A few thoughts: first of all you'd most likely want a dedicated box for that task, not your phone/iPad that also runs tons of other applications, which could introduce conflicts. Just like you don't use Flight management system computing resources to stream videos for the in-flight entertainment system. Further, you'd probably want the thing hooked up to additional sensors, eg. airspeed, maybe a more reliable gyro that is installed in a fixed position, properly calibrated; etc. Inexpensive, commercial-off-the-shelf technology, not certified, suitable for use in an experimental a/c, at your own risk, something like this:
iEFIS