Narrative:

We were climbing [and] flying runway heading; when the departure controller cleared us on course. 'Rnp' was now displayed on both primary flight display's / attitude direction indicator's (ADI). The course to our first fix was displayed as approximately 275 degrees. We initiated a turn to approximately 240 degrees to intercept. The course line was continuously moving away; maintaining a 10 NM intercept; with increasing map shifting; and the displayed distance to the fix was increasing. The controller asked if we were deviating; and we said yes; as there was a build in front of us. After deviating for the buildup; it became apparent that the GPS position was not reflecting our position accurately; or the position to the next fix. We advised the controller we were experiencing a navigational malfunction; and requested a heading to the next fix. We were issued a heading of 180 degrees. We were flying approximately 260 degrees at the time; as verified by ATC. As we were issued the new heading; the wet compass was checked and agreed with the heading shown on the display. We manually selected the VOR frequency and proceeded directly to it via navigation 2 off of the assigned vector; initially navigating with use of the radio magnetic indicator (RMI).we looked in the QRH for a procedure for a FMS failure as it pertained to our current situation; but there wasn't one. We checked the circuit breaker panels and noted all were in appropriate positions. We plotted the route on the jeppesen enroute charts; and checked that the operational service volumes of the vors along our course were adequate. One exception was noted; and this was remedied by an amended clearance onto the arrival in our destination. We requested the center controller contact our filed destination airport to verify they would accept us into the terminal airspace.at this point; we contacted dispatch and maintenance control. The connection was extremely poor; but we were able to relay our situation; and get confirmation that at FL280; the remaining distance; time; burn; extra and fuel remaining was more than sufficient to continue to our filed destination (landing fuel 8.0).as the flight progressed; the GPS began to slowly correct its position. Its latitude was never off by more than a mile; but longitude was; at its worst; 310 NM east of our actual position. The disparity continually lessened as we reached approximately 400 NM into our flight. Near the midpoint VOR the latitude/longitude were compared against the jeppesson charts and found to be accurate; and further verified at the next VOR. The GPS was then used to supplement the VOR navigation for the remainder of the flight.we landed without incident.we were climbing [from departure airport] ATC asked if we were performed any/all recommended preventative measures to ensure the reliability of the navigation equipment.

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Original NASA ASRS Text

Title: A MD-80 flight crew determined a GPS and or FMS malfunction after takeoff resulted in a large track deviation. As the flight progressed; the 310 NM error gradual decreased to zero.

Narrative: We were climbing [and] flying runway heading; when the Departure Controller cleared us on course. 'RNP' was now displayed on both Primary Flight Display's / Attitude Direction Indicator's (ADI). The course to our first fix was displayed as approximately 275 degrees. We initiated a turn to approximately 240 degrees to intercept. The course line was continuously moving away; maintaining a 10 NM intercept; with increasing map shifting; and the displayed distance to the fix was increasing. The controller asked if we were deviating; and we said yes; as there was a build in front of us. After deviating for the buildup; it became apparent that the GPS position was not reflecting our position accurately; or the position to the next fix. We advised the controller we were experiencing a navigational malfunction; and requested a heading to the next fix. We were issued a heading of 180 degrees. We were flying approximately 260 degrees at the time; as verified by ATC. As we were issued the new heading; the wet compass was checked and agreed with the heading shown on the display. We manually selected the VOR frequency and proceeded directly to it via NAV 2 off of the assigned vector; initially navigating with use of the Radio Magnetic Indicator (RMI).We looked in the QRH for a procedure for a FMS failure as it pertained to our current situation; but there wasn't one. We checked the circuit breaker panels and noted all were in appropriate positions. We plotted the route on the Jeppesen enroute charts; and checked that the operational service volumes of the VORs along our course were adequate. One exception was noted; and this was remedied by an amended clearance onto the arrival in our destination. We requested the Center controller contact our filed destination airport to verify they would accept us into the terminal airspace.At this point; we contacted Dispatch and Maintenance Control. The connection was extremely poor; but we were able to relay our situation; and get confirmation that at FL280; the remaining distance; time; burn; extra and fuel remaining was more than sufficient to continue to our filed destination (landing fuel 8.0).As the flight progressed; the GPS began to slowly correct its position. Its latitude was never off by more than a mile; but longitude was; at its worst; 310 NM east of our actual position. The disparity continually lessened as we reached approximately 400 NM into our flight. Near the midpoint VOR the latitude/longitude were compared against the Jeppesson charts and found to be accurate; and further verified at the next VOR. The GPS was then used to supplement the VOR navigation for the remainder of the flight.We landed without incident.We were climbing [from departure airport] ATC asked if we were performed any/all recommended preventative measures to ensure the reliability of the navigation equipment.

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.