Date: 202202
Local time of day: 0601-1200
Location: ZZZ.TRACON, US
Flight conditions: IMC
Weather elements / visibility: 8
Light: Daylight
Aircraft: Citation II S2/Bravo (C550)
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class C ZZZ
ATC / advisory: TRACON ZZZ
Aircraft component: GPS & Other Satellite Navigation
Component problem: Malfunctioning
Reporter organization: Corporate
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Instrument
Human factors: Workload; Communication Breakdown; Troubleshooting
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Overcame Equipment Problem; Flight Crew Overrode Automation; General Maintenance Action
Contributing factors: Procedure; Weather; Aircraft
Primary problem: Aircraft

Narrative: On Date we were arriving in Aircraft X to ZZZ at about XA:30. We were on a flight from ZZZ1 to ZZZ. After we took off from ZZZ1 partway into the flight we discovered an issue with our autopilot. Our autopilot was having trouble maintaining its GPS course. We spent the flight troubleshooting our GPS and trying to correct the heading. We thought we had it corrected and as it would maintain course; but then later went off course again. We were on the ZZZZZ6 arrival for the ILS for [Runway] XXL with the ZZZZZ transition. When we came down to ZZZZZ we were using the GPS until ZZZZZ to transition to the ILS for [Runway] XXL. When I realized the GPS didn't intercept at ZZZZZ I took the autopilot off to correct it. I was then asked if I could make it down and I replied yes. I then thought I was given a heading of 210 and maintain 2;500 feet. I later realized that I was given a different heading. I was then told to turn to the right and climb to another altitude. We made the turn and got vectors back around for the ILS for [Runway] XXL. We then completed the ILS with no further issues.My First Officer was flying the airplane for most of the flight and it was her first time flying Aircraft X in several months. While I have many hours flying Citations; it was my first day in Aircraft X. We completed 2 other flights that morning with no issues. When I realized the GPS was not making the correct turn at ZZZZZ I took over flight in the aircraft manually to correct the problem. We should have notified ATC that we were having issues with our GPS earlier and asked for a heading to our destination.


Second narrative: On Date we were arriving in Aircraft X to ZZZ at about XA:20 am. We were on a flight from ZZZ1 to ZZZ. Partially into our flight we discovered an issue with our autopilot maintaining GPS course. We tried trouble shooting the issue several times and thought upon the time of the arrival we had the situation resolved. (ZZZZZ6 arrival for the ILS Runway XXL with the ZZZZZ transition) I was Pilot Flying until we realized the GSP didn't intercept at ZZZZZ. The Captain disengaged the auto pilot to correct for the error becoming Pilot Flying. We were then asked if we could make it down? The Captain replied 'yes'. Then ATC gave us a heading/altitude change the caption acknowledged it. He queried me on the heading; and I thought it was 210. In the time compression with high work load we should have slowed down and asked for confirmation instead of rushing. We were then queried about why we turned right instead of left. Then a different controller came on with a different heading and altitude. I replied back with the reminder radio transmission as Pilot Monitoring until landing. We then completed the ILS the second time with no further issues. We have since reached out to our avionics department and are trouble shooting the issue so this doesn't happen going forward.We started early in the morning at XT:30 and had two uneventful flights. When we started the third and final flight of the day and recognized we had an auto pilot problem we should of error on the side of caution; not accepted the arrival; and asked ATC to give us vectors to the ILS. When workloads are high such as with the ILS and making the incorrect turn we should establish checks and balances for example: Pilot Monitoring heading left 220/ Pilot Flying heading left 220/ Pilot Monitoring heading left 220 confirmed to avoid confusion so it is received; accepted; and confirmed. I realized how important crew resource managements is and there was a break down in CRM and this is an area we are going to focus on more going forward.


Synopsis: CE-500 Captain and First Officer reported reported a breakdown in CRM during troubleshooting a GPS failure resulted in confusion and turn in the wrong direction.