Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Engineer; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 60; Flight Crew Total 1200; Flight Crew Type 780
Other / Unknown; Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Provided Assistance; Flight Crew Executed Go Around / Missed Approach; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Weather
Flight from ZZZ-YIP after the PETTE2 arrival we received a vector in IMC toward YIP. We broke out of clouds at 3;500 MSL and advised Controller. Controller then prompted us to look for YIP with a direction and distance. Seeing an airport in that direction with a runway we believed to be 23 we believed that we saw YIP. As we turned onto final we saw that there was no parallel runway and the localizer did not intercept.  Also we saw a smaller aircraft much closer to the airport on a base leg to the same runway. We immediately broke off the approach; climbed and turned and contacted Tower and then contacted approach for a vector back to YIP. Detroit Approach advised we were lined up for ARB and gave us a vector. We then had visual on YIP; notified ATC and were cleared for the visual 23 left once more. As me made our turn toward the airport the Captain continued to turn following a localizer that had captured what we later determined was the back course. I advised him the airport was to our left. It was hard to see in the haze. But he believed that airport to be DTW. I advised ATC we lost contact with YIP and would need a vector to ILS 23 left. We safely landed the aircraft.
Corporate Jet First Officer reported discontinuing a visual approach to YIP airport when it became apparent they lined up for the wrong airport.