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Calibration and Applications of a rotational sensor Chin-Jen Lin, George Liu Institute of Earth Sciences, Academia Sinica, Taiwan

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Outlines Calibration of the following rotational sensors R-1 R-2 Two applications to find true north Attitude Estimator (inertial navigation) North Finder 2

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Various technologies of a rotational sensor MEMS (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 3

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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-2 R-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 4

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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. 5 MEMS FOG MET R-2 R-1

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Aerotech TM Rotation Shaker reference sensor FOG (VG-103LN) (DC~2000 Hz) Frequency Response R-1 (20s~30 Hz) 6 Swept sine!

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Frequency Response 5 R-1s and 2 R-2s were tested R-2 R-1 Phase response of the R-1 TM is not normalized; these particular R-2s TM are improved. 7

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Shaker VS Coil-calibration (R-2) Blue: via shake table Green: via coil-calibration Blue: via shake table Green: via coil-calibration At low frequency, both results are almost identical At high frequency, the results from the shake table are systematically higher 8 R-2 #A201701 R-2 #A201702

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Linearity R-2 R-1 6 % error, input below 8 mrad/s 9 2 % error, input below 8 mrad/s Linearity of R-2 is improved! 9 Frequency responses under various input amplitude (0.8 ~ 8 mrad/s)

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R-1: Aging problem (1 of 2) Apr-12Jan-13difference (%) #A20150446.145-2.4% 47.2481.7% 4643.8-4.8% #A20150552.951.3-3.0% 43.643.2-0.9% 55.851.7-7.3% #A20150659.257.4-3.0% 60.257.1-5.1% 55.454.1-2.3% Sensitivity decreases… 3 R-1 samples 10

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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 ∘ 11

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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 12

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Applications for Finding True north Attitude Estimator Trace orientation in three-dimension (inertial navigation) North Finder Find true north 13

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Attitude Estimator (track the sensor’s orientation) Euler angle-rates Rotational measurements (sensor frame) 14 Euler angles composed of: Roll Pitch Yaw 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 14 Euler angles for rotation 6 degree-of-freedom motion

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Compare with AHRS … 15 ( Attitude Heading Reference System) Xens MTI-G-700-2A5G4 SN: 07700075 Attitude Estimator FOG 3-axis VG-103LN Dynamic Roll and pitch are within 0.5 ∘ Dynamic Yaw is within 2 ∘

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The attitude estimator can … track orientation of sensor frame guide sensor frame from one orientation to another one Ex., plot perpendicular line or parallel line on the ground

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North Finder ~(find azimuth angle) North-finding is important, especially for: tunnel engineering inertial navigation Missile navigation Submarine navigation seismometer deployment mobile robot navigation North can be found by several techniques: Magnetic compass Sun compass Astronomical GPS compass Gyro compass 17

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Magnetic compass Advantage : very easy to use Disadvantage : Subject to large error sources from local ferrous material, even a hat rim or belt buckle Need to correct for magnetic declination 18

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Tiltmeter Determine tilt angle from a projection of the gravity g 0.5g 30 o g tilt = g*sinθ 19 North Finder Determine azimuth angle from projection of Earth’s rotation vector Principle?

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Earth rotation axis equator gyro Principle Earth’s rotation-rate projection of Earth’s rotation-rate Gyro frame 20 latitude azimuth angle ω e : earth rotation rate ω e1 : local projection of earth rotation rate φ: latitude θ: azimuth angle ωx :earth rotation rate about X-axis of gyro ωy :earth rotation rate about X-axis of gyro

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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 21

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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 AVAR: Allan variance AD: Allan deviation τ: average time y i : average value of the measurement in bin i n: the total number of bins resolution average time

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Bias stability copied from Crossbow Technology ~VG700CA TM, made by Crossbow TM Allan Deviation Analysis (2 of 2)

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EXPERIMENTS SDG-1000 made by Systron Donner (USA) MEMS bias stability: <3.7E-4 deg/s angle random walk: <1.7E-3 deg/s TRS-500 made by Optolink (Russia) Fiber Optic Gyro bias stability: <1.4E-4 deg/s angle random walk: <1.7E-4 deg/s 24

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SDG-1000 TRS-500 Resolution 0.14° Projection of the Earth’s rotation rate 3.7E-3 °/s (latitude 25°) 25 1000 s Resolution 2° 20 s Allan Deviation Analysis

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Other challenges… rotation Two fixed points DC offset sensitivity 26

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Mechanical misalignment Sensor frame Platform frame Find true north… ~ from sun compass These two orientation lines were made from sun compass 50 cm 0.1 cm 50 cm 40.1 40.2 Theodolite & GPS Need a reference of true north 27 error = 0.11 °

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Work on seismic station StationdataExisting azimuth*Deviation** TWKB2011/10/3359.0 MASB2011/10/3359.8-0.2 SBCB2011/5/11358.8-1.2 WUSB2011/6/22New station0 VWDT2011/6/23New station0 NACB2011/7/140.3 YULB2011/7/18357.7-2.3 TPUB2011/7/20359.0 CHGB2011/7/22359.8-0.2 YHNB2011/9/07359.4-0.6 ANPB2011/9/201.9 NNSB2011/9/272.3 TDCB2011/9/2711 VDOS2011/12/7358-2 Danda station (central Taiwan) *previous north direction is found by sun compass (BATS, Broadband Array in Taiwan for Seismology) 28 **standard deviation is 1.3°

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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 29

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Thank you! Your comments and questions are greatly appreciated! 30

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