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
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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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