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

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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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)

10. 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

11. R-1: Aging problem (2 of 2) After a half-year deployment: amplitude differs about +/- 0.5 dB phase differs about +/- 2.5 ∘ 11

12. 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

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

14. 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

15. 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 ∘

16.  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

17. 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

18. 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

19. 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?

20. 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

21. 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

22. 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

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

24. 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

25. 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

26. Other challenges… rotation Two fixed points DC offset sensitivity 26

27.  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 °

28. 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°

29. 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

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