DISCOVERED 13 MI OFF COURSE BY CTR; A FALCON 50 CREW COULD NOT VERIFY IT WITH THEIR INSTRUMENTATION. LATER IN THE FLT FAILURES BEGAN TO APPEAR INDICATING A FAILURE RELATED TO THE AIR DATA REF PANEL ACCORDING TO THE SYS INTERNAL DIAGNOSTIC SYS.

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ON A FLT FROM KEFLAVICK ICELAND TO WINNIPEG; CANADA ON SEP/FRI/04; WE HAD BEEN RE-ROUTED FROM OUR ORIGINAL FLT PLAN TO A NEW FIX OF N6330 W080 DIRECT PIKMO INTXN DIRECT CYWG. BTWN THE NAV FIX OF N6330 W080 AND PIKMO INTXN WE WERE INSTRUCTED TO CONTACT EDMONTON CTR. AFTER CHKING WITH EDMONTON CTR; CTR ADVISED US THAT WE WERE 13 MI OFF COURSE. MY OTHER PLT AND I CHKED AND RECHKED OUR INPUTS INTO THE ACFT'S FMS AS WELL AS OUR PAPER FLT PLAN AND BOTH CONCURRED THAT THE CORRECT INPUTS WERE MADE. WE THEN VERIFIED THE CORRECT NAV FIXES THAT WE HAD BEEN CLRED TO AND BOTH OF US WERE IN AGREEMENT THAT THE PROPER ENTRIES WERE MADE. NOT LONG AFTER THIS EVENT OCCURRED; WE BEGAN TO EXPERIENCE PROBS WITH THE CAPT'S SIDE INSTRUMENTATION THAT FURTHER LED TO CONCERN IN THE COCKPIT. THESE PROBS CONSISTED OF FLUCTUATIONS IN THE SET ALTIMETRY; SET MACH SPD; AND OTHER FLUCTUATIONS ON THE CAPT'S SIDE EFIS DISPLAY. UPON LNDG AT WINNIPEG; CANADA WE EXPERIENCED A HARD FAILURE OF THE ACFT; WHICH WAS DETERMINED TO BE THE ACFT'S ARP (AIR DATA REF PANEL) COMPUTER. THE FLT WAS TERMINATED AND MAINT WAS DISPATCHED FROM ZZZ TO TRAVEL TO WINNIPEG TO REPAIR THE ACFT. PER GENERAL DYNAMICS MAINT TECHNICIAN; I WAS INFORMED THAT THE ARP COMPUTER IS LINKED TO THE ACFT'S IAPS (INTEGRATED AUTOPLT SYS) AND HAS DIRECT INTERFACE TO THE ACFT'S ADC (AIR DATA COMPUTER) AS WELL AS AHRS (ATTITUDE HDG REF SYS) SYS. APPROPRIATE STEPS PER DASSAULTS AND ROCKWELL COLLINS PRESCRIBED MAINT PROCS WERE TAKEN AND THE ACFT WAS RETURNED TO SVC. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE INITIAL DETERMINATION BY MANUFACTURER REPRESENTATIVE MAINT WAS ARP FAILURE. ON THE NEXT FLT A SIMILAR FAILURE OCCURRED AFTER 2 HRS IN FLT. SUCCESSFUL COMPLETION OF THE FLT WAS MADE USING THE REVERSION MODE OF THE NAV SYS. THE PROB WAS; AT THIS POINT; SUSPECTED TO BE FAULTY SWITCHES IN THE ARP WHICH WAS REPLACED. ON A THIRD FLT A SIMILAR FAILURE OCCURRED DURING AN ARR AFTER ABOUT 2 HRS OF FLT. THE MANUFACTURER AND AVIONICS PROVIDER HAS HAD THE ACFT FOR ANALYSIS FOR SEVERAL WKS. THE DETERMINATION HAS BEEN THAT THERE IS AN OVERHEATING PROB ASSOCIATED WITH THE CROSS TIE BUS BTWN THE AIR DATA COMPUTERS.