By: Vikas Kumar SinhaControl Systems (M.Tech)

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Inertial Navigation Sensor Calibration

Introduction Inertial Navigation sensor Accelerometer Gyroscope Methods of calibration Applications Conclusion References

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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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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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Figure 1: The body and global frames of reference[10].

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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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Figure 2: Inertial measurement unit [12].

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• 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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Figure 3: Aircraft Axes

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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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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= forcem= massa=accelerationx= displacement

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In this way X α A ………(4)

Figure 4: basic sturcture of accelerometer [8]

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Figure: 5

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A gyroscope is a device for measuring of maintaining orientation based on the principle of angular momentum(rotation momentum)

Figure 6: Gyroscope 01/27/15 16

Uses Coriolis effect using vibrating elements▪ Fc -Force m -mass w -angular velocity v –velocity

Figure 7: Coriolis effect [10]

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Figure 8: types of errors

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Figure 9: Relationship between the output voltage of the accelerometer(gyro) and the measured force(angular rate) [10].

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….(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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Six Position Static Test

Improved Six Position Static Test

Multi-Position Calibration Method

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…(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

….(11)

the ideal accelerations would be measured as:

…(12)01/27/15 24

The raw output of the sensors (in volts) constitutes the matrix Y:

…(13)

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Using the least squares method as follows:

…(14)

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Figure 10: Misalignment to n-frame [23].

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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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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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...(21)

The accelerometers on the IMU axes sense the following values:

. .. ..(22)

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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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The observation equations for the accelerometer sensors on the IMU axis triad will be obtained as below:

...(24)

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The true values for the specific force vector components are found as:

(25)

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calibration models for gyroscope and accelerometer errors:

…(26)

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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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.

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

Navigation Use in quadcopter Tracking Robotics Aircraft

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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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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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[17] CLAUDIA C. MERUANE NARANJO, "Analysis and Modeling of MEMS based Inertial Sensors", Signal Processing, School of Electrical Engineering, XR-EE-SB 2008:011, Stockholm 2008.

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[22] Niu X, “Micromachined Attitude Measurement Unit with Application in Satellite TV Antenna Stabilization”, PhD Dissertation, Department of Precision Instruments and Machinery, Tsinghua University, 2002.

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[25] IEEE Std 952, "IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros", 1997.

[26] IEEE Std 1293, "IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, Non-gyroscopic Accelerometers", 1998.

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