Calibration and Applications of a rotational sensorChin-Jen Lin, George LiuInstitute of Earth Sciences, Academia Sinica, Taiwan

Outlines

Calibration of the following rotational sensorsR-1 R-2

Two applications to find true northAttitude Estimator (inertial navigation)North Finder

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Various technologies of a rotational sensorMEMS (Micro Electro-Mechanical System)FOG (Fiber Optic Gyroscope)RLG (Ring Laser Gyroscope)MET (Molecular Electronic Transducers)

R-1 R-2

Commercial and aerospace use

Observatory stage only to date

DC-response

Band-pass response

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Specification and Calibration

Self-Noise Level High frequency Low frequency

Frequency Response Sensitivity Linearity Cross-effect

Linear-rotation Rotation-rotation

Nigbor, R. L., J. R. Evans and C. R. Hutt (2009). Laboratory and Field Testing of Commercial Rotational Seismometers, Bull. Seis. Soc. Am., 99, no. 2B, 1215–1227.

--- PSD (power spectrum density)--- Allan Deviation

R-2R-1

The R-2 is the second generation of R-1.The R-2 improvements:• increased clip level• lower pass-band• differential output• Linearity• MHD calibration electronics

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Self-noise (PSD) A good way to test sensor noise at high frequency

Noise comparison at high frequency band: MET > FOG > MEMS

R-2 does not improve resolution over the R-1.

R-1 and R-2 are corrected for instrument response.

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MEMSFOGMET

R-2

R-1

AerotechTM

Rotation Shaker

reference sensorFOG (VG-103LN)(DC~2000 Hz)

Frequency ResponseR-1(20s~30 Hz)

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Swept sine!

Frequency Response

5 R-1s and 2 R-2s were tested

R-2R-1

Phase response of the R-1TM is not normalized; these particular R-2sTM are improved.

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Shaker VS Coil-calibration (R-2)

Blue: via shake tableGreen: via coil-calibration

• At low frequency, both results are almost identical

• At high frequency, the results from the shake table are systematically higher

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R-2 #A201701 R-2 #A201702

Linearity

R-2R-1

6 % error, input below 8 mrad/s 92 % error, input below 8 mrad/s

Linearity of R-2 is improved!

9Frequency responses under various input amplitude (0.8 ~ 8 mrad/s)

R-1: Aging problem (1 of 2)

Apr-12 Jan-13 difference (%)#A201504 46.1 45 -2.4%

47.2 48 1.7%46 43.8 -4.8%

#A201505 52.9 51.3 -3.0%43.6 43.2 -0.9%55.8 51.7 -7.3%

#A201506 59.2 57.4 -3.0%60.2 57.1 -5.1%55.4 54.1 -2.3%

Sensitivity decreases…

3 R-1 samples

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R-1: Aging problem (2 of 2)

After a half-year deployment:• amplitude differs about +/- 0.5 dB • phase differs about +/- 2.5∘

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Conclusions (Calibration)

Both R-1 and R-2 can provide useful data, however:

R-1 Frequency response is not flat Sensitivity is not normalized Has aging problem (needs regular calibration) Linearity is about 6% (under 8 mrad/s input)

R-2 Instrument noise is somewhat higher than the R-1 Sensitivity and frequency response are not normalized The pass-band is flatter than R-1 Linearity is improved (2%, under 8 mard/s input) Self calibration works well at low frequency but not high

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Applications for Finding True north

Attitude EstimatorTrace orientation in three-dimension (inertial navigation)

North FinderFind true north

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Attitude Estimator(track the sensor’s orientation)

Z

Y

X

Z

Y

X

θθθ

secsec00

tantan1

(t)ψ(t)ψ(t)ψ

YXYX

XX

YXYX

CSSC

CS

Euler angle-rates

Rotational measurements(sensor frame)

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Euler angles composed of:• Roll• Pitch• Yaw

Reference frame

Sensor frame

displacement for translation

Lin, C.-J., H.-P. Huang, C.-C. Liu and H.-C. Chiu (2010). "Application of Rotational Sensors to Correcting Rotation-Induced Effects on Accelerometers."

Attitude equation

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Euler angles for rotation

6 degree-of-freedom motion

Compare with AHRS … 15

( Attitude Heading Reference System)

XensMTI-G-700-2A5G4SN: 07700075

Attitude EstimatorFOG3-axis VG-103LN

• Dynamic Roll and pitch are within 0.5∘

• Dynamic Yaw is within 2∘

The attitude estimator can … track orientation of sensor frameguide sensor frame from one orientation to

another oneEx., plot perpendicular line or parallel line on

the ground

North Finder ~(find azimuth angle)

North-finding is important, especially for:tunnel engineeringinertial navigationMissile navigationSubmarine navigationseismometer deploymentmobile robot navigation

North can be found by several techniques:Magnetic compassSun compassAstronomicalGPS compassGyro compass

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Magnetic compassAdvantage : very easy to useDisadvantage :

Subject to large error sources from local ferrous material, even a hat rim or belt buckle

Need to correct for magnetic declination

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TiltmeterDetermine tilt angle from a projection of the gravity

g

0.5g

30o

gtilt = g*sinθ

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North FinderDetermine azimuth angle from projection of Earth’s rotation vector

Principle?

Earth rotation axis

equator

gyro

Principle

e

cosee1

coscoseY

Earth’s rotation-rate

projection of Earth’s rotation-rate

Gyro frame

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sincoseX

latitude

azimuth angle

ωe : earth rotation rateωe1: local projection of earth rotation rateφ: latitude

e

θ: azimuth angleωx :earth rotation rate about X-axis of gyroωy :earth rotation rate about X-axis of gyro

Resolution …

Resolution is related to the accuracy of the mean value

How much time it takes to determine the mean value with most accuracy??

→ Allan Deviation Analysis is the proper way to evaluate accuracy

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Allan Deviation Analysis (1 of 2) 22

A quantitative way to measure • the accuracy of the mean value → resolution• for any given averaging time

212

121

ii yyn

AVAR

AVAR: Allan variance

AD: Allan deviation

τ: average time

yi: average value of the measurement in bin i

n: the total number of bins

resolution

average time

Bias stability

copied from Crossbow Technology~VG700CATM, made by CrossbowTM

Allan Deviation Analysis (2 of 2)

EXPERIMENTS

SDG-1000made by Systron Donner (USA)MEMSbias stability: <3.7E-4 deg/sangle random walk: <1.7E-3 deg/s

TRS-500made by Optolink (Russia)Fiber Optic Gyrobias stability: <1.4E-4 deg/sangle random walk: <1.7E-4 deg/s

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SDG-1000

TRS-500

Resolution 0.14°

Projection of the Earth’s rotation rate 3.7E-3 °/s (latitude 25°)

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1000 s

Resolution 2°

20 s

Allan Deviation Analysis

Other challenges…

offsetk inputoutput rotation

Two fixed points

DC offset

sensitivity

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Mechanical misalignment

Sensor framePlatform frame

Find true north…~ from sun compass

These two orientation lines were made from sun compass

50 cm

Maximum error

0.1 cm50 cm

40.1 40.2

Theodolite&

GPS

Need a reference of true north

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error = 0.11 °

Work on seismic station

Station data Existing azimuth* Deviation**

TWKB 2011/10/3 359.0 -1

MASB 2011/10/3 359.8 -0.2

SBCB 2011/5/11 358.8 -1.2

WUSB 2011/6/22 New station 0

VWDT 2011/6/23 New station 0

NACB 2011/7/14 0.3 0.3

YULB 2011/7/18 357.7 -2.3

TPUB 2011/7/20 359.0 -1

CHGB 2011/7/22 359.8 -0.2

YHNB 2011/9/07 359.4 -0.6

ANPB 2011/9/20 1.9 1.9

NNSB 2011/9/27 2.3 2.3

TDCB 2011/9/27 1 1

VDOS 2011/12/7 358 -2

Danda station (central Taiwan)

*previous north direction is found by sun compass

(BATS, Broadband Array in Taiwan for Seismology)

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**standard deviation is 1.3°

conclusions

North finder and attitude estimator can be and are implemented by DC-type gyro.

An efficient way to find the true north is: First, use a north finder to find arbitrary azimuth

angle Second, rotate that azimuth angle with an attitude

estimator

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Thank you!Your comments and questions are greatly appreciated!

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