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here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the translational part we need the norm of the linear velocity and for the rotational part the norm of the angular velocity is needed. the sensor output delivers the angular velocity values (3D) but no linear velocity. It seems we need to conduct an acceleration integral to estimate linear velocity but the noise and drift issue is there. Also the sensor is body framed reference not inertial. For linear velocity we need to have an Eulerian frame but the sensor output is in Lagrangian frame.

Does anyone has an idea on this?