Narrative:

Shortly after takeoff from lax we received a message (to be honest I'm not sure if these are correct or not because we were very busy at that time) of either verify FMC-GPS or verify IRS-FMC. I was the pm and looked at the various position pages and noticed nothing unusual. It was not until we were told to go direct to a point in LNAV and the controller questioned where we were going. I responded with the waypoint and about that time noticed that the anp was more than 2 miles off. I then told ATC that we may be more than 2 miles off course and that we needed radar vectors and had no FMC/RNAV capabilities. We switched to VOR navigation at that time and were given a reroute that complied with our capabilities. I saw that the anp (actual navigation performance) went as far as 12 miles off course and later noticed that the IRS positions were very far off. Our map display did not match anything at that point and we switched to the VOR display. On approach to ZZZ I noticed that the GPS was regaining its proper position and the anp was normal by the time we were on final approach. After landing we had to wait for our gate so at that point with the aircraft parked I looked at the position page again and noticed that the FMC and GPS agreed but the irss were still very far away. I left the irss aligned at the gate for maintenance to troubleshoot and once they boarded I explained what I saw.

Related reports:

Google
 

Original NASA ASRS Text

Title: B737NG Captain reported a track deviation occurred when his position sensing capabilities were degraded for unknown reasons.

Narrative: Shortly after takeoff from LAX we received a message (to be honest I'm not sure if these are correct or not because we were very busy at that time) of either VERIFY FMC-GPS or VERIFY IRS-FMC. I was the PM and looked at the various position pages and noticed nothing unusual. It was not until we were told to go direct to a point in LNAV and the Controller questioned where we were going. I responded with the waypoint and about that time noticed that the ANP was more than 2 miles off. I then told ATC that we may be more than 2 miles off course and that we needed radar vectors and had no FMC/RNAV capabilities. We switched to VOR navigation at that time and were given a reroute that complied with our capabilities. I saw that the ANP (Actual Navigation Performance) went as far as 12 miles off course and later noticed that the IRS positions were very far off. Our map display did not match anything at that point and we switched to the VOR display. On approach to ZZZ I noticed that the GPS was regaining its proper position and the ANP was normal by the time we were on final approach. After landing we had to wait for our gate so at that point with the aircraft parked I looked at the position page again and noticed that the FMC and GPS agreed but the IRSs were still very far away. I left the IRSs aligned at the gate for Maintenance to troubleshoot and once they boarded I explained what I saw.

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.