On the effects of angular acceleration in orientation estimation using inertial measurement units

Determining the orientation of a rigid body using an inertial measurement unit is a common problem in many engineering applications. However, sensor fusion algorithms suffer from performance loss when other motions besides the gravitational acceleration affect the accelerometer. In this paper, we show that linear accelerations caused by rotational accelerations lead to additional zeros in the linearized transfer functions, which are strongly dependent on the operating point. These zeros lead to non-minimum phase systems, which are known to be challenging to control. In addition, we demonstrate how Mahony and Madgwick filters can mitigate the effects of the additional acceleration, but at the cost of reduced bandwidth. This generates insights into a fundamental problem in estimation, that are transferable to many practical applications.