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) North Finder 2 Various technologies of a rotational sensor 3 MEMS (Micro Electro-Mechanical System) Commercial and aerospace use DC-response FOG (Fiber Optic Gyroscope) RLG (Ring Laser Gyroscope) MET (Molecular Electronic Observatory stage only to date Transducers) Band-pass response R-1 R-2 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 --- PSD (power spectrum density) Low frequency --- Allan Deviation Frequency Response Sensitivity R-2 R-1 Linearity Cross-effect Linear-rotation Rotation-rotation 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 Self-noise (PSD) 5 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 Frequency Response R-1 (20s~30 Hz) reference sensor FOG (VG-103LN) (DC~2000 Hz) AerotechTM Rotation Shaker Swept sine! 6 7 Frequency Response R-2 R-1 Phase response of the R-1TM is not normalized; these particular R-2sTM are improved. 5 R-1s and 2 R-2s were tested Shaker VS Coil-calibration (R-2) R-2 #A201701 8 R-2 #A201702 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 Linearity Frequency responses under various input amplitude (0.8 ~ 8 mrad/s) R-1 9 R-2 Linearity of R-2 is improved! 6 % error, input below 8 mrad/s 2 % error, input below98 mrad/s R-1: Aging problem (1 of 2) 10 Sensitivity decreases… #A201504 #A201505 #A201506 Apr-12 46.1 47.2 46 52.9 43.6 55.8 59.2 60.2 55.4 Jan-13 difference (%) 45 -2.4% 48 1.7% 43.8 -4.8% 51.3 -3.0% 43.2 -0.9% 51.7 -7.3% 57.4 -3.0% 57.1 -5.1% 54.1 -2.3% 3 R-1 samples R-1: Aging problem (2 of 2) After a half-year deployment: • amplitude differs about +/- 0.5 dB • phase differs about +/- 2.5∘ 11 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 Attitude Estimator 14 14 (track the sensor’s orientation) Attitude equation ψ X (t) 1 ψ Y (t) 0 ψ Z (t) 0 Euler angle-rates 6 degree-of-freedom motion S X tan Y CX S X sec Y C X tan Y θ X SX θ Y C X sec Y θ Z 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) displacement for translation Euler angles for rotation Sensor frame Reference frame Euler angles composed of: • Roll • Pitch • Yaw Compare with AHRS … 15 ( Attitude Heading Reference System) Xens Attitude Estimator MTI-G-700-2A5G4 SN: 07700075 FOG 3-axis VG-103LN • Dynamic Roll and pitch are within 0.5∘ • Dynamic Yaw is within 2∘ 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 North Finder 17 ~(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 Magnetic compass 18 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 Principle? 19 Tiltmeter Determine tilt angle from a projection of the gravity 0.5g gtilt = g*sinθ 30o g North Finder Determine azimuth angle from projection of Earth’s rotation vector Principle 20 Earth rotation axis Gyro frame Earth’s rotation-rate e e gyro latitude equator azimuth angle Y e cos cos X e cos sin e1 e cos projection of Earth’s rotation-rate ωe : earth rotation rate θ: azimuth angle ωe1: local projection of earth rotation rate ωx :earth rotation rate about X-axis of gyro φ: latitude 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 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 AVAR 2 1 2 n 1 y i 1 y i 2 AD: Allan deviation τ: average time yi: average value of the measurement in bin i n: the total number of bins resolution average time Allan Deviation Analysis (2 of 2) ~VG700CATM, made by CrossbowTM copied from Crossbow Technology Bias stability EXPERIMENTS 24 SDG-1000 TRS-500 made by Systron Donner (USA) made by Optolink (Russia) MEMS Fiber Optic Gyro bias stability: <3.7E-4 deg/s bias stability: <1.4E-4 deg/s angle random walk: <1.7E-3 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 Other challenges… 26 sensitivity output k input offset DC offset Two fixed points rotation Mechanical misalignment These two orientation lines were made from sun compass 27 50 cm Sensor frame Platform frame Need a reference of true north Find true north… ~ from sun compass 40.2 40.1 Theodolite & GPS Maximum error error = 0.11 ° 0.1 cm 50 cm Work on seismic station 28 (BATS, Broadband Array in Taiwan for Seismology) Danda station (central Taiwan) Station data Existing azimuth* Deviation** TWKB 2011/10/3 359.0 -1 MASB 2011/10/3 359.8 -0.2 SBCB 2011/5/11 358.8 -1.2 WUSB 2011/6/22 New station 0 VWDT 2011/6/23 New station 0 NACB 2011/7/14 0.3 0.3 YULB 2011/7/18 357.7 -2.3 TPUB 2011/7/20 359.0 -1 CHGB 2011/7/22 359.8 -0.2 YHNB 2011/9/07 359.4 -0.6 ANPB 2011/9/20 1.9 1.9 NNSB 2011/9/27 2.3 2.3 TDCB 2011/9/27 1 1 VDOS 2011/12/7 358 -2 *previous north direction is found by sun compass **standard deviation is 1.3° conclusions 29 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 30 Thank you! Your comments and questions are greatly appreciated!