One of them is to compute the domain of possible next inputs values given the actual values and state of the system (this is how stateful inspection firewall work for example). In a measuring system, input with impossible values can be filtered out of the redundancy set. In case of an aircraft, it's probably possible to compute the domain of possible next inputs values from the energy state, control surface positions, and external environment given that it will not change abruptly at the sub second scale. Should be very effective against erratic spike like experienced on the QF72.
External environment may change very quickly. Microbursts will cause rapid changing wind direction and speed. Temperature inversions have an effect on several parameters at the same time like SAT, TAT, wind speed and direction as well. Those changes may happen very fast. You look at your airspeed indicator, knowing that an inversion will happen, because other crews reported them, and in a split second, you are 20kts slower or faster. The environment can be extreme. I understand your approach, however developing (air data) systems with an integrity to cover all the external factors still sounds like far away to me.
For position computation a system like the one you described already exists. It is called AIME:http://www.northropgrumman.com/Capabilities/AIME/Pages/default.aspx
The air data computers itself have a monitoring, which will help discarding wrong computer outputs.
There is actually a big focus on deep learning neuronal network to train to predictor the next state of a system given as much of inputs as possible. In case of a aircraft the idea is that a variation of the state is not specific to a single input and so it sensibility is minimized in case it go erratic. It's for example maybe possible to have a big chunk of structural force sensors inside the air frame that react with enough sensibility together to approximate some of the primary sensors values. This is highly speculating, I don't even know is someone plan to do that experimentally. Certifying a such system will be a nightmare, if even possible, as most scientists admit that there don't fully understand how there predictor network is actually working in the details. A rather extreme point of view is to say that we don't fully understand the human brain either, and that indications of a deep learning neuronal network could help making a decision. More and more medical diagnostics try to be improved with this innovative approach.
Sounds innovative, for sure. But you need to make that system reliable, understandable and safe for airplane operation. There is no need for another system with it's own set of specific failures. Moderns aircraft are complex. The abnormal sections in the FCOM gets longer and longer. Unless you fully understand this neuronal network I don't want to have it installed in an airplane.
Unfortunately a lot was learned after
airplane crashes, not before.
An other way to detect sensors problem is to purposely add a know stimulation to the sensor and to subtract it from the measured values. The stimulation could be continuous; in that case it's designed to have some unique feature that make it easy to recognize and subtract without affecting the desired measuring dynamic. Many RF receivers could be said to work that way because of the local oscillator mix to the input signal. The simulation could be discontinuous. For example many seismic instruments have the capability to inject a periodic test pulse to the sensors. The test pulse is analysed to grant the functionality and calibration of the sensors. It also act as kind of 'ping' in remote deployed sensors network to assert that the sensors it still working as it usually only transmit rare event over a threshold. On a aircraft adding a know stimulation to the sensors would be quit challenging.
This is done already at a certain level. The TAT (Rosemount) probe is used to measure the total air temperature. This will only work if the probe is not full of ice. Therefore the temperature sensing probe is heated. As you know exactly how much energy you put in the probe for heating, you are able to subtract this energy from the measured value and you will get a proper TAT result.
By the way a nice indicator for ice crystal icing. In case the TAT probe will fill up with ice crystals, because there are too many around exceeding the heating capability of the probe, you will get a reading of ±0°C, as the heated probe is measuring the melting point of the ice crystals. So when you are in cirrus clouds and you get a TAT of 0°C all of the sudden, you might experience ice crystal icing. Unfortunately there is no trigger in the TAT system (or flight warning system) that will highlight this sudden change in TAT to the crew. This might be one application possibility of the energy state and value prediction for the future.
Last on my list is vision analyzing. A camera monitor the system and the images are processed to measure values to assert the safety of the system. Some high risk machines get new feature like this to protect workers. Maybe the AoA could be monitored that way. Pitot will be more interesting...
A camera gives you an optical image of the probe. You might see that it is bent by a birdstrike for example. But can you see a wrongly installed probe? Are you able to identify, when having different probes, which one is correct? I am not discarding your idea, but I am not convinced so far.
If you have a system where essentials sensors could fail, you can add multiple copy of it and/or add alternative sensors or way to evaluate the value (maybe less accurate but sill valuable). Then you can use basic redundantly algorithm or/and use next state predictors to detect and filter out defective sensors.
This is done already. Modern aircraft have 3 or 4 independent sets of pitot, static, AoA, Sideslip probes, TAT an so on. Filtering of defective sensors is already done. Still, computers don't comprehend if there is 1 failed and 2 correct or 2 failed and 1 correct. Of course you put a number x of sensors on a plane and the majority of sensors with the same value wins. But you still have the possibility of all sensors going mad at the same time (Pitot tubes in a volcanic ash environment as an example).
One last point, as aircraft control system look more and more like a network of computers, all the network protection and redundancy must apply too: each node act like a sensor for the next nodes.
My answers to your ideas sound totally repellent. Sorry for that. I don't want to be harsh in any way and it sounds like you know your business. On the other hand there are aircraft manufacturers with lots of engineers that know both worlds, aviation and computers (if that is your business). They are constantly researching alternatives to the current designs. However, coming back to unreliable air data, the pitot/static system prevails for a long time already. It looks like there is no easy solution solving unreliable air data.
Still it is good to be open minded. Thinking out of the box is helpful in any case.