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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– 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 #A 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 (%) #A % % % #A % % % #A % % % 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: 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°) 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 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/ MASB2011/10/ SBCB2011/5/ WUSB2011/6/22New station0 VWDT2011/6/23New station0 NACB2011/7/140.3 YULB2011/7/ TPUB2011/7/ CHGB2011/7/ YHNB2011/9/ ANPB2011/9/201.9 NNSB2011/9/272.3 TDCB2011/9/2711 VDOS2011/12/ 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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