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August 2016
DT0059 Rev 2
1/6
www.st.com
Ellipsoid or sphere fitting for sensor calibration
By Andrea Vitali
Main components*
LSM303AGR
Ultra compact high-performance e-compass: ultra-low-power
3D accelerometer and 3D magnetometer
LSM6DS3
iNEMO inertial module: 3D accelerometer and 3D gyroscope
Purpose and benefits
This design tip explains how to compute offsets, gains, and cross-axis gains for a 3-axis
sensor by performing a sphere (ellipsoid) fitting. The technique is typically used to calibrate
and compensate magnetometers, but it can also be used with other sensors, such as
accelerometers.
Benefits:
Added functionality with respect to calibration provided by the MotionFX library which
only provides offsets for the Magnetometer.
Short and essential implementation, which enables easy customization and
enhancement by the end-user (osxMotionFX is available only in binary format, not as
source code)
Easy to use on every microcontroller (osxMotionFX can only be run on the STM32 and
only when the proper license has been issued by Open.MEMS license server).
Algorithm description
Measurements are taken on a number of positions (N) and combined to find the unknowns
(offsets, gains and cross-axis gains).
For 6-tumble calibration, positioning the sensor accurately is required. However, for the
ellipsoid fitting described here, there is no need to know the true stimulus of the sensor, as
the only requirement is that the modulus of the true stimulus be constant (square root of
sum of squares of X, Y, and Z).
For the case of the magnetometer: in order to measure only the earth magnetic
field, any other spurious (and often time varying) magnetic anomalies must be
absent; the modulus of the true stimulus is then the modulus of the earth magnetic
field

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