Slide 1

Calibration and Applications of a rotational sensor Chin-Jen Lin, George Liu Institute of Earth Sciences, Academia Sinica, Taiwan Slide 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 Slide 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 Slide 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, 12151227. --- 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 Slide 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 Slide 6 Aerotech TM Rotation Shaker reference sensor FOG (VG-103LN) (DC~2000 Hz) Frequency Response R-1 (20s~30 Hz) 6 Swept sine! Slide 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 Slide 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 Slide 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) Slide 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 Slide 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 Slide 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 Slide 13 Applications for Finding True north Attitude Estimator Trace orientation in three-dimension (inertial navigation) North Finder Find true north 13 Slide 14 Attitude Estimator (track the sensors 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 Slide 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 Slide 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 Slide 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 Slide 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 Slide 19 Tiltmeter Determine tilt angle from a projection of the gravity g 0.5g 30 o g tilt = g*sin 19 North Finder Determine azimuth angle from projection of Earths rotation vector Principle? Slide 20 Earth rotation axis equator gyro Principle Earths rotation-rate projection of Earths rotation-rate Gyro frame 20 latitude azimuth angle e : earth rotation rate e1 : local projection of earth rotation rate : latitude : azimuth angle x :earth rotation rate about X-axis of gyro y :earth rotation rate about X-axis of gyro Slide 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 Slide 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 : average time y i : average value of the measurement in bin i n: the total number of bins resolution average time Slide 23 Bias stability copied from Crossbow Technology ~VG700CA TM, made by Crossbow TM Allan Deviation Analysis (2 of 2) Slide 24 EXPERIMENTS SDG-1000 made by Systron Donner (USA) MEMS bias stability: