What was found
(CAN) AIRPORT WEATHER WAS RAINY WITH CB TS IN THE AREA, AND IMC CONDITIONS UP TO APPROX. FL300 DURING TAKEOFF WE HAD A MASTER CAUTION COMING ON TOGETHER WITH THE CAS MSG "EFIS MISCOMPARE" AND A HDG FLAG ON BOTH THE PFDS WITH A HDG DIFFERENCE OF 6 DEGREES. AS THIS HAPPENED TO US SEVERAL TIMES BEFORE AND ALWAYS WENT BACK TO NORMAL AFTER GOING TO DG MODE AND BACK, WE DECIDED TO CONTINUE THE TAKEOFF. AFTER ROTATION WE NOTICED THAT THE DIFFERENCE BETWEEN THE TWO HEADINGS WAS INCREASING AND THE FMS POSITIONS OBVIOUSLY DID NOT MATCH ANYMORE AS THE RIGHT HAND SIDE ALREADY INDICATED THE INITIAL TURN WHILE ON THE LEFT SIDE WE HAD TO FLY STILL STRAIGHT AHEAD. WITH THE MASTER CAUTION COMING ON COUPLE OF TIMES DURING THE DEPARTURE WE TRIED TO GO TO DG AND BACK FOR SEVERAL TIMES AS WELL AND EVERY TIME WE HAD DIFFERENT READOUTS AND ALSO WERE NOT ABLE TO VERIFY WHICH SIDE MATCHES THE STANDBY COMPASS. AT SOME STAGE WE HAD DIFFERENCES OF MORE THAN 90 DEGREES BETWEEN LEFT AND RIGHT SIDE. WHILE TROUBLESHOOTING, THE CONTROLLER ALSO ASKED WHERE WE WERE HEADING TO AND IF IT WAS FOR WEATHER. ATC THEN TOLD US WE WERE COMPLETELY OFF TRACK AND TOLD US HE HAS A READOUT OF ALSO MORE THAN APPROX 60 DEGREES OFF. AFTER TELLING HIM THAT WE STRUGGLE TO NAVIGATE AND ASKING FOR HEADING VERIFICATION HE SUDDENLY TOLD US WE WERE COMMENCING A RIGHT TURN WHILE OUR INDICATIONS AND INTENSION WAS TO DO A TURN TO THE LEFT. AT THIS STAGE ALL OUR HORIZONTS SHOWED A TURN TO THE LEFT AND SHOWED THE SAME BANK ANGLE. AFTER COUPLE OF MINUTES WE HAD A AHRS FAIL ON BOTH SIDES TOGETHER WITH A RED HDG INDICATION ON ALL FOUR DISPLAYS. THE ATTITUDE INDICATION WAS STILL "WORKING" AT THIS TIME. ALONG WITH THAT WE ALSO LOST THE INDICATION OF OUR POSITION ON THE MFDS OF COURSE AND THE FMS WENT TO DR. WHEN THE AHRS CAME BACK ONLINE AFTER APPROX 1 MINUTE, WE TRIED TO CONFIRM THE HDG WITH ATC AND THE INDICATION MATCHED THE ONE WE GOT FROM THE CONTROLLER. FROM THIS POINT.