B737-700
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 159; Flight Crew Type 4053
Confusion; Distraction; Human-Machine Interface
Conflict Ground Conflict; Critical; Ground Event / Encounter Weather / Turbulence
Flight Crew Overcame Equipment Problem
Environment - Non Weather Related
Taxing into X at night. It was dark and the ramp area had moisture/ice present. Self-park system was active. There was evidently 2 lead -in lines to this gate; but I lined up on the wrong line to the right. Both the FO (First Officer) and myself; thought we had the correct lead-in line and never saw the other line (probably due to the glare from the terminal lights and the wet/icy ramp). I verbalized the aircraft type (737-700) and call sign were correctly displayed on the parking system; and began proceeding inbound to park. However; we were so far right of the actual lead-in line the display was not normal. When just a little right or left; chevrons are displayed showing the direction to turn. In this case however; it was  a very flattened chevron pattern and it looked odd. My first thought was this is a new system I am unfamiliar with. I suppose because we were lined up  on the line (confirmation bias) and because the ground handler watched without signaling or showing any concern; I proceeded inbound; thinking it would begin to display properly. I was also tired. The First Officer was watching the right wing and instructed me to stop which I did. Our right wing was close to the a jet bridge. We ended up shutting down the engines and requested to be towed in after realizing we were on the wrong line.
After landing on XXR in ZZZ we taxied to gate X; shutting down the number two engine on the taxi. When arriving in the gate area we had an auto park system illuminated with proper indications and a marshaler in the area although he was not providing guidance. We lined up on what we thought was the correct line; although it ended up being the wide body line; and noticed there was a push back tug in what would appear to be the parking area. The marshaler walked over and moved the tug out of our way but at no time gave us any stop indication. As we were pulling in both the Captain and I voiced concern that something about this felt off. As I was watching the area I noticed we were encroaching on a jet bridge on the right side of the aircraft and that our wing was getting very close to it. I called a stop and we set the parking brake and shut down the number one engine. After opening the window and yelling to the ground crew; there were still no marshaling signals given; we confirmed that we were on the wrong lead in line. We coordinated with the ground crew and alley for them to reposition us back and onto the proper line. We kept the Flight Attendants and passengers informed and seated until completely re-positioned and parked. The rest of deplaning was normal.It should be noted that the autopark system was showing a green lead in line and correct aircraft during the whole event. The Captain mentioned after we shut down that he wasn't getting proper guidance from the yellow arrows; I had not noticed because of the parallax on my side I ignored the detail except that they were present. The other clue that something was wrong was as we approached what should have been the stop point we had no feet to go countdown except for a momentary flash of '55 feet' when we were about 15 feet from the jet bridge on the right side of the aircraft.
Pilots reported following the ground self parking system at the gate to find it off by quite a bit. The aircraft had to be towed into gate area.