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Calibration and Applications of a rotational sensor

Calibration and Applications of a rotational sensor. Chin-Jen Lin, George Liu Institute of Earth Sciences, Academia Sinica , Taiwan. Outlines. Calibration of the following rotational sensors R-1 R-2 Two applications to find true north Attitude Estimator (inertial navigation)

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Calibration and Applications of a rotational sensor

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  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

  3. Various technologies of a rotational sensor 3 • 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 DC-response Observatory stage only to date Band-pass response

  4. Specification and Calibration 4 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. • Self-Noise Level • High frequency • Low frequency • Frequency Response • Sensitivity • Linearity • Cross-effect • Linear-rotation • Rotation-rotation • --- 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

  5. Self-noise (PSD) A good way to test sensor noise at high frequency MEMS FOG MET R-1 and R-2 are corrected for instrument response. R-2 R-2 does not improve resolution over the R-1. R-1 Noise comparison at high frequency band: MET> FOG > MEMS

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

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

  8. Shaker VS Coil-calibration (R-2) R-2 #A201702 R-2 #A201701 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

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

  10. R-1: Aging problem (1 of 2) Sensitivity decreases… 3 R-1 samples

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

  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

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

  14. Attitude Estimator(track the sensor’s orientation) 14 Attitude equation 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." Rotational measurements (sensor frame) Euler angle-rates 6 degree-of-freedom motion displacement fortranslation Euler angles forrotation • Euler angles composed of: • Roll • Pitch • Yaw Sensor frame Reference frame

  15. Compare with AHRS … (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

  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

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

  20. Principle Gyro frame Earth’s rotation-rate Earth rotation axis latitude gyro azimuth angle equator projection of Earth’s rotation-rate ωe: earth rotation rate ωe1: 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 timeit takes to determine the mean value with most accuracy?? →Allan Deviation Analysis is the proper way to evaluate accuracy

  22. Allan Deviation Analysis (1 of 2) 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 yi: average value of the measurement in bin i n: the total number of bins resolution average time

  23. Allan Deviation Analysis (2 of 2) copied from Crossbow Technology ~VG700CATM, made by CrossbowTM Bias stability

  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

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

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

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

  28. Work on seismic station (BATS, Broadband Array in Taiwan for Seismology) *previous north direction is found by sun compass Danda station (central Taiwan) **standard deviation is 1.3°

  29. conclusions • North finder and attitudeestimator 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

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

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