This document discusses inertial navigation sensor calibration. It provides an introduction to inertial navigation sensors and methods for calibrating accelerometers and gyroscopes. It describes the components of an inertial measurement unit and common calibration methods like the six position static test. Applications of inertial sensors in areas like navigation, tracking, and robotics are also mentioned.

1. By: Vikas Kumar Sinha
Control Systems (M.Tech)
01/27/15 1
Inertial Navigation Sensor Calibration

2.  Introduction
 Inertial Navigation sensor
 Accelerometer
 Gyroscope
 Methods of calibration
 Applications
 Conclusion
 References
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3. Navigation is a field of study that
focuses on the process of monitoring
and controlling the movement of a
craft or vehicle from one place to
another.
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4. 01/27/15 4

5. 01/27/15 5

6.  Inertial navigation is a self-contained
navigation technique.
 In which measurements provided by
accelerometers and gyroscopes.
 To track the position and orientation of an
object relative to a known starting point.
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7. Figure 1: The body and global frames of reference[10].
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8.  An inertial measurement unit (IMU)
measures linear and angular motion in
three dimensions without external
reference.
 The IMU consists of two orthogonal
sensor triads, one consisting of three
accelerometers, the other of three
gyroscopes
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9. Figure 2: Inertial measurement unit [12].
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10. • If we can measure the acceleration of a vehicle we can
• integrate the acceleration to get velocity
• integrate the velocity to get position
• Then, assuming that we know the initial position and
velocity we can determine the position of the vehicle at
ant time t.
Formula: ..(1)
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11. Figure 3: Aircraft Axes
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12. The three axes of the aircraft are:
The roll axis which is roughly parallel to the line joining the nose
and the tail
Positive angle: right wing down
The pitch axis which is roughly parallel to the line joining the
wingtips
Positive angle: nose up
The yaw axis is vertical
Positive angle: nose to the right
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13.  Accelerometers are defined as acceleration
sensors that measure the non-gravitational
linear acceleration along their sensitive
axis.
 F=m*a …(2)
 F=k*x …(3)
Where:
F= force
m= mass
a=acceleration
x= displacement
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14.  In this way
X α A ………(4)
Figure 4: basic sturcture of accelerometer [8]
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15. Figure: 5
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16.  A gyroscope is a device for measuring of
maintaining orientation based on the
principle of angular momentum(rotation
momentum)
Figure 6: Gyroscope
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17.  Uses Coriolis effect using vibrating elements
▪ Fc -Force m -mass w -angular velocity v –velocity
Figure 7: Coriolis effect [10]
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19. Figure 8: types of errors
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20. Figure 9: Relationship between the output voltage of the
accelerometer(gyro) and the measured force(angular rate) [10].
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21. ….(5)
….(6)
Where:
a = true specific force vector
ω = body frame rotation rate vector
b = bias vector
S = scale factor matrix
N = non-orthogonality error matrix
η = non-deterministic accelerometer errors
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22.  Six Position Static Test
 Improved Six Position Static Test
 Multi-Position Calibration Method
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23. …(7)
…(8)
…(9)
..(10)
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Where,
= sensor measurement when sensitive axis is pointed upward.
= sensor measurement when the sensitive axis is pointed
downwards

24. ….(11)
 the ideal accelerations would be measured
as:
…(12)01/27/15 24

25. The raw output of the sensors (in volts)
constitutes the matrix Y:
…(13)
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26.  Using the least squares method as follows:
…(14)
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28. Figure 10: Misalignment to n-frame [23].
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29. General calibration model as below for accelerometer :
…(17)
By using the same methodology, we can derive the general model for the
gyros as:
…(18)
Where ωe is the true Earth rotation rate.
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30. Rotation matrix:
, Ry
…(19)
The non-orthogonality of the z axis can be expressed by two consecutive rotations;
rotation about the x axis by θzx and about the y axis by θzy.
…(20)
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31. ...
(21)
 The accelerometers on the IMU axes sense the following values:
. .. ..(22)
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32.  Inclusion of the major errors, bias and
scale factor error, into the IMU data is
done by the equation below:
..(23)
 Where Ya , b, a ,s IMU observation, bias
and scale factor error, respectively, for the
accelerometer and i = x, y and z.
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33.  The observation equations for the accelerometer sensors
on the IMU axis triad will be obtained as below:
...(24)
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34.  The true values for the specific force
vector components are found as:
(25)
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35. 01/27/15 35
calibration models for gyroscope and accelerometer errors:
…(26)

36.  The XSENS 300 MTi-G is an integrated GPS
and Inertial Measurement Unit (IMU).
 Small size,
 Weight,
 Low cost and low complexity in use
 wide range of interface options
 XSENS 300 MTi-G gives output if it is
rotated in three dimension space.
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37. 01/27/15
Figure 11: XSENS 300 MTi-G.
37

38. 01/27/15 38
Figure 12 : MT Manager showing a 3D view of an MTi-G-700 GPS/INS.

39. 01/27/15 39
Figure 13: MT Manager showing inertial data of an MTi-G-700 GPS/INS.

40.  Navigation
 Use in quadcopter
 Tracking
 Robotics
 Aircraft
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41.  We estimate the value of bias, scale and
non-orthogonality errors.
 By using these methods we will get an error
less IMU sensor.
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42.  To calibrate the INS by optimization
 To evaluate the contribution of the
calibration and stochastic error modeling
with thermal compensation
 Investigation of a general model including
both deterministic and stochastic noise
terms
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