ChinJen Lin George Liu Institute of Earth Sciences Academia Sinica Taiwan Outlines Calibration of the following rotational sensors R1 R2 Two applications to find true north Attitude ID: 180878
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Slide1
Calibration and Applications of a rotational sensor
Chin-Jen Lin, George Liu
Institute of Earth Sciences, Academia
Sinica
, TaiwanSlide2
Outlines
Calibration
of the following rotational sensors
R-1 R-2Two applications to find true northAttitude Estimator (inertial navigation)North Finder
2Slide3
Various technologies
of a rotational sensor
MEMS
(Micro Electro-Mechanical System)FOG (Fiber Optic
G
yroscope)
RLG (Ring Laser Gyroscope)MET (Molecular Electronic Transducers)R-1R-2
Commercial
and aerospace
use
Observatory stage only to date
DC-response
Band-pass response
3Slide4
Specification and Calibration
Self-Noise Level
High
frequency Low frequency
Frequency Response
Sensitivity
LinearityCross-effectLinear-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
4Slide5
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-1Slide6
Aerotech
TM
Rotation Shaker
reference sensor
FOG (VG-103LN)
(DC~2000 Hz)
Frequency Response
R-1
(20s~30 Hz)
6
Swept sine!Slide7
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.
7Slide8
Shaker
VS
Coil-calibration (R-2)
Blue
: via shake table
Green
: via coil-calibration
At low frequency
, both results are almost identicalAt high frequency, the results from the shake table are systematically higher
8
R-2 #A201701
R-2 #A201702Slide9
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) Slide10
R-1: Aging problem (1 of 2)
Apr-12
Jan-13
difference (%)
#A201504
46.1
45
-2.4%
47.2
48
1.7%
46
43.8-4.8%
#A20150552.9
51.3-3.0%
43.643.2
-0.9%
55.8
51.7
-7.3%
#A201506
59.2
57.4
-3.0%
60.2
57.1
-5.1%
55.4
54.1
-2.3%
Sensitivity decreases…
3 R-1 samples
10Slide11
R-1: Aging problem (2 of 2
)
After a half-year deployment:
amplitude differs about +/- 0.5 dB
phase differs about +/- 2.5
∘
11Slide12
Conclusions (Calibration)
Both R-1 and R-2 can provide useful data, however:
R-1
Frequency response is not flatSensitivity is not normalizedHas 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-1Linearity is improved (2%, under 8 mard/s input)Self calibration works well at low frequency but not high12Slide13
Applications for Finding True north
Attitude Estimator
Trace orientation in three-dimension (inertial navigation)
North Finder
Find
true
north13Slide14
Attitude
Estimator
(track the sensor’s orientation)
Euler angle-rates
Rotational measurements
(sensor frame)
14
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 motionSlide15
Compare with AHRS …
15
(
Attitude Heading Reference System)
Xens
MTI-G-700-2A5G4
SN: 07700075
Attitude Estimator
FOG3-axis VG-103LN
Dynamic Roll and pitch are within 0.5
∘Dynamic Yaw is within 2∘Slide16
The attitude estimator can …
t
rack orientation of sensor frame
guide sensor frame from one orientation to another oneEx., plot perpendicular line or parallel line on the groundSlide17
North Finder
~(
find azimuth angle)North-finding is important, especially for:
tunnel engineering
inertial navigation
Missile navigationSubmarine navigationseismometer deploymentmobile
robot navigationNorth can
be found by several techniques:
Magnetic compassSun compass
AstronomicalGPS compassG
yro compass
17Slide18
Magnetic compass
Advantage
: very easy to useDisadvantage
:
Subject to large
error sources from local ferrous material, even a hat rim or belt buckleNeed to
correct for magnetic declination
18Slide19
Tiltmeter
Determine
tilt angle
from
a projection of the gravity
g
0.5g
30
o
g
tilt
= g*sin
θ
19
North
Finder
Determine
azimuth angle
from
projection of Earth’s rotation vector
Principle?Slide20
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
e
1
: local projection of earth
rotation rate
φ
:
latitude
θ
: azimuth angle
ω
x
:earth rotation rate about X-axis of gyro
ω
y
:earth rotation rate about X-axis of gyroSlide21
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
21Slide22
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 timeSlide23
Bias stability
copied
from Crossbow
Technology
~VG700CA
TM
,
made
by
Crossbow
TM
Allan
Deviation Analysis (2 of 2
)Slide24
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
G
yro
bias stability: <1.4E-4
deg
/s
angle random walk: <1.7E-4
deg
/s
24Slide25
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 AnalysisSlide26
Other challenges…
rotation
Two fixed points
DC offset
sensitivity
26Slide27
Mechanical
misalignment
Sensor frame
Platform frame
Find true north…
~ from sun compass
These two orientation lines were made from sun compass
50 cm
Maximum error
0.1 cm
50 cm
40.1
40.2
Theodolite
&
GPS
Need a reference of true north
27
error =
0.11
°Slide28
Work on seismic station
Station
data
Existing
azimuth*
Deviation**
TWKB
2011/10/3
359.0
-1MASB
2011/10/3359.8
-0.2
SBCB2011/5/11
358.8-1.2
WUSB2011/6/22
New station0
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
Danda
station (central Taiwan)
*previous north direction is found by
sun compass
(BATS,
B
roadband
A
rray in
T
aiwan for
S
eismology)
28
**standard deviation is
1.3
°Slide29
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 angleSecond, rotate that azimuth angle with an attitude estimator
29Slide30
Thank you!
Your comments and questions are greatly appreciated!
30