Learjet 35
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 200; Flight Crew Total 28700; Flight Crew Type 300
Situational Awareness
Aircraft Equipment Problem Less Severe; Airspace Violation All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors; Aircraft
We were flying our Learjet from LAS to ZZZ on the SHEAD1 SID.  During the en-route climb portion of our flight; at some altitude above 14;000 feet MSL; we were crossing SHEAD intersection on coursed to DBIGE intersection.  We monitored our autopilot as it flew the course.  Our FMS/GPS navigational screen showed us on course. The LA ARTCC called us and questioned our on course position.  We showed that our aircraft was past SHEAD intersection and on course.  We continued on course; and later were advised to contact the LA ARTCC Supervisor by telephone when we reached our destination.  During that conversation; he told us that the ARTCC Controller observed an encroachment into restricted airspace.  Our FMS/GPS depicted restricted airspace west of our on course position.  From our conversation we arrived at a possible explanation to the situation; and that was that there may have been some GPS signal anomaly that occurred during that portion of the flight.
Reporter wasn't completely sure what caused the problem.
Learjet pilot reported navigational problems that were associated with the FMS; and GPS issues.