Narrative:

Departing runway 1 [and] while on the initial climbout on the DOCTR3; I called for navigation mode around 150 ft; and began a shallow left turn to intercept the course and avoid P-56. The FMS captured and I flew the flight director. We proceeded to make the turns with the course showing centered. Shortly thereafter; the departure controller asked if we were flying the departure. We stated yes. He advised us of a possible pilot deviation and provided a number for me to call upon reaching [our destination]. As the flight continued and getting closer to [our destination]; we got a GPS not available message on the FMS. I called the washington TRACON on the ground; supplied the appropriate/requested information; as well as advised him of the GPS not available message that appeared later in flight in case it would be pertinent to their investigation.

Related reports:

Google
 

Original NASA ASRS Text

Title: CRJ-700 Captain reported a course deviation occurred departing DCA that may have been related to a GPS anomaly.

Narrative: Departing Runway 1 [and] while on the initial climbout on the DOCTR3; I called for NAV mode around 150 ft; and began a shallow left turn to intercept the course and avoid P-56. The FMS captured and I flew the Flight Director. We proceeded to make the turns with the course showing centered. Shortly thereafter; the Departure Controller asked if we were flying the departure. We stated yes. He advised us of a possible pilot deviation and provided a number for me to call upon reaching [our destination]. As the flight continued and getting closer to [our destination]; we got a GPS Not Available message on the FMS. I called the Washington TRACON on the ground; supplied the appropriate/requested information; as well as advised him of the GPS not available message that appeared later in flight in case it would be pertinent to their investigation.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.