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Freescale Semiconductor Document Number: AN4399
Application Note Rev. 2.0, 10/2015
© 2013, 2015 Freescale Semiconductor, Inc. All rights reserved.
Contents
High-Precision Calibration of a
Three-Axis Accelerometer
by Mark Pedley
1 Introduction
Three-axis accelerometers supplied for the consumer
market are typically calibrated by the sensor
manufacturer using a six-element linear model
comprising a gain and offset in each of the three axes.
This factory calibration will change slightly as a result of
the thermal stresses during soldering of the
accelerometer to the circuit board. Additional small
errors, external to the accelerometer, including rotation
of the accelerometer package relative to the circuit board
and misalignment of the circuit board to the final
product, will also be introduced during the soldering and
final assembly process.
The original factory accelerometer calibration will still
be adequate for the vast majority of consumer
applications. Manufacturers of premium products
looking to obtain improved accuracy from a consumer
accelerometer may, however, wish to perform their own
calibration either by repeating the calibration performed
by the accelerometer manufacturer or by using a more
sophisticated calibration model.
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Key words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Absolute or Relative Calibration . . . . . . . . . . . . . . . . . . . 3
3 Original Factory Six Parameter Calibration . . . . . . . . . . . 4
4 Final Product Six Parameter Calibration . . . . . . . . . . . . . 6
5 Optimal Measurement Orientations. . . . . . . . . . . . . . . . 11
5.1 Two measurement orientations. . . . . . . . . . . . . . . 12
5.2 Three measurement orientations. . . . . . . . . . . . . . 14
5.3 Four measurement orientations. . . . . . . . . . . . . . . 15
5.4 Six measurement orientations. . . . . . . . . . . . . . . . 17
5.5 Eight measurement orientations . . . . . . . . . . . . . . 19
5.6 Distribution of measurements . . . . . . . . . . . . . . . . 21
6 Linear Least Squares Optimization . . . . . . . . . . . . . . . . 23
7 Final Product 12 Parameter Calibration . . . . . . . . . . . . 25
8 Including Temperature Dependence . . . . . . . . . . . . . . . 33
