The actual study is here [0] and the abstract and introduction do a much better job of describing what the study is actually about.
I encourage you to read at least those before you dismiss the research and its real-world applications.
TL;DR: The purpose of the research is to try out a new way of figuring out which sound is going into the user's ears, so that it can be cancelled out. Current methods work for lower frequencies but not for higher frequencies.
They "cheated" because they're testing one component of the system and the "cheating" component is immaterial to the research they're doing.
They "cheated" because they did the easy part, and the "other component" has no known solution.
What they're handwaving away is the real problem. The reason why current methods work for lower frequencies and not for higher frequencies is that your microphone, emitter, and ear all need to be enclosed within a volume << the minimum wavelength you can handle, to eliminate sound field and propagation time effects and let you treat the noise cancellation problem as a point problem in space.
Once you put the ears in open air and the emitters away from them, the problem isn't figuring out the sound that's going into the users' ears, it's figuring it out in advance. The ANC speakers have to send the complement signal before the original signal arrives at the ears, so they both arrive coincidentally.
In other words, the "missing part" to make this research work is time travel (if you use their sensing technology as the only input). Or maybe full-volume sound field sampling and characterization technology (if you don't). Neither of which exist, and which are orders of magnitude more difficult than this research.
The handwave part is "The constraint of the possible locations [of microphones] would affect the control performance and this remains a topic to be further studied in the ANC community."
Yes, it would completely destroy high frequency performance, which is what they were trying to achieve, in anything but lab scenarios (such as the sound sources still being loudspeakers and the microphones being directly in line between them and the user). Real world noise doesn't come from loudspeakers, it comes from all around you. Good luck using distant microphones to compute the expected sound at a user's ear in advance, with any kind of accuracy in the high frequencies.
At best I imagine they could achieve adaptive cancellation for a set of slowly moving pointlike sources in an otherwise simple room, with a number of microphones greater than the number of sources. It's like RF MIMO systems. But again, this is orders of magnitude more work to implement, and real world constraints are going to kill your high frequency response. And for larger sources - forget it. You just can't characterize the transform for that. Not enough dimensions in your input data to solve for it. So anything mechanical, stuff where the noise isn't coming from a literal speaker with a 1-dimensional input signal - nope. As the uncertainty and source size grows, your high frequency response goes down the drain.
No, the missing part is not time travel. Sound comes from the skin and engines of the plane, where microphones could be located, and could potentially predict sound throughout the plane well in advance with an appropriate microphone array. You'd need a fair number of microphones, but I suspect the noise profile isn't too chaotic, which helps. You're talking about things like jet engines (which are repetitive), turbulence (which seems chaotic, but in practice, you shed vertices at a known rate), and a known cabin configuration (modulo people moving about). I suspect while the general solutions suffers from the curse of dimensionality, the specific one probably doesn't. A reasonable number of microphones, combined with decent models, could characterize the whole sound field.
Speakers, located in the seats, if they knew where ears were, could play sound to cancel that.
Decent microphones are $2, and what was expensive were things like microphone preamps, ADC, and the whole data pipeline. From there, we need a shit-ton of computation which really wasn't practical until... big-ass computation systems came out for the rise of ML.
The problem is hard today, but definitely not impossible. I don't think I would have given that same answer a decade ago. An NVidia Titan V brings over 100 teraflops. That's a lot of cycles one can throw at trying to predict sound by my ear from sound at the skin of the airplane in real-time.
If you've ever been in an airplane, you'll know that airplane cabin noise is largely uncorrelated rumble, not fixed-pitch components from the jet engines and such. Good luck solving for the response at a user's position for that, no matter how many microphones you throw at the problem.
I get that this is HN, but no, ML and AI do not magically solve all problems.
Thankfully, most of the energy is in the low frequencies, which existing noise cancellation systems can already do a god job of dealing with in the near field.
Research is an incremental process and even if their proposal has no practical application right at this very second, it's still a new idea that hadn't been tried before they did it.
Instead of focusing on the fact that these researchers didn't singlehandly revolutionise ANC in a single study, how about we focus on what they did do?
That's why I'm confused as to why they're selling this as being relevant for ANC (optimizing for the news cycle?), when it would be a lot more useful to talk about things like optimizing free space speaker systems for a user's position, say, for VR.
Like, the idea of remotely sensing where a user's ears are and what they're picking up is useful. Just not for far field ANC.
I encourage you to read at least those before you dismiss the research and its real-world applications.
TL;DR: The purpose of the research is to try out a new way of figuring out which sound is going into the user's ears, so that it can be cancelled out. Current methods work for lower frequencies but not for higher frequencies.
They "cheated" because they're testing one component of the system and the "cheating" component is immaterial to the research they're doing.
[0]: https://www.nature.com/articles/s41598-020-77614-w