Do aircraft inertial measurement systems ever provide linear velocity information that isn't trash? I had assumed not (except for special cases where you can do e.g. a zero-velocity update)
An inertial measurement system cannot measure velocity. It's insensitive to which inertial frame it is in. (to move from a non moving frame to a moving frame, you must accelerate, which it could detect. but then you have to integrate these accelerations over time)
Your assertion is simply demonstrated to be untrue.
Inertial systems integrate all measured accelerations over time to compute present velocity and position. They are periodically corrected with external references. The accuracy is limited to the accuracy of the accelerometers, the sampling frequency and the accuracy of the digital math, among other things.
This IMU idea could be used, but I am not aware of any current commercial IMUs in airliners - but I am not an airline pilot so that does not count for much.
If I were given conflicting information I would see how the plane is acting. I have flown planes with various primary instrument failures over my decades, some in actual instrument conditions, and always had sufficient secondary sources of data to determine the situation. As an example in a piston plane: Tachometer fails? Cross check fuel flow, manifold pressure and airspeed - subject to mixture control which can be reasonably set using "lean to roughness and enrich" method. Been there, done that. I have had an altimeter fail insidiously slowly, when water got into the static lines (despite redundant ports and properly routing them upward), while in actual near minimums in a non precision approach. (I used GPS altitude cross reference and odd seeming behavior of altimeter needle to diagnose and switch to alternate static.)
Importantly, if the plane is flying straight and level and sufficiently fast, over time this becomes a "feel" and you can tell if something is extraordinary. Maybe not on airliners, but definitely the piston planes I fly a lot and probably the small jets I fly on occasion.
This is why some of these things are mystifying to me. If your engines are set to a certain power and seem to be operating properly, and your attitude is just so, in the absence of unusual meteorological conditions your plane should be performing in a manner consistent to your last experience. If your stall warning is going off, well, maybe the instrument broke. Air France is really scary mystifying.
Look, I am a software engineer so I get it, people can get locked into a misconception about a fault and not step away long/far enough to consider other alternatives. It happens a lot in debugging. But for whatever reason my brain works much faster and more dynamically when shit happens in the left seat of an airplane having problems.
I already mentioned that acceleration measurements can be integrated to get velocity. I asked a question about the reliability of the velocity information available to an IMU, and your reply did not address that.
Ground speed (which is what inertial system would indicate) is not very helpful for the pilot. All piloting relies on airspeed which is how fast the aircraft travels in relation to surrounding air.
The difference between ground-speed and airspeed is the wind. In normal conditions, ground-speed is a useful proxy for airspeed - perhaps not good enough for an airliner precision approach, but more than adequate for normal flight.
For the Lion flight, winds were light and the aircraft was at low altitude, so ground-speed would have been very close to airspeed.
In any case (as pointed out by earlier comments) a proficient pilot should have no trouble flying in daylight and good conditions using only the "Mark I eyeball". It appears the aircraft crashed because the crew didn't fly it - a surprisingly common occurrence for automation-dependent crews!
"An inertial navigation system (INS) is a navigation aid that uses a computer, motion sensors (accelerometers), rotation sensors (gyroscopes), and occasionally magnetic sensors (magnetometers) to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the need for external references.[1] It is used on vehicles such as ships, aircraft, submarines, guided missiles, and spacecraft."
Inertial Navigation System (INS) measures linear acceleration (via accelerometers), angular velocity (via gyros) and optionally magnetic heading. Using integration and filtering (Kalman or similar) you get aircraft velocity, position and attitude. Without constant correction (GPS for example) calculations based on INS measurements degrade over time (due to instrumental and calculation errors) but in range of minutes they are pretty accurate.
The comment I was replying to implied that checking with the inertial measurement system was an alternative to checking against GPS.
I still think I'll be surprised if accelerometers provide useful velocity information over timescales useful to a pilot. But maybe that's because I only have experience with cheap MEMS accelerometers from around 15 years ago.
In any event, what would be the use of inertia-based calculations, when airspeed (through an atmosphere always changing) is the important more bit to keep the plane in the air?
Aviation does not usually require the precision assumed here. The aircraft would have flown fine anywhere between (say) 150k and 300k, so an initial-nav indication of (say) 250k +/- 20k would tell the crew that things are "close-enough".
More useful at the time would be to set a "sensible" power level and maintain approximate altitude ... and looking out the window is usually helpful!
An inertial measurement system cannot measure velocity. It's insensitive to which inertial frame it is in. (to move from a non moving frame to a moving frame, you must accelerate, which it could detect. but then you have to integrate these accelerations over time)