TBM 960 corporate pilot reported an instrument malfunction which resulted in ATC issuing a low altitude alert. The pilot stopped the descent and continued the approach and landed.

Narrative

I was conducting what should have been a benign and routine flight from ZZZ1 to ZZZ and back. Flying as a single pilot with two passengers onboard. The initial start up; run up; and departure process was uneventful. At some point during the flight path to intercept the ZZZ2.ZZZ2 1 STAR; Center queried if I would like a shortcut to ZZZZZ; which I accepted. I was instructed then to fly DIRECT ZZZZZ and descend to 7000. I activated the fix from the preloaded and active flight plan then instructed the avionics to descend to 7000. Shortly before intercepting ZZZZZ I was handed off to Approach Control who asked if I was direct ZZZZZ still. I stated that I was and referenced the avionics to make sure everything was in order. At this time I noticed that the aircraft was flying adjacent to the magenta line (Garmin G3000 suite); off by what appeared to be a half mile and continuing to slowly deviate. I instructed the avionics to go direct ZZZZZ ('Direct to' function) and checked to ensure the appropriate NAV mode was active and that NAV was indicated at the top of the PFD (Primary Flight Display). However no change occurred when the Direct function was utilized. The aircraft continued to fly its' present heading and did not change as requested. At this point the Approach Controller instructed a 20 degree right turn and to descend to 3000 to intercept the localizer for the ILS XXR via the IAF ZZZZZ1. I turned the NAV mode to HDG ('Heading Mode') and turned 20 degrees to the right; pressed the NAV APR button ('Approach Mode') and instructed the aircraft to descend to 3000 via VS mode ('Vertical Speed'). As the aircraft was intercepting the localizer and turning on course; the Approach Controller then asked what altitude I was at. I told them I was indicating about 3;600 for 3;000. The Controller stated he was showing 2;800 and suggested no lower as a low altitude alert would be necessary. He then referenced the local altimeter which I verified on my avionics. I stopped the descent and instructed the aircraft to immediately climb to 3600 to try and correct for the low altitude situation. It was at this time I noticed the ESIS (Electronic Standby Instrument System) (Back up AHRS instrument) and secondary MFD (Multi-function Flight Display) were displaying the correct altitude of around 2;800 ft. Confused I elected to utilize the secondary MFD to accomplish the rest of the flight. At this time the Controller instructed me of having issued a Low Altitude Alert and queried if I had the field in sight. When the aircraft was stabilized I looked out to find the airport of the nose and verified to the controller I had it in sight. He asked if I could keep the airport in sight and when I told him I was able; he cleared for a Visual Approach XXR into ZZZ and handed me off to the Tower. I apologized for the situation; stating I was not sure what was wrong with my avionics but was flying by secondary instruments and switched to tower. The remainder of the flight into ZZZ was uneventful. Once landed and the passengers had departed from the GA terminal; I returned to the aircraft and started up the avionics. I inspected the diagnostics page for any discrepancies and verified the altimeters were reading appropriately. All three (Primary; Secondary; and Backup) read within a margin of ~20-30 feet. Weather had improved since and I elected to fly back to ZZZ1 after cycling the avionics a few times; inspecting pitot/static ports; and running through system checks. No anomalies appeared at this time. The return flight to ZZZ1 was largely uneventful as the avionics all appeared to function properly until the initial descent into ZZZ1 occurred. At 16;000 MSL cleared to 4;000' I began a descent utilizing the Vertical Navigation Mode (VNV). When the navigation path was intercepted and captured the aircraft began a 3.0 degree descent to 4;000. However the Left Hand (Primary) PFD did not indicate it had captured the descent path. However the Right Hand (Secondary) MFD indicated correctly. Once again; I began to rely on the Secondary MFD for the remainder of the flight. At this time I also toggled the PFD from the default AHRS/ADC1 data to AHRS/ADC2 data. Producing a yellow caution on both MFDs; however the PFD still did not indicate the proper descent path indication. Center cleared me for the RNAV XX Approach via ZZZZZ2. When I activated the approach I noticed the Garmin unit had bypassed ZZZZZ2 and was attempting to make a ~120 degree left hand turn to intercept ZZZZZ3; the Final Approach Fix (FAF). As this was a sharp turn I instructed the avionics to go Direct to ZZZZZ3. It did not do as requested. At this point; as I had not yet started the approach; I removed the RNAV XX approach from the flight plan and then instructed the avionics to fly Direct to ZZZZZ3 in NAV mode. The avionics then did as it was supposed to. I re-loaded the approach and activated it. It loaded the approach correctly to begin at ZZZZZ3 with a course reversal in hold as intended. The rest of the flight was uneventful.Two days later after we discussed the issue with maintenance and looked at the avionics further; no issues had been discovered and we took the aircraft on a VFR test flight to ZZZ3 and back to ZZZ1. All functions operated predictably and properly.