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Amcl has the ability to "snap" the odometry to a new reference point. This can produce the uneven results you're seeing. (It's as if your robot instantly jumped to the new position, so your output is the true instantaneous velocity according to AMCL.)

Typically, Odometry is actually fairly well estimated velocities and angular velocities integrated. AMCL is there to handle the accumulated integral error. Most applications do not require more accurate velocities and angular velocities than wheel encoders/gyros/IMUs produce. Are you trying to calibrate the system in an online manner?

Also, I suspect that the large jumps in angular velocity may be subtracting radians instead of quaternions. The angular difference between 3.1 and -3.1 is 0.08 radians, not -6.2 radians (Unless your robot spins very quickly).