inertial navigaton systems11

By: Vikas Kumar SinhaControl Systems (M.Tech)

01/27/15 1

Inertial Navigation Sensor Calibration

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

01/27/15 2

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.

01/27/15 3

01/27/15 4

01/27/15 5

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.

01/27/15 6

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

01/27/15 7

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

01/27/15 8

Figure 2: Inertial measurement unit [12].

01/27/15 9

• 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)

01/27/15 10

Figure 3: Aircraft Axes

01/27/15 11

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

01/27/15 12

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

01/27/15 13

In this way X α A ………(4)

Figure 4: basic sturcture of accelerometer [8]

01/27/15 14

Figure: 5

01/27/15 15

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]

01/27/15 17

01/27/15 18

Figure 8: types of errors

01/27/15 19

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

01/27/15 20

….(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

01/27/15 21

Six Position Static Test

Improved Six Position Static Test

Multi-Position Calibration Method

01/27/15 22

…(7) …(8)

…(9) ..(10)

01/27/15 23

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)

01/27/15 25

Using the least squares method as follows:

…(14)

01/27/15 26

01/27/15 27

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

01/27/15 28

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.

01/27/15 29

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)

01/27/15 30

...(21)

The accelerometers on the IMU axes sense the following values:

. .. ..(22)

01/27/15 31

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.

01/27/15 32

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

...(24)

01/27/15 33

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

(25)

01/27/15 34

01/27/15 35

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.

01/27/15 36

01/27/15

Figure 11: XSENS 300 MTi-G.

37

01/27/15 38

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

01/27/15 39

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

Navigation Use in quadcopter Tracking Robotics Aircraft

01/27/15 40

We estimate the value of bias, scale and non-orthogonality errors.

By using these methods we will get an error less IMU sensor.

01/27/15 41

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

01/27/15 42

[1] M. Li, A.I. Mourikis, ''3-D Motion Estimation and Online Temporal Calibration for Camera-IMU Systems,'' Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 2013.

[2] M. Li, B. Kim, A.I. Mourikis, ''Real-time Motion Tracking on a Cellphone using Inertial Sensing and a Rolling Shutter Camera,'' Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 2013.

[3] M. Li, A.I. Mourikis, ''Optimization-Based Estimator Design for Vision-Aided Inertial Navigation,'' Proceedings of the Robotics: Science and Systems Conference (RSS), Sydney, Australia, July 2012.

[4] M. Li, A.I. Mourikis, ''High-Precision, Consistent EKF-based Visual-Inertial Odometry,'' International Journal of Robotics Research (IJRR), Volume 32, No 6, May 2013.

[5] M. Li, A.I. Mourikis, ''Vision-aided Inertial Navigation with Rolling-Shutter Cameras,'' International Journal of Robotics Research (IJRR).

01/27/15 43

[6] S. Thomas, The Last Navigator: "A Young Man, An Ancient Mariner, the Secrets of the Sea", McGraw-Hill, New York, 1997.

[7] Adem G. Hayal, "Static Calibration of Tactical Grade Inertial Measurement Units", Geodetic Science Report No. 496, The Ohio State University Columbus, Ohio 43210, Sep 2008.

[8] Priyanka Aggarwal, Zainab Syed, Aboelmagd Noureldin, Naser El-Sheimy, "MEMS Based Integrated Navigation", GNSS Technology and Application Series, ISBN-13: 978-1-60807-043-5, 2010.

[9] Hofmann-Wellenhof, B., Lichtenegger, H., and Collins, J., "GPS Theory and Practice", Fifth Edition, Austria: Springer, 2004.

[10] Grewal, M.S., Weill, L., and Andrews, A.P., "Global Positioning Systems, Inertial Navigation, and Integration", Second Edition, New Jersey: John Wiley & Sons, 2007.

01/27/15 44

[11] 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.

[12] Lotters J C, Schipper J, Veltink P H, Olthuis W and Bergveld P, "Procedure for in-use calibration of triaxial accelerometers in medical application", Sensors Actuators A68221–8, 1998.

[13] N. El-Sheimy, S. Nassar and A. Noureldin, "Wavelet De-Noising for IMUAlignment", IEEE Aerospace and Electronics Systems Magazine, vol. 19, pp. 32- 39, Oct. 2004.

[14] Aggarwal, P., et al., "A Standard Testing and Calibration Procedure for Low Cost MEMS Inertial Sensors and Units", Journal of Navigation, Vol. 61, No. 2, 2007, pp. 323–336.

[15] Hou, H., and El-Sheimy, N., "Inertial Sensors Errors Modeling Using Allan Variance," Proceedings of ION GNSS 2003, Portland, Oregon, Sept. 9–12, 2003.

[16] Hide, C.D., Integration of GPS and Low Cost INS Measurements, Ph.D. thesis, Institute of Engineering, Surveying and Space Geodesy, University of Nottingham, U.K., 2003.

01/27/15 45

[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.

[18] El-Sheimy N, " Inertial Techniques and INS/DGPS Integration", Dept. of Geomatics Enggineering., University of Calgary, Calgary, Canada, 2003.

[19] Ren Wei Zhang Tao, Zhang Hai-yun, Wang Lei-gang, Zhaou Yong-jie, Luan Mengkai, Liu Hui-feng, Shi Jing-wei,"A Research on Calibration of Low-Precision MEMS Inertial Sensors", 25th Chinese Control and Decision Conference (CCDC), 2013.

[20] 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.

[21] Titterton, D. H. and Weston, J. L. (1997). "Strapdown Inertial Navigation Technology". Peter Peregrinus Ltd, UK.

01/27/15 46

[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.

[23] Shin E-H and El-Sheimy N, "A New calibration Method for Strapdown Inertial Navigation Systems", Z. Vermess, 127 1-10, 2002.

[24] Lawrence C. Ng and DarryII J. Pines. (1997), "Characterization of Ring Laser Gyro Performance Using the Allan Variance Method" , Journal of Guidance, Control, and Dynamics, Vol. 20, No. 1: Engineering Notes, p 211 -214. January - February, 1997.

[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.

[27] I. Skog and P. H¨ and el, "Calibration of a MEMS inertial measurement unit", in XVII IMEKO World Congress, 2006.

[28] Oliver J. Woodman," An introduction to inertial navigation". University of Cambridge 2007.

01/27/15 47

01/27/15 48

01/27/15 49