# IMU gyroscope calibration based on accelerometer values

I need to calibrate some IMUs for a project. I am planning on using an algorithm proposed by Alberto Pretto et al (Google Shcolar link), based on two assumptions:

1. The common the magnitude of the static acceleration measured must equal that of the gravity.
2. And the gravity vector measured using a static triaxial accelerom- eter must equal the gravity vector computed using the IMU orientation integration algorithm, which in turn uses the angular velocities measured using the gyroscopes, and it starts the orientation integration from a direction given by the static triaxial accelerometer itself.

(these properties are mentioned not in the paper, but in a Bachelor thesis related with paper, available here)

While the first property is obvious, I am having trouble gaining an intuitive understanding of the second one. In the approach, gyroscope calibration is done through optimization of a cost function $L$: the difference between the calibrated accelerometer values and an acceleration computed from the integration of the angular velocities of the gyroscope (measured during a static period).

I cannot grasp this concept and how acceleration vectors can be compared to the integration of angular velocities (which yield orientations). I think the fact static angular velocities are considered is important, but can't progress further than that, so any pointers are appreciated.