EMB145 FLT CREW HAS A TRACK AND HDG DEV DURING LGA 1 DEP.

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DEP CLRNC WAS THE LGA 9 WHITESTONE CLB. ON TKOF THE HDG SHOWED APPROX 10 DEGS L OF COURSE. WHEN TURNING R TO 180 DEGS THE COURSE APPEARED TO BE MORE THAN 60 DEGS R OF COURSE WHEN TURNING AT ACCELERATION ALT. WHICH WAS MORE THAN EXPECTED. UPON REACHING 2.9 DME OFF THE LGA VOR THE HDG OF 040 DEGS WAS SELECTED AND THE TURN WAS STARTED. THE CTLR ASKED IF WE HAD STARTED OUR TURN WHICH WE RESPONDED TO 'YES WE ARE IN THE TURN' AND THE LGA DME SHOWED 3.4 AT THIS TIME. DURING THE TURN THE CTLR ASKED US TO INCREASE OUR TURN RATE AS WE WERE FURTHER S THAN EXPECTED. WE WERE THEN GIVEN A NEW HDG OF 360 DEGS. WE THEN WERE GIVEN DIRECT COL AND THEN DIRECT WHITE. THE HDG INDICATION FOR BOTH THE CAPT AND FO AGREED; HOWEVER THE MAGNETIC COMPASS WAS ABOUT 25 DEGS R OF OUR CURRENT HDG. THE FMS SHOWED US DIRECT COL WITH A WIND INDICATION OF 119 KTS FROM THE L. WHEN THE FMS SHOWED US OVER COL THE CTLR GAVE US A HDG OF 250 DEGS AND SAID WE WERE 2 MI E AND PAST THE COL VOR. THE CTLR THEN GAVE US DIRECT WHITE AGAIN AND WHEN SELECTED; THE FMS SHOWED DIRECT WHITE; HOWEVER; THE CTLR'S COURSE TO WHITE WAS 15 MORE THAN THE FMS INDICATED IN THE NAV MODE. WE THEN LET THE CTLR KNOW WE WERE GOING TO USE VOR'S AS OUR PRIMARY NAV. THE CTLR GAVE US DIRECT CYN VOR AND AFTER CYN A HDG OF 250 DEGS. AFTER CYN WERE GIVEN DIRECT RIC WHEN ABLE. WHILE HDG 250 DEGS THE FMS AND VOR SHOWED A BETTER ALIGNMENT AROUND THE VILLS INTXN. WHEN WE ASKED THE CTLR IF VILLS WAS AT 19 MI AND 10 DEGS L OF COURSE; THE CTLR HAD 17 MI AND 10 DEGS L. IT APPEARED AT THIS TIME THE ALIGNMENT OF THE FMS HAD CORRECTED ITSELF.