An inertial measurement unit (IMU) measures linear and angular motion in three dimensions without external reference.

1. AHRS
By: Vikas Kumar Sinha
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2.  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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3. Fig 1: Inertial measurement unit
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4. Fig 2: The body and global frames of reference.
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5. • 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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6. Fig: 3
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7. 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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8.  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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9.  Applications
 Motion,
 vibration, blast,
 shock wave
 In this way
X α A ………(4)
Fig 4: basic sturcture of accelerometer
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10. Fig: 5
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11.  A gyroscope is a device for measuring of
maintaining orientation based on the
principle of angular momentum(rotation
momentum)
Fig: 6
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12.  Uses Coriolis effect using vibrating elements
▪ Fc -Force m -mass w -angular velocity v –velocity
Fig: 7
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15. Fig: 8
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16. Fig: 9
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17. ….(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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18.  Six Position Static Test
 Rotation Rate Test
 Thermal Test
 Multi-Position Calibration Method
 Modified Multi-Position Calibration Method
 Allan Variance approach
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19. …(7)
…(8)
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20.  ….(9)
 the ideal accelerations would be measured
as:
 …(10)
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21.  design matrix (A) for the least squares
…(11)
 The raw output of the sensors (in volts)
constitutes the matrix U:
…(12)
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23.  Using the least squares method as follows:
…(14)
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25. Fig: 10
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26. 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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27. 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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28. ...
(21)
 The accelerometers on the IMU axes sense the following values:
. .. ..(22)
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29.  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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30.  The observation equations for the accelerometer sensors
on the IMU axis triad will be obtained as below:
….(24)
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31.  The true values for the specific force
vector components are found as:
(26)
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32.  Navigation
 Use in quadcopter
 Tracking
 Robotics
 Aircraft
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33.  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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34.  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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35.  P. Aggarwal, Z. Syed, X. Niu, and N. El-Sheimy, "A standard
testing and calibration procedure for low cost MEMS inertial
sensors and units," Journal of navigation, vol. 61, pp. 323-
336, 2008.
 W. Fong, S. Ong, and A. Nee, "Methods for in-field
user calibration of an inertial measurement unit without
external equipment," Measurement Science and Technology,
vol. 19, p. 085202, 2008
 S. Nassar, “Improving the inertial navigation system (INS)
error model for INS and INS/DGPS applications” University
of Calgary, Department of Geomatics Engineering, 2003.
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36. Thank You…
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37. Any quastions?
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