B737-300 FLT CREW HAS A TRACK HDG DEV DURING THE TYSSN 1 ARR TO LAS.

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UPON ARR AT THE KADDY INTXN ON THE TYSSN 1 RNAV ARR INTO LAS; THE AUTOPLT MADE AN APPROX 60 DEG R TURN AT THE KADDY INTXN. ATC CALLED TO ASK US WHERE WE WERE GOING. OUR RESPONSE WAS THAT WE WERE ON THE ASSIGNED RNAV ARR JUST PAST KADDY INTXN. HIS REPLY STATED THAT WE HAD TURNED APPROX 6 NM EARLY ON THE ARR AND NOW WE WERE N OF COURSE. WE THEN REQUESTED RADAR VECTORS TO A VISUAL APCH. UPON FURTHER INVESTIGATION; FOUND OUT THAT THE FMS WAS NOT AUTO UPDATING THE POS RELATIVE TO AVAILABLE NAVAIDS ALONG OUR RTE. WE HAD BEEN CLRED DIRECT TO DIFFERENT FIXES AND NAVAIDS ALONG OUR RTE; NEVER ACTUALLY REACHING THE NAVAID PRIOR TO BEING CLRED FURTHER DOWNLINE TO OTHER FIXES. THE FIRST INDICATION WE WERE OFF COURSE WAS THE CTR CALL. OUR FMS'S SHOWED THE IRS'S WERE WITHIN .2 NM OF THE COURSE AND POS ASSIGNED. COMING DOWN FINAL THE FMS SHOWED THAT WE WERE ON THE RWY AT THE FAF. THE CAPT MANUALLY UPDATED THE FMS AND THE MAP THEN SHOWED THE CORRECT POS. I BELIEVE THIS WAS A MAP SHIFT THAT WE DIDN'T READILY IDENT. ALTHOUGH I'M AWARE OF THE POSSIBILITY OF MAP SHIFTS; I HAD NEVER SEEN ONE AND HAD NO REASON TO BELIEVE THAT I WAS OFF COURSE.