Document MT0605P.E
© Xsens Technologies B.V.
MTi User Manual
40
4.9 Sensors data outputs
4.9.1
Physical sensor model
This section explains the basics of the individual calibration parameters of each MTi. This explains the
values found on the
MT Test and Calibration Certificate
that comes with each MTi.
The physical sensors inside the MTi (accelerometers, gyroscopes and magnetometers) are all
calibrated according to a physical model of the response of the sensors to various physical quantities,
e.g. temperature. The barometer and GPS receiver do not require calibration. The basic model is
linear and according to the following relation:
𝑠 = 𝐾
𝑇
−1
(𝑢 − 𝑏
𝑇
)
The model really used is more complicated and is continuously being developed further. From factory
calibration each MTi has been assigned a unique gain matrix,
K
T
and the bias vector,
b
T
This
calibration data is used to relate the sampled digital voltages,
u
, (unsigned integers from the 16 bit
ADC’s) from the sensors to the respective physical quantity,
s
.
The gain matrix is split into a misalignment matrix,
A
, and a gain matrix,
G
. The misalignment specifies
the direction of the sensitive axes with respect to the ribs of the sensor-fixed coordinate system (
S
)
housing. E.g. the first accelerometer misalignment matrix element
a
1,x
describes the sensitive direction
of the accelerometer on channel one. The three sensitive directions are used to form the misalignment
matrix:
𝐴 = [
𝑎
1,𝑥
𝑎
1,𝑦
𝑎
3,𝑧
𝑎
2,𝑥
𝑎
2,𝑦
𝑎
2,𝑧
𝑎
3,𝑥
𝑎
3,𝑦
𝑎
3,𝑧
]
𝐺 = [
𝐺
1
0
0
0
𝐺
2
0
0
0
𝐺
3
]
𝐾
𝑇
= [
𝐺
1
0
0
0
𝐺
2
0
0
0
𝐺
3
] [
𝑎
1,𝑥
𝑎
1,𝑦
𝑎
3,𝑧
𝑎
2,𝑥
𝑎
2,𝑦
𝑎
2,𝑧
𝑎
3,𝑥
𝑎
3,𝑦
𝑎
3,𝑧
] + 𝑂
With
O
representing higher order models and temperature modelling, g-sensitivity corrections, etc.
Each individual MTi is modeled for temperature dependence of both gain and bias for all sensors and
other effects. This modeling is not represented in the simple model in the above equations, but is
implemented in the firmware.
The basic indicative parameters in the above model of your individual MTi can be found on the
MT
Test and Calibration Certificate
and in the MT Manager (MT Settings dialog).
