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Pose tracking of magnetic objects
Niklas Wahlstrom
Department of Information Technology, Uppsala University, Sweden
February 2, 2018
[email protected] VASCO workshop
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Magnetometer measurement models
1. Common use: Magnetometer provides orientationinformation.
Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.
2. My use: Magnetometer(s) to provide position andorientation information.
I Magnetic mapping: Build a map of the (indoor) magneticfield.
I Magnetic tracking: Measure the position and orientation of aknown magnetic source.
1 / 17 [email protected] VASCO workshop
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Magnetometer measurement models
1. Common use: Magnetometer provides orientationinformation.
Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.
2. My use: Magnetometer(s) to provide position andorientation information.
I Magnetic mapping: Build a map of the (indoor) magneticfield.
I Magnetic tracking: Measure the position and orientation of aknown magnetic source.
1 / 17 [email protected] VASCO workshop
![Page 4: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/4.jpg)
Magnetometer measurement models
1. Common use: Magnetometer provides orientationinformation.
Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.
2. My use: Magnetometer(s) to provide position andorientation information.
I Magnetic mapping: Build a map of the (indoor) magneticfield.
I Magnetic tracking: Measure the position and orientation of aknown magnetic source.
1 / 17 [email protected] VASCO workshop
![Page 5: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/5.jpg)
Magnetic mapping
Build a map of the indoor magnetic field. This map can be usedfor localization.
We have used Bayesian models (Gaussian processes) to model suchfields with good results
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Magnetometer measurement models
1. Common use: Magnetometer provides orientationinformation.
Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.
2. My use: Magnetometer(s) to provide position andorientation information.
I Magnetic mapping: Build a map of the (indoor) magneticfield.
I Magnetic tracking: Measure the position and orientation of aknown magnetic source.
3 / 17 [email protected] VASCO workshop
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Sensor setup
We use a sensor network with four three-axis magnetometers todetermine the position and orientation of a magnet.
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Magnetic tracking
Advantages
I Cheap sensors
I Small sensors
I Low energy consumption
I No weather dependency
I Passive unit, requires nobatteries
5 / 17 [email protected] VASCO workshop
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Magnetic tracking
Advantages
I Cheap sensors
I Small sensors
I Low energy consumption
I No weather dependency
I Passive unit, requires nobatteries
5 / 17 [email protected] VASCO workshop
![Page 10: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/10.jpg)
Magnetic tracking
Advantages
I Cheap sensors
I Small sensors
I Low energy consumption
I No weather dependency
I Passive unit, requires nobatteries
5 / 17 [email protected] VASCO workshop
![Page 11: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/11.jpg)
Magnetic tracking
Advantages
I Cheap sensors
I Small sensors
I Low energy consumption
I No weather dependency
I Passive unit, requires nobatteries
5 / 17 [email protected] VASCO workshop
![Page 12: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/12.jpg)
Magnetic tracking
Advantages
I Cheap sensors
I Small sensors
I Low energy consumption
I No weather dependency
I Passive unit, requires nobatteries
5 / 17 [email protected] VASCO workshop
![Page 13: Pose tracking of magnetic objects - it.uu.se filePose tracking of magnetic objects Niklas Wahlstrom Department of Information Technology, Uppsala University, Sweden February 2, 2018](https://reader030.vdocuments.us/reader030/viewer/2022041202/5d4e7aff88c993986c8bd0b4/html5/thumbnails/13.jpg)
Mathematical model - dipole field
The magnetic field can be described with a dipole field.
J(r′)
mr
B(r)
B(r) =µ0
4π‖r‖5(3r · rT − ‖r‖2I3
)︸ ︷︷ ︸
=C(r)
m
m ,1
2
∫r′ × J(r′)d3r′
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Sensor model - single dipole
The measurements can be described with a state-space model
xk+1 = Fkxk +Gkwk, wk ∼ N (0, Q),
yk,j = hj(xk) + ek, ek ∼ N (0, R)
Point target sensor model (one dipole)
hj(xk) = C(rk − θj)mk, xk = [rTk vTk mT
k ωTk ]
T
C(r) =µ0
4π‖r‖5 (3rrT − ‖r‖2I3),
Measurement from a sensor network ofmagnetometers positioned at {θj}Jj=1.
Degrees of freedom
I 3D position
I 2D orientation
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Experiment 1
0.2
0.1-0.1
-0.2
-0.05
y-coordinate [m]
0
Trajectory
0
-0.1
0.05
x-coordinate [m]
0.1
z-co
ordi
nate
[m]
0 -0.1
0.15
0.2
0.1
0.25
-0.20.2
0.3
Trajectory
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2y-coordinate [m]
-0.1
-0.05
0
0.05
z-co
ordi
nate
[m]
0.1
0.15
0.2
0.25
0.3
Theaccuracy is
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Experiment 2 - results - position
20 25 30 35 40 45 50
−0.2
−0.1
0
0.1
0.2
0.3
Time [s]
Posi
tion
[m]
Black: Ground truth position. Color: Estimated position
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Experiment - results - orientation
20 25 30 35 40 45 50−200
−100
0
100
Time [s]
Ori
enta
tion
[deg
ree]
Black: Ground truth orientation. Color: Estimated orientation
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Stylaero AB
I In February 2017 acompany was startedaround this technology
I In total seven people areinvolved in the companyon part-time.
I Collaborations with bothgaming companies andindustrial partners.
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