Small transport pilot reported an altitude deviation occurred while trying to reprogram the aircraft's autopilot that may have been potentially caused by a GPS anomaly. The aircraft's autopilot; which was set up for an RNAV approach; initiated a turn off course. As the pilot disconnected the autopilot and tried to determine the cause of the issue; the aircraft descended below the assigned altitude and the pilot was admonished by ATC. After landing; ATC stated that there had been numerous cases of GPS issues on the approach as of recent and asked if the pilot may have also experienced a GPS anomaly.

Narrative

I descended 300 ft. below my assigned altitude. I was cleared to DARTS intersection; which is also the IF for the RNAV 21 approach into SMO and told to expect the RNAV 21 approach into SMO. I changed the next fix in my GNS 530 from DARTS in Enroute Mode to DARTS in the Approach Mode. A minute or so later; I noticed the CDI swing to the final approach course; which [was] about 120 degrees off the course I was on; and the aircraft; which was on autopilot; initiated a turn to the right. I had not yet reached DARTS; and still did not know why the airplane made a turn towards the next fix on the approach before it reached the fix I had input as Direct To. In any event; I decoupled the autopilot; rolled the airplane level; and was beginning to try to figure out where I was and what the box was doing; when ATC gave me a vector; a crossing altitude at and for DARTS - which my airplane had just turned away from for reasons unknown; and cleared me for the approach. I read it back; but was not sure where I was and was trying to fly the airplane and work the box; when I noticed I had descended 300 ft. below the assigned altitude. I immediately climbed back up; and at the same time ATC cleared me to a lower altitude; and then admonished me for having descended below the initial assigned altitude. I acknowledged his admonition; but was still distracted trying to figure out how to get the box to reflect the approach and get the airplane on the approach. I finally figured it out and flew the rest of the approach uneventfully.Upon landing; after exiting the runway; Tower asked me if I had experienced any GPS anomalies; stating that they had had numerous complaints over the past several days about GPS issues on the approach. I replied in the affirmative.A contributing factor is how ATC works us on that approach. The crossing altitude at DARTS is supposed to be 4;200 ft. but they hold us higher; and the crossing altitude they give is usually much higher than that; as it was today; which sets us up for a 'slam dunk' destabilized approach. Within seconds we get descents; approach clearance; and vectors; which result in a high work load at a critical time. It sets us up for the classic destabilized approach.Long story short; I am not sure what happened. I already have scheduled a sim session with a CFII to work on that approach to see if there is anything I did to cause the CDI swing; but I've been flying behind this box for a good 15 years; just had an IPC (Instrument Proficiency Check); and don't think I did anything incorrectly.