40.1 IMU measurement model

Parent: [IMU index](imu index.md),  probabilistic models-for-imu Backlinks: [IMU motion model](imu motion model.md), imu kinematic model using euler integration

An IMU measures, relative to an inertial frame, acceleration and rotation rate.

• The measurements are corrupted by bias and noise (often assumed to be white Gaussian noise ).  mkok-2017
• Additionally, the acceleration measured is affected by gravity.
• Note the [assumptions in modelling the true angular velocity in IMUs](assumptions in modelling the-true-angular-velocity-in-imus.md)

Sensor readings in the body frame Notation in  Solà 2017 :

Notation in  Forster 2017 :

where is the instantaneous angular velocity of the IMU (B) relative to the world (W), expressed in (B) coordinates

Another term for the acceleration is the specific force measured by the IMU.  MKok 2017

True acceleration and angular velocity, based on noisy and biased IMU measurements Notation in  Solà 2017 :

true acceleration = acceleration due to inertial forces acting on B + acceleration due to gravity [ Source ]

See also: Modelling noise and bias for IMU