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!