The trick is to detect conditions like this with virtually zero false positives. Say the sensor fails one in 100,000 times and your algorithm has a 1/100 change of flagging a false positive in the case where the sensor is in fact working properly. Then the chance of a real failure successfully detected is:

    0.00001 * 0.99 = 0.0000099

The chance of a false alarm is:

    0.99999 * 0.01 ~= 0.01

Thus:

    P(failure|alarm) =  P(alarm|failure)*P(failure)
                        ---------------------------
                                P(alarm)

                     =   0.99 * 0.00001
                        ----------------
                        0.0000099 + 0.01

                    ~= 0.001

 

So alerts from your seemingly ok-ish algorithm will be false alarms 99.9% of the time!

Maybe you could have a pair of vanes. Each vane is physically limited to a portion of possible angles. Vane A would only work above say -10 degrees AOA and vane B below +10 degrees AOA. This would give you a regular test of both sensors when the AoA changes in normal flight. You have more bounding of correct values.

Majority vote is a very simple system to reason about. What you’re describing adds a whole bunch more complexity.

For the noise sensor scenario, is the sensor failing or is the ancillary (and single point of failure) noise sensor failing? What happens when you have a false positive like that and a false negative on another sensor?

For the correlation scenario, when you have two systems that disagree, how do you determine which one is failing? Are their precisions and tolerances sufficiently close that you’ll get a warning at a useful point in time?

It probably could, but you'd have to code for that, rather than expecting the majority of 3 sensors to always be right.