EMB ERJ 135 ER/LR
Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface; Troubleshooting
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance; Aircraft Aircraft Damaged; Flight Crew Overcame Equipment Problem; Flight Crew Requested ATC Assistance / Clarification; General Maintenance Action
Aircraft
I was the Captain of Aircraft X; a scheduled public charter operated under FAR Part 135; and an Embraer EMB-135.  We had flown 3 flight legs this day and we were departing on our 4th leg of the day without any re-set or shutdown of the aircraft avionics.During our climbout on the SID while passing through approx. 4;000 feet; TRACON asked us; '[Aircraft X]; where are you going?'  We advised them that we are on the SID and they advised us that we were approximately a mile west of our intended course.  We cross checked both navigation displays and noticed a very significant position error between the left and right navigation systems.  The left and right navigation displays were approximately 6 miles different from each other.We advised ATC we were dealing with a navigation issue and we obtained radar vectors while we determined what was going on.  As we climbed above 15;000 feet we noticed that the two navigation systems were slowly syncing back together.  We were able to continue on course and climb to cruise altitude without any other issue.  During the remainder of the flight we did not notice any other system anomalies.Upon arrival; we wrote up the navigation system in the aircraft logbook and advised our maintenance technicians about the issue.  The technician that met the flight advised us that he has seen this same issue being reported by aircraft that have departed ZZZ and that the anomaly is also usually resolved when the aircraft climb up above 10;000 feet.I have been flying this type of aircraft out of ZZZ for about one year and have never heard or seen this issue before.
[Report narrative contained no additional information.]
EMB-135 Captain reported a momentary navigation system malfunction that resulted in a course deviation.