x-IMU3 User Manual v0.11
April 6, 2022
by Equation (2) where
v
c
is the calibrated voltage measurement obtained from the uncalibrated voltage
measurement,
v
u
, given the sensitivity,
s
v
. The units of
v
c
and
v
u
are volts.
s
v
is a ratio and therefore
has no units. The calibration parameter
s
v
can be accessed as a device setting.
v
c
=
s
v
v
u
(2)
4.3
Inertial sensors
The inertial sensors are the gyroscope, accelerometer, and high-g accelerometer. Each inertial sensor is
calibrated for axis sensitivity, axis offset, inter-axis misalignment, and package misalignment. The inertial
calibration model is described by Equation (3) where
i
c
is the calibrated inertial measurement obtained from
the uncalibrated inertial measurement,
i
u
, given the misalignment matrix,
M
, the sensitivity vector,
s
, and the
offset vector,
b
. The inertial calibration model is expanded as Equation (4) to express the model as 15 scalar
quantities. The units of
i
c
,
i
u
, and
b
are degrees per second for the gyroscope, and g for the accelerometer
and high-g accelerometer.
M
and
s
are ratios and therefore have no units. The calibration parameters
M
,
s
,
and
b
for each inertial sensor can be accessed as device settings.
i
c
=
Ms
(
i
u
−
b
)
(3)
i
cx
i
cy
i
cz
=
m
x x
m
x y
m
x z
m
y x
m
y y
m
y z
m
zx
m
zy
m
zz
s
x
s
y
s
z
i
ux
i
uy
i
uz
−
b
x
b
y
b
z
(4)
4.4
Magnetometer
The magnetometer is calibrated for soft iron and hard-iron characteristics.
Soft iron characteristics are
distortions that alter the intensity and direction of the magnetic field as measured by the magnetometer.
Soft iron calibration also accounts for magnetometer axis sensitivity, inter-axis misalignment, and package
misalignment. Hard iron characteristics are unintended magnetic fields generated by the device that offset
magnetometer measurements. Hard iron calibration also accounts for magnetometer axis offset.
The magnetometer calibration model is described by Equation (5) where
m
c
is the calibrated magnetometer
measurement obtained from the uncalibrated magnetometer measurement,
m
u
, given the soft iron matrix,
S
, the hard iron vector,
h
. The magnetometer calibration model is expanded as Equation (6) to express the
model as 12 scalar quantities. The units of
m
c
,
m
u
, and
h
are a.u..
S
is a ratio and therefore has no units.
The calibration parameters
S
,
h
can be accessed as device settings.
m
c
=
Sm
u
−
h
(5)
m
cx
m
cy
m
cz
=
s
x x
s
x y
s
x z
s
y x
s
y y
s
y z
s
zx
s
zy
s
zz
m
ux
m
uy
m
uz
−
h
x
h
y
h
z
(6)
4.5
Calibration certificate
Each device is supplied with a calibration certificate unique to that device. The calibration certificate details
all calibration parameters, the calibration date, the ambient temperature and device temperature during
calibration, and any equipment used during the calibration process. The certificate also includes graphs
demonstrating the accuracy of the device over the measurement range. Calibration certificates are provided
as a Portable Document Format (PDF) file. There are three ways to access the calibration certificate for a
device:
1. Scan the Quick Response (QR) code on the back of the device.
2. Open the “Calibration Certificate.html” file stored on the Secure Digital (SD) card.
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