Air carrier Captain reported a fumes event during approach which was described as an acrid electrical odor. The flight crew continued to a safe landing.

Narrative

During takeoff on Runway XX in ZZZ1; the HUD takeoff indications disappeared. Thankfully I had just briefed the pages; noted ZZZZZ and also said the words; take off turn left and get the flaps up. Take off; turn left. The vertical guidance was also not available in the HUD or the primary flight display. After acceleration and flap retraction it was noted that the VNAV was no longer activated. We reactivated the VNAV. After a minute or two it deactivated. We reactivated it and went through the FMS to see if we had done something wrong. We continued to ZZZ after we noted no deficiencies. ZZZ1 would have been an overweight and near cross wind component landing and it was deemed better to continue to the destination of ZZZ. Cruise went completely normal. On decent below 18000 the VNAV again disengaged. This a happened several times. Passing through 11000 we smell an acrid electrical smoke smell and then I had some eye irritation. I said that we should put on the masks rather than continue on without the masks. We did the memory item of masks. [Requested priority handling] on the radio with ZZZ approach. The VNAV would not reengage and I lost the bird in the HUD and vertical guidance on the primary flight display. The First Officer (FO) quickly went through the QRC and QRH and completed the smoke and fume elimination checklist. I continued on raw data; no Autopilot or auto throttles with the mask on while executing the ILS to Runway XY. We were met by the trucks and taxied to the gate. The gate agents were not there and we waited for several minutes until one arrived. We demasked at the gate since we would be able to open the window if necessary. Crash Fire Rescue (CFR) followed us to the gate. We did not see smoke in the cockpit. The number 1 Flight Attendant (FA) did state that he could smell smoke coming from the cockpit. Aircraft maintainers found that the AOA vain was problematic on post flight.My recent training during recurrent prepared me for this event. I am very happy that one of the profiles in training is the handflown cat 3 approach. Major Kudos to the training department.