Magnetic tracking is one of miscellaneous motion capture methods, and maybe the oldest. However, its working principle is rarely introduced in detail perhaps due to its early adaptation resides in military and medical industry. Due to my interest in VR & animation MoCap, I’ve spent some time digging into the very depth of it and would like to share some non-confidential knowledge of it with you. In this slide, a short history of magnetic tracking will be visited, followed by its working principle and algorithm simulation. Hope you enjoy it. If you wanna discuss something in depth with me, please don’t hesitate to contact me via: dibao.wang@gmail.com

1. Magnetic Tracking
-- talking from Magic Leap One
James Wang
20th Aug 2018

2. Magnetic tracking is one of miscellaneous motion capture methods, and
maybe the oldest. However, its working principle is rarely introduced in
detail perhaps due to its early adaptation resides in military and medical
industry. Due to my interest in VR & animation MoCap, I’ve spent
some time digging into the very depth of it and would like to share
some non-confidential knowledge of it with you.
In this slide, a short history of magnetic tracking will be visited, followed
by its working principle and algorithm simulation. Hope you enjoy it.
If you wanna discuss something in depth with me, please don’t
hesitate to contact me via: dibao.wang@gmail.com

3. Content
• Tech. Overview
• Working Principle
• Modeling & Simulation
• Conclusion

4. Tech. Overview

5. Old But Still Sexy
• Magnetic tracking was first used in military, medical and animation industry
• Although it’s old, with patents expired, it’s still powerful in short-range
tracking … even the latest Magic Leap One adopts it as a key component
1990
2011
2013
2018

6. Raab et al @ 1979
• Remote Object Position And Orientation Locater (US 4,314,251)
• Filed: Jul. 30, 1979
• Almost all EMTS (electromagnetic tracking system) traces back to this patent
filed by Raab

7. Ascension since 1990
• Wired multi-point tracking by DC-magnetic field emission/detection

8. Razer Hydra 2011
• Wired two-controller tracking with AC-type magnetic field emission/detection
• Should be the first consumer product of magnetic tracking

9. Sixsens STEM 2013~
• Wireless 5-point (hands, head and legs) AC magnetic field tracking
• Failed to manufacture until now (a notorious Kickstarter project)

10. Magic Leap @2017
• Electromagnetic tracking with augmented reality systems (US2017/0307891)
• Filed: Apr. 24, 2017

11. Magic Leap One @2018
• A wireless 2-controller tracking by AC (or DC) magnetic field
• Thanks for the teardown by iFixit (link)
Receiver Coils
Transmitter
Coils

12. Limitation
• Near-field error & signal saturation (r< 0.2m)
• Solution: non-linear numerical algorithm, auto-gain control
•
• Far-field noise (r > 1.0 m)
• Solution: sensor fusion
• Metal-induced distortions
• Solution: N/A (old issues though)
• Complex calibration in production site
• Solution: N/A (company like Sixsense seemed to fail at this point)

13. Working Principle

14. How Does It Work?
• A 3-axis current loop (emitter) generates magnetic field (DC or AC)
• A 3-axis magnetic sensor (magnetometer or induction coil) measures the field quantity
at surrounding position with any orientation
• A signal processing method to extract the signal components regarding sensor-
emitter pairing relationship
• A pre-built field-pose algorithm reverses the pose of the sensor w.r.t. the emitter
( 𝑟 𝑇𝑥
𝑅𝑥
, 𝑅 𝑇𝑥
𝑅𝑥
)Tx
Rx
Emission
Detection
Extraction
Reversion

15. M-field Emission
• Biot-Savart law quantitatively determines the magnetic field generated
by a piece of current wire segment
• It’s a building block of magnetic-field modeling
∆Bk=
𝜇0I
4𝜋
∆Lk × rk
rk
3
B =
k
∆Bk
rk
W
∆Lk
∆Bk
I

16. Magnetic Field
• Circular and square coils are two often used emitter coil
• The point-symmetric property indicates the non-uniqueness of solution
B(−r)
B(r)B(r)
B(−r)

17. 3D-Coil
• EMTS usually uses XYZ-coil for transmitter and receiver
• If the field-pose relationship is built, then a tracking device can be made
• Ideally, m-field generated by XYZ-coil can be approximated by magnetic
dipole, 𝐵 =
𝑘
4𝜋r3 3 𝑟 𝑟′ − 𝐼 𝐼 𝑥𝑦𝑧, which will be used to build the field-pose
relationship

18. M-Field of XYZ Coil
• Four coordinate frames will be used
• W: world reference
• Tx: transmitter
• Rx: receiver
• Rd: radial-direction (with x-axis aligned with r)
•
• Two orientation transform matrices used
• 𝑻 𝒕 ≡ 𝑅 𝑇𝑥
𝑅𝑑
… translation related
• 𝑻 𝒓 ≡ 𝑅 𝑇𝑥
𝑅𝑥
… rotation related
• Given Tx & Rx pose, the sensed m-field signal
tensor is like 𝐵 = Tr′Tt(
𝑘
r3 𝐶 𝑑 𝑇𝑡
′
𝐼 𝑥𝑦𝑧)
W

19. Pose Reversion Alg.
• Given measured B, Tr & Tr can also be solved with the algorithm flow
summarized as below
• Then 6D-pose (Rx_in_Tx) can be solved as
• 𝑇𝑟 = 𝑅 𝑇𝑥
𝑅𝑥
• 𝑟 = 𝑟𝑇𝑥
𝑅𝑥
= (𝑟𝑐𝛽𝑐𝛼, 𝑟𝑐𝛽𝑠𝛼, 𝑟𝑠𝛼)
𝑈 = 𝑆 𝑝,𝑚𝑒𝑎𝑠
′
𝑆 𝑝,𝑚𝑒𝑎𝑠
𝑟 =
2
3
𝑡𝑟 𝑈
1/6
𝑆 𝑟 = 𝑟3 𝑆
𝑋 =
4
3
( 𝑆 𝑟′ 𝑆𝑟 −
1
4
𝐼)
𝛼′ = tan−1(𝑋22/𝑋12) 𝒐𝒓 tan−1(𝑋22/𝑋12) + 𝜋
𝛽′ = ± sin−1(𝑋33)
𝑇𝑟 = [ 𝑆 𝑟(4 𝑆𝑟′ 𝑆𝑟 − 3 𝐼)]′

20. Algorithm Issue (1)
• Near-field Error
• Dipole model approximates square or circular loop only when distance
>> coil diameter, as shown below. This causes near-field pose error

21. Algorithm Issue (2.1)
• Hemisphere ambiguity
• Two possible position solutions exist, which requires
• angular boundary judgement
• sensor fusion with IMUs

22. Algorithm Issue (2.2)
A-B Search Algorithm:
1. Given starting point 𝛼, 𝛽 𝑖𝑛𝑖𝑡
2. Calculate 4 possible 𝛼′, 𝛽′ 𝑘 for t(k)
3. Re-arrange 𝛼 to [0,2𝜋]
4. Find best choice to satisfy
• Minimum distance between 𝛼′, 𝛽′ 𝑘 and
𝛼, 𝛽 𝑘−1
• norm( 𝑋(𝛼′, 𝛽′)- 𝑋)/norm( 𝑋) < Thr
5. Update solver output 𝛼, 𝛽 𝑘
6. Repeat 2->5

23. Modeling & Simulation

24. Modeling & Sim. Flow
• Pose & Current Signal to drive emitter field generation
• The solved pose will be compared with the input one
EM-Tx
Emission
RxCoil & ADC
Extraction
Sig. Gen.
Pose Solver
DAC & TxCoil
𝑡𝑖𝑚𝑒 ( 𝑝, 𝑄)
𝐵
PCM
( 𝑝′, 𝑄′)
𝐼(t)
(𝑠1, 𝑠2, 𝑠3)
Calibration
[𝑣1 𝑣2 𝑣3]
𝑆𝑖𝑗
𝜎𝑖𝑗
compare
Pose
Modeling

25. Tx-Coil Excitation
• Here is an example of Tx-coil excited by square wave current input (DC)
• In most modern cases, excitation uses sinusoidal wave (AC)
B 𝑅𝑥

26. Pose Check (1)
• Comparison between pose input and solver output are performed for:
• Position, Quaternion and Orientation Matrix

27. Pose Check (2)
• 3D trajectory and Distance/Angle Error
Model error and boundary crossing
Model error and filter-delay bias

28. Conclusion

29. Still More …
• This slide just aims to provide a brief introduction for those who want to
develop magnetic tracking system. Of course, there are still more to know
before get it useful and reliably such as (I’ll publish another slide to talk
about them soon)
1. Using AC signal to enhance signal magnitude and enlarge operation
distance
2. Auto-gain control to deal with radical change of field magnitude
3. Accurate but cost effective calibration process for emitter and receiver
4. IMU-fusion to suppress noise in far field
5. Apply quadratic excitation to reduce metal distortion