Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Executed Go Around / Missed Approach
Weather
While established on the ILS 10 approach; ATC asked us if we were correcting back on the LOC. I announced that we were showing centered on the LOC. We had no course deviation indications showing. We continued on the approach. He again told us we were off course and gave us a PRM breakout. The FO (First Officer) initiated the breakout then said 'your controls' and gave them to me. I continued with the maneuver and we got vectored around for the same approach. We didn't have any issues the second time.There was a 55 knot direct crosswind at approach altitude and there were many other aircraft having the same issue also reporting that they were indicating no deviation.
Air Carrier Captain reported going around after ATC advised off course; even though there was no off course indication.