Inertial Navigation Systems

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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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.
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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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