Kalman filter... Learned that during my (50 Years ago, state paid
) ab initio airline pilot training, 2,5 Yr course, 250 hrs of which close to 100 hrs on twin engine jets... )... Had trouble to understand it completely, it was at the time no one owned a PC, programming was for aliens only.
Never heard that name back again.
Yes airliners are always lagging behind in cockpit features. The answer is simple, You cannot convert one, or part of a large fleet, it is simply too costly, not only the hardware/down time, but then suddenly cockpit crews, maintenance staff everywhere need to have had conversion training. The fleet is kinda split in two with different route structures it can/needs to fly. Spare parts will double (some at outstations).
Biz jets are a different story, many of them are a one-off, equipped to the likes of the new owner. Much quicker new electronics can be adapted to the top line of their model ranges.
GA flight schools (club operated) consist of a gaggle of used Cessna/Pipers that have been collected over the years. Standardisation... forget it.
Not sure if it was an urban legend, but NASA once was reported scouring the world to find suitable 286 motherboards to keep the Space shuttles flying....long after the first one flew.