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Calibration of an LSM303AGR accelerometer and magnetometer.

LSM303AGR is a MEMS device that includes a 3D accelerometer, a 3D magnetometer and a thermometer (datasheet: https://www.st.com/resource/en/datash... ). The magnetometer has a sensitivity of 1.5 milligauss (0.15 μT) per LSB and a dynamic range of plus / minus 4.9152 mT. It is quite small (2mm * 2mm * 1mm), is available pre-soldered in modules and communicates using I2C/SPI. Before using it in a magnetometer for magnet evaluation, I decided to calibrate it. As a first step, I installed it in a probe including an AVR to control it and transmit the readings. I decided to use it with the following parameters: Thermometer: ----Temperature measurement ON Accelerometer: ---- Continuous measurements at 10Hz ---- Normal mode ---- 3 axes enabled ---- Block data update and ---- High resolution. Magnetometer: ---- Enable temperature compensation ---- High resolution ---- Continuous mode at 10Hz ---- Set pulse every 63 measurements ---- Offset cancelation and ---- Low pass filter I followed one of the methods proposed by the manufacturer, the Rotated Ellipsoid Fitting as described in the Design Tip DT0059 ( https://www.st.com/resource/en/design... ). The method does not require accurate sensor positioning, nor exact knowledge of the stimulus (acceleration of gravity or earth’s magnetic field). It is only assumed that the stimulus remains constant. It requires at least 9 measurements (the more the better) and can be used both for the accelerometer and the magnetometer. DT0059 includes the corresponding MATLAB code with some clarifying comments. In order to collect the measurements, I went outdoors, fixed the probe on a PVC tube, attached to the head of a spherical panoramic head on an aluminum tripod. In this way the magnetometer would not be very close to ferromagnetic materials and we can assume that the local magnetic field of the earth is constant. In total 320 samples were taken and each measurement is the average of 80 measurements of Acceleration (X, Y, Z), Magnetic field (X, Y, Z) and Temperature with the probe standing still. The method was applied both to the accelerometer and the magnetometer data. The results were offsets, gains and rotation matrixes. The figures look quite reasonable. In order to control the results, the magnitudes of acceleration and magnetic field were computed for each measurement and the deviation from the mean value was noted. A remarkable concentration of the values around the mean is visible after the calibration. DISCLAIMER The rest of the this calibration procedure is not described in the DT0059 document. It is my small personal contribution to the art of calibrating sensors. Up to this point, the accelerometer and magnetometer have been calibrated independently. There is no guarantee that the axes of the two calibrated sensors are aligned. But the two sensors are in the same package and rigidly fixed to each other. They also measure two constant vectors: gravity and earth’s magnetic field. The angle between these vectors is also constant and can be measured. This angle is the complement of the inclination of the earth’s field and is well known for every location and elevation. For my location, the inclination is about 54.8 degrees. For the correction of the misalignment of the sensors I inserted a new final rotation (without any deformation) of the axes of the magnetometer. In order to find the optimal rotation angles, the GRG (Generalized Reduced Gradient) Non Linear method as implemented in Excel is used. Starting values are 0 degrees for the three axes. After this correction, we see a very significant improvement of the calculated inclination angle. It is interesting that this rotation is about 21 degrees. If you have any thoughts on this finding, please comment.