTOPLT AND PROCEEDED TO HAND FLY THE APCH. I WAS UNABLE TO REGAIN A SUITABLE TRACK TO THE RWY AND WAS NOT CONFIGURED APPROPRIATELY FOR OUR PHASE OF APCH. I ELECTED TO EXECUTE ANOTHER MISSED APCH PROC. WE ASKED THE TWR TO MAKE SURE HIS LOC WAS SHOWING A GOOD SIGNAL. THE TWR INDICATED HE HAD RESET THE LOC AND IT WAS OPERATING. WE ELECTED TO EXECUTE ANOTHER ILS APCH. WE BRIEFED EACH OTHER THAT IF LOC INTEGRITY WAS AGAIN IN QUESTION BELOW 1000 FT WE WOULD EXECUTE ANOTHER MISSED APCH AND DIVERT. ON THE SECOND ILS APCH; THE SAME SERIES OF EVENTS TRANSPIRED WITH THE LOC SHIFTING R AND L OF CTR. WE EXECUTED A MISSED APCH AT AROUND 1000 FT AND DIVERTED. AT ZZZ TSTMS IN THE AREA MADE AN ILS APCH A POOR CHOICE; SO WE CHOSE A VOR APCH TO RWY 36. WHEN ESTABLISHED ON THE INBOUND COURSE AND HAVING BEEN CLRED FOR THE APCH AND TOLD TO SWITCH TO CTAF; THE VOR COURSE STARTED TO VARY L AND R OF COURSE WITH THE AUTOPLT FOLLOWING THE COURSE. I ONCE AGAIN DISCONNECTED THE AUTOPLT. AT THIS POINT THE L FUEL TANK QUANTITY WAS SHOWING AMBER. I DETERMINED WE WERE IN AN EMER SITUATION WITH AN UNRELIABLE NAV SYS; LOW FUEL AND TSTMS IN THE AREA. I EXERCISED CAPT'S EMER AUTH AND SWITCHED MY PRIMARY NAV FROM THE VOR TO THE FMS VOR APCH. WE LANDED FROM THIS APCH.