Detect instrument errors before they matter
Historically, accidents have commonly been caused by misleading instrument readings. In 1996, Birgenair flight 301 crashed into the Pacific after a series of errors initiated by a failure of the captain’s ASI. In a similar accident, another Boeing 757, AeroPeru flight 603, crashed due to altimeter failure. The initial cause of the loss of Air France 447 was pitot icing.
In these cases, the crew actually had enough good information from the other instruments to diagnose the error and recover, but failed to do so under the stress of the emergency because of confusion over which instrument they should believe.
It seems to me that the risk of this kind of accident could be easily (and cheaply) reduced by the following expedient:
Nowadays, the readings of all the instruments are, or surely could be, made available as analogue or digital signals. It would be simple to apply these signals to a continuously-running mathematical model of the aircraft's behaviour, detect which of them is inconsistent with the state derived from the other instruments, and display the appropriate warning. Where instrument redundancy is provided (e.g. captain and co-pilot have independent ASI), this task becomes trivial. Input to the model from the functioning ASI would provide an internally self-consistent state: Input from the faulty one would not. I suggest that most single-point failures could be identified in this way, and even multiple failures (such as might result from damage or ice) could be detectable, if not identifiable.
As a mere earthbound engineer, this may already be current practice that I am unaware of. If it isn't, perhaps some qualified person on this forum could comment or suggest objections to the idea.