There have been a lot of ANC responses focusing on the A (active) part. There are two parts to nose cancellation: active and passive. I agree ANC are sweet and all… The other comments have that covered.

If you’re interested in exploring a potentially low cost alternative to expensive ANR headphones or earbuds… Know that there are two parts to noise cancelling: active and passive. Passive nose cancelling is how much the headphones or earbuds reduce the outside noise before the active part needs to step in.

SO, an option I haven’t seen discussed yet would be to get some standard low cost earbuds and get some over-ear ear muffs to put around them.

Edit: literacy is for everyone… I didn’t see the bit about using this for sleep. Over ear muffs plus earbuds wouldn’t be very comfortable. Another option might be just finding some noise sounds you prefer over the nose you like. There are different standard noises… White noise, pink noise, brown noise… These might help make the frequency of unwanted sound your looking to block. This is a link related to noise colors after a quick search: https://www.hatch.co/blog/exploring-color-noises-for-better-sleep-with-hatch

Along these lines, I’m a fan of the idea that electric school buses could be essentially massive mobile energy storage systems that occasionally transport people around. Disaster in the area? Stresses power grid in the neighboring town? Drive over and plug in on demand!