Challenger Jet Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Overcame Equipment Problem; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Aircraft
Seconds after departure; FMS Number 1 lost position. Since this was an RNAV departure we were cleared RNAV ZZZZZ. As we had reviewed the departure before takeoff I knew there was a left turn coming up. This is when we were fully aware of the FMS position error. I started the left turn; but turned too far and ATC gave us a heading. We were told to review the departure by ATC. We advised ATC that we had lost FMS position and would need vectors until we could sort out the problem. I put the FMS into independent mode as FMS Number 2 was MELed. I then updated the Number 1 FMS using [a nearby] VOR as a reference. This worked and we completed the trip using FMS Number 1 and backup using VOR NAV. [We] asked ATC for vectors until we sorted out the position error.
Challenger Captain reported an FMS malfunction on departure; causing a deviation from their IFR clearance.