inertial navigation systems navigation systems.pdf · strapdown gimbailed 10 in gimbailed...
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017 1
Inertial Navigation Systems
Kiril Alexiev
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Navigation
2
Estimate the position and orientation.
Inertial navigation – one of possible instruments.
Newton law is used:
F = am
Acceleration and angular velocity are measured.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Inertial Sensors
3
Most common inertial sensors:
• Accelerometers
The accelerometers detect the combined magnitude
and direction of linear and gravitational
accelerations
• Gyros
The gyroscopes measure the angular rate of rotation
about one or more axes. They are not dependent on
gravity.
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Institute of Information and Communication Technologies
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University of Pavia March 2017
Accelerometers
4
Proof mass and two springs, g will be also measured
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Institute of Information and Communication Technologies
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University of Pavia March 2017 5
3D Accelerometers
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Gyroscope
6
Gyroscope measures the angles of rotation according
initial position
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Institute of Information and Communication Technologies
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Gyrostabilazed platform with
accelerometersAccelerometers
measure acceleration
in a fixed coordinate
system. These INS
are called gimbaled
system.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Strapdown INS
8
In late sixties there was proved that gimbals could be
modeled mathematically and gimbals could not be
used. Such kind of INS were called strapdown,
because the inertial sensors are fixed on the body of
moving object. Technical advanced in electronics
reduced the size and cost of inertial sensors. They
became MEMS. Lower cost and higher reliability
supported replacement of mechanisms in classical
understanding with electronics.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Types of INS
9
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Strapdown Gimbailed
10
In gimbailed navigation
systems, the inertial sensors
are mounted on gimbals
whose orientations are
nominally stationary
relative to either the
intermediate or the
reference coordinate frame.
The inertial sensors of a strapdown system fully follow the vehicle's angular motion. Hence, the measurement of specific force must be transformed from the body frame into that reference coordinate frame in which the integrations of acceleration are to take place.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017 11
The performance of a strapdown system is limited
primarily by two factors not present in gimballed
navigation systems. In gimbailed navigation systems, the
inertial sensors are mounted on gimbals whose
orientations are nominally stationary relative to either the
intermediate or the reference coordinate frame. The
inertial sensors of a strapdown system fully follow the
vehicle's angular motion. Hence, the measurement of
specific force must be transformed from the body frame
into that reference coordinate frame in which the
integrations of acceleration are to take place.
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Institute of Information and Communication Technologies
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University of Pavia March 2017 12
Each small rotation increment represents a finite
rotation. However, finite rotations do not commute,
since Rotation A followed by Rotation B does not, in
general, produce the same result as Rotation B
followed by Rotation A. Consequently, coordinate
transformations computed from these finite
increments include, to some degree, errors resulting
from the noncommutativity of finite rotations. The size
of these errors depends upon the size of the increment
and upon the sophistication of the algorithm used in
updating the coordinate transformation.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
Why MEMS?
13
These sensors are inexpensive: most MEMS sensors
in mass production quantities cost a few dollars.
These sensors are truly miniature - usually less than
(10x10x5 mm) in size, and they consume little power
(< 50 mA).
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Institute of Information and Communication Technologies
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Why not MEMS?
14
The biases of MEMS gyros can be brought down to a
level of less than 300 degrees per hour after
appropriate temperature compensation. Such a large
drift, even assuming an accurate initialization of
attitude, will lead to very large position errors after
almost 10 seconds of INS-only navigation.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017 15
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017 16
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The Coriolis-effect
22
Let assume a mass that is vibrating in the
radial direction of a rotating system. Due
to the Coriolis force working perpendicular
to the original vibrating direction, a new
vibration will take place in this direction.
The amplitude of this new vibration is a
function of the angular velocity. MEMS
gyros (MicroElectroMechanical Systems),
“tuning fork”and “wineglass”gyros are
utilizing this principle. Coriolis-based
gyros are typically cheaper and less
accuratethan mechanical, ring laser or
fiber optic gyros.
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Optical gyros
36
The Sagnac-effect.The inertial characteristics of lightcan
also be utilized, by letting two beams of light travel in a
loop in opposite directions. If the loop rotates clockwise,
the clockwise beam must travel a longer distance before
finishing the loop. The opposite is true for the counter-
clockwise beam. Combining the two rays in a detector, an
interference patternis formed, which will depend on the
angular velocity.
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Institute of Information and Communication Technologies
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RING LASER GYROS
37
• An electronic processor calculates the difference
between the frequencies of the two laser beams.
• The rate of rotation of the gyro determines the phase
difference of the frequencies. Each particular phase
difference coincides with a unique rate of turn which
the processor can thus calculate.
• Each ring laser gyroscope only rotates on one axis,
therefore three of them are required to register
changes in pitch, roll, and yaw.
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ADVANTAGES
38
• Few moving parts
• Small size and light weight
• Rigid construction
• High tolerance to shock, acceleration, and vibration
• High level of accuracy
• Low cost over the lifetime of the gyro
• Because there are no rotating gimbals as in a
mechanical gyro, there is no friction, and therefore no
errors caused by real precession
• Less power consumed than mechanical gyros because
there are fewer moving parts.
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DISADVANTAGES
39
• Base cost of Laser ring gyros is more expensive than
mechanical gyros.
• Laser ring gyros are susceptible to an error known as
“LOCK-IN”
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LOCK-IN
40
When the rate of turn is very small, the frequency
difference between the two beams is small.
There is a tendency for the two frequencies to “couple”
together and “lock-in” with each other.
As a result of lock-in, a zero turning rate is indicated.
While lock-in errors are not substantial, they can be
accounted for by using more complex ring laser gyro
systems.
By mechanically moving or twisting the system, the
coupling of frequencies does not occur.
This mechanical adjustment is called DITHERING.
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IMU
44
Several inertial sensors are often assembled to form an
Inertial Measurement Unit (IMU).
Typically the unit has 3 accelerometers and 3 gyros (x, y
and z), often 3 magnitometers (compass).
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Example (Strapdown IMU)
45
Honeywell HG1700 ("medium quality"): 3
accelerometers, accuracy: 1 mg, 3 ring laser gyros,
accuracy: 1 deg/h, Rate of all 6 measurements: 100 Hz
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
IMU - history
46
… torpedoes, rockets, airplanes, submarines - military
weaponry.
• Nokia N95 – 2007 – one of the first smart phones
It has GPS, a built-in accelerometer, originally used for
video stabilization and photo orientation.
• Latter Nokia has allowed software to use the data from
inertial sensors and Pandora’s box was opened and all the
“evils” of the world were available for … about 2 billions
users of smart phones today.
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Institute of Information and Communication Technologies
Bulgarian Academy of Sciences
University of Pavia March 2017
IMU - history
47
… earlier – few specialists designed the algorithms in
secret laboratories on several places in the world, like
Drapper Laboratory in MIT with unique multimillion
equipment.
… now – hundreds of thousands programmers application
hungry
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Option panel of sensor stream
application
48
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Sensor panel of sensor stream
application
49
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INS Functional Diagram
50
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1) If the accelerometer measures acceleration with
error, the corresponding distance error will be ,
e.g. proportional to the square of the time.
2) If the gyro measures turn rate with error, after
integration the error in attitude will be proportional to
. But the attitude is applied to correct the
orientation of acceleration vectors. The attitude error is
spread over distance calculation and consequences are
measured as .
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Accuracy Analysis of IMU
52
Find a reference!
1) If you have a measuring equipment with at least
one order of magnitude more accurate sensors.
2) If you have rotating device, which gives “exact”
information about attitude and position
3) If you model sensors measurement
4) With real sensor data, but you plan the experiments
with points with fixed position and attitude
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Attitude computation
Naive integration approach for attitude
calculation
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Attitude computation
Attitude calculation through Euler - Krylov
algorithm
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Attitude computation
55
Using Poison differential equation for attitude calculation
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Attitude computationQuaternion approach
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The structure of IMU simulator
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IMU simulator interface
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Modeled gyros data
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Modeled gyros data
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Real gyros data
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Experimental results
62
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0 1 2 3 4 5 6 7-20
0
20
40Gyro raw data deg/sec
0 1 2 3 4 5 6 7-20
0
20
40Gyro shift correction deg/sec
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0 1 2 3 4 5 6 7-15
-10
-5
0
5Accelerometers raw data m/s2
0 1 2 3 4 5 6 7-15
-10
-5
0
5Accelerometers after calibration (scale and shift) m/s2
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Calibration
66
a_x = (data_arr(6,:)-s1)/a1;
a_y = (data_arr(7,:)-s2)/a2;
a_z = (data_arr(8,:)-s3)/a3;
The shifts s1, s2, s3 and scaling coefficients a1,a2,a3
are estimated by optimization procedure with averaged
data from several positions of the sensors
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w_x_mean = mean(data_arr(2,1:70))
w_y_mean = mean(data_arr(3,1:70))
w_z_mean = mean(data_arr(4,1:70))
(no motion)
gyro_x = data_arr(2,:) - w_x_mean;
gyro_y = data_arr(3,:) - w_y_mean;
gyro_z = data_arr(4,:) - w_z_mean;
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Problem: nonconsistency:s1 = -0.103644505886850;
s2 = -0.163611281148368;
s3 = 0.025479105123220;
a1 = 0.936997180377589;
a2 = 0.932347804777772;
a3 = 0.871907702114871;
g = 9.72112896
s1 = -0.057858055368620;
s2 = -0.148024907905120;
s3 = 0.025066179054880;
a1 = 0.930790162818945;
a2 = 0.927854935493497;
a3 = 0.874878855049987;
g = 9.687243
s1 = -0.083761479495474;
s2 = -0.2075773931498450;
s3 = 2.360384019177096;
a1 = 1.021526216348697;
a2 = 1.009070389156962;
a3 = 1.109508357634151;
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1
1.05
1.1
0.85
0.9
0.95
1
0.99
1
x
trajectory of the body
y
z
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0 1 2 3 4 5 6 7-1.6
-1.4
-1.2
t
vs time in deg
0 1 2 3 4 5 6 7-5
0
5
t
vs time in deg
0 1 2 3 4 5 6 7-5
0
5
t
vs time in deg
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0 1 2 3 4 5 6 7-0.2
0
0.2
t
v xvx vs time m/s
0 1 2 3 4 5 6 7-0.1
0
0.1
t
v y
vy vs time m/s
0 1 2 3 4 5 6 7-0.05
0
0.05
t
v z
vz vs time m/s
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Initial angles determination: based on averaged data
from non-moving accelerometers (no other information,
we do not use compass)
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Extended Kalman and fuzzy
adaptation
75
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An approach for error
reduction in IMU
76
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Now…
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Оpen problems
86
1. Mathematical model
2. Calibration procedure
- Initial alignment
- real time (optimization procedure)
3. Kalman filter
4. Mathematical model for aided systems (integration with
another sensor, fusion)
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References1. http://www.vectornav.com/index.php?&id=76
2. David H. Titterton, John L. Weston Navigation
Technology - 2nd Edition, The Institution of Electrical
Engineers, 2004, ISBN 0 86341 358 7
3. Grewal, M.S., Weill L.R., Andrews A.P., Global
Positioning Systems, Inertial Navigation, and
Integration, John Wiley & Sons, 2001, ISBN 0-471-
20071-9.
4. Oliver J. Woodman, An introduction to inertial
navigation, Technical Report UCAM-CL-TR-696,
ISSN 1476-2986, 2007.
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5. http://www.sbir.gov/sbirsearch/detail/87111
6. http://www.americangnc.com/products/rtgis.htm
7. https://www.slideshare.net/gokullakshmanan/theory-
of-gyrocompass-43492651
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Questions?