A C182 with a student and instructor pilots aboard suffered a track deviation when both VOR CDIs showed on course inbound on the VOR/DME approach when they were; in fact; tracking south of course. A GPS used primarily for situational awareness provided the initial awareness of the deviation.

Narrative

My instrument student had just completed 3 VOR/DME Runway 16 Instrument Approaches at MCC and the airplane's navigational equipment appeared to function normally. We then proceeded to ARTEY Intersection for the VOR/DME Runway 22L Instrument Approach at Mather Field MHR.After completing the procedure turn and establishing ourselves on the final approach course (intermediate approach segment) we noted that the GPS (Garmin 296--used for situational awareness only) depicted us flying south; away from the final approach course. However; both CDIs remained centered. This caused me and my student to question the accuracy of the airplane's equipment. I tuned the IMHR LOC frequency in NAV Two and the CDI indicated that we were south of the Localizer. Since we were VFR I contacted MHR Tower and canceled our IFR Clearance and proceeded to the airport VFR and landed. I notified the Tower of our navigational discrepancy and after parking also notified NORCAL Approach Control as well just in case there was a problem with the SAC VOR. My student and I trouble shot the VORs on the ground and could not determine if a problem existed with the airplane or the SAC VOR.I also wanted to mention that MHR Tower did an excellent job of observing our course divergence and pointing it out to us.