B737-800
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Overcame Equipment Problem
Aircraft
Shortly after takeoff; a route discontinuity appeared between us and ZZZZZ1 which is the first fix on the ZZZZZX RNAV DEPARTURE at ZZZ. This was accompanied by a FMC (Flight Management Computer) scratchpad message. I don't recall what the scratchpad message said because I quickly entered direct to ZZZZZ1 and when executed the scratchpad message went away. Everything appeared to be normal.Sometime later; Center asked us if we were proceeding direct to the next fix and I told them that we were direct.Later in the flight; we were asked again by a different sector controller if we were showing direct to YUYUN which is on the BEREE 1 RNAV Arrival to DFW. We were direct according to the FMS (Flight Management System) and ND (Navigation Display). A short time later; ATC told us that we appeared to be on a diverging course and not heading direct to the fix. I began investigating. Everything appeared to be functioning normally but I did notice that the magenta line and YUYUN were now splitting off to the right from the white aircraft track line (white center line) on the ND even though the aircraft remained centered on the magenta line. We never saw any failure flags or lights and no scratchpad messages besides that first one after takeoff. All systems were operating with no differences between left and right. All updating (GPS; IRS; VOR) was on.I knew we had a problem when I noticed that the ANP (Actual Navigation Performance) was significantly higher than the RNP (Required Navigation Performance). RNP enroute default is 2.0 nm and we were showing 14+ nm and increasing.ATC gave us a heading and some time to investigate.With no known failure indications; I did not find any QRH procedures that I felt could be used. I did not want to try an inflight realignment outside of a specific procedure. There is no 'map shift' procedure that doesn't involve an accompanying failure indication.The VORs confirmed our position and we negotiated with ATC to transition to the CEDAR CREEK 8 ARRIVAL which can be flown using VORs. We discontinued using the FMS and RNAV systems (LNAV and VNAV) for navigation.We flew the CEDAR CREEK 8 arrival to DFW using the VORs and complied with all altitudes and speeds on the arrival. I entered the CEDAR CREEK 8 arrival into the FMS for reference but the problem persisted. The ANP reached as high as 25.3 nm. Approach vectored us to the runway 31R localizer and we flew a visual approach backed up with the ILS. Normal approach and landing. The weather was clear VFR.We did not declare an emergency and ATC never mentioned any deviations; violations or loss of separation.At the gate; I called Dispatch to report the issue and was phone patched to [Maintenance] to advise them and confirm the best wording for the maintenance log entry.I made two additional [logbook] entries that might be worth mentioning. Shortly after reaching cruise altitude; the number 1 flight attendant called to report that the WiFi system was not functioning and all the power ports on the right side of the aircraft were not working.
B737-800 Captain reported being advised of a track deviation and noticed a much higher than normal ANP; even though no failures or anomalies were annunciated.