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Calculating Free Acceleration

Free acceleration is expressed as the acceleration vector rotated in the global Earth-reference frame with the gravity component subtracted from it. It is possible to calculate free acceleration from acceleration data, obtained from the accelerometer, and orientation data, obtained through the Xsens sensor fusion algorithms XKFCore [1]. This article is particularly helpful for users that use the recording feature in Xsens DOT App. In the recording mode, the free acceleration data output is not supported by the firmware. For real-time streaming mode, note that free acceleration is available by Xsens DOT App in multiple data modes. For further information on free acceleration and how it differs from acceleration expressed in a sensor reference frame you can check out this article.

In order to compute free acceleration it is necessary to know the following data:

  • Acceleration in the sensor frame: given by the accelerometer
  • Orientation data: this will allow to transition from the sensor to local (global reference frame). This can be represented as  quaternion, Euler angles or rotation matrix.

The steps required to calculate free acceleration are the following:

  • Rotate acceleration expressed in the sensor frame (accelerometer data) to local (global reference frame) using the orientation estimate.   This article can further explain the relationship between different reference frames.
  • Subtract the gravity vector, defined as [0, 0, 9.81]**

**9.81 m/s^2 is an approximate value of the gravity acceleration vector. If high-accuracy is required for your calculation, keep in mind that the earth’s gravitational acceleration varies and is a function of the user’s position on the Earth and altitude.

[1] Xsens DOT User Manual

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