Electromagnetic tracking system

Polhemus Liberty, a typical commercial electromagnetic tracking system

A coil trio used as transmitter or receiver. This trio is from PLUME, an open-source EM tracker project.

A 3D Guidance trakSTAR system, one of Ascension's electromagnetic 3D tracking systems

6DOF tracking system block diagram, from Raab. Blood, Steiner, and Jones

An electromagnetic tracking system (EM tracking system) is a type of 3D tracking system that uses magnetic fields to sense the position and rotation of objects. EM 3D tracking systems are used for handheld controllers and head-mounted displays for virtual reality and augmented reality. Electromagnetic tracking systems have the highest speed and accuracy of all types of 3D tracking systems in many indoor environments.

EM tracking can track high detail and speed movement, like a flick of a finger.

Examples of electromagnetic tracking systems are the 3D Guidance systems from Ascension and the Razer Hydra.

There are multiple types of EM 3D tracking. The two commercialized types are AC electromagnetic tracking and DC electromagnetic tracking. AC was the first. DC was commercialized as an alternative that performs better near metal.

EM tracking can be used for 6DOF tracking and 5DOF tracking.

An EM tracking system that does digital calculations requires an analog-to-digital converter to convert the analog signals from the sensor coils.

Most electromagnetic tracking systems use a transmitter that has three coils, one for each X, Y, and Z direction. An example of a transmitter in this architecture is the Polhemus TX2. It is possible to use trihedral sources instead.

Principle of operation

The principle of operation of electromagnetic 3D tracking systems is as follows:

There is a transmitter and a sensor.

In a Polhemus system, the angle of the sensor is determined first using the AC component of a magnetic field created by the transmitter, then the translational offset to the transmitter is determined using a combination of the DC component (DC offset) of the generated field and the angle measurement that was just made. Or this can be done in one step using a matrix.

The transmitter can be a physical spinning magnet, or coils of wire instead. Orthogonal coils fed with phase-quadrature currents is equal to a mechanical rotating magnetic dipole.

The transmitter's magnet rotates or nutates. Based on the timing of when the field is the strongest at the sensor, it is possible to determine the angle of the sensor relative to the transmitter.

A nutating field can be used for 6DOF due to DC offset providing additional environmental information for the purpose of determining translational offset.

The geometric aspects of magnetic tracking are similar to a military scanning radar, but magnetic. Like radar, there is a rotating field that acts as a sweep scanner. The difference in magnetic tracking is the equations are in the quasistatic regime and there is a direct measurement at the object point.

The sensor is coils of wire. The transmitter generates a magnetic field, and the sensor detects it. There are three coils in the sensor and if using coils for the transmitter, three for the transmitter.

In general, electromagnetic tracking uses quasistationary fields, also called quasistatic fields, which act like non-moving magnetic fields. A feature of quasistationary fields is that it is possible to derive the angle of a sensor independent of distance by doing a phase measurement. The quasistatic condition means that the electromagnetic wavelength in free space is much larger than any dimensions in the system, including the coil diameters.

Each coil is oriented along the X, Y, or Z axis. For each 6DOF pose to be detected, nine signal measurements are made. Each receiver coil receives a signal from each of the three receiver coils.

The position is given by intersecting the three toroids that yields two solutions. Each time the field turns on (each pulse) it’s possible to calculate a surface on which the sensor must lie. The trick is that the surface is not a sphere, it’s a toroid centered on and aligned with the core of the transmitter. After doing this three times the three toroidal surfaces are intersected, providing two possible places where the sensor is located. This is the case for AC and DC systems alike.

In an EM spatial tracking system, there are transmitters and sensors. Transmitters and sensors are a set of three perpendicular coils.

There must be an analog to digital converter (ADC), a coil of magnet wire (enameled wire), and a processor which may be a microcontroller. The ADCs used can be successive approximation ADCs, sigma-delta ADCs, or flash ADCs. For example, the Ascension SpacePad uses successive approximation and the Polhemus Viper uses sigma-delta.

The most popular type of transmitter is three colocated orthogonal coils. A receiver also is three colocated orthogonal coils. The transmitter and receiver are approximated as magnetic dipoles.

Early Polhemus systems rotated the magnetic field in space, whereas the Model 1 uses three separate frequencies.

Hardware

EM tracking uses analog-to-digital converters (ADCs) to convert the electric pulses from the electromagnetic coils into digital data. An SEU does this, and feeds the data into an internal microcontroller whose firmware does the mathematics and sends the pose data to a computer. Before the signals are fed into the ADC, they need to be amplified.

See List of coils for electromagnetic 3D tracking systems

In first-generation systems, there is a system electronics unit (SEU). It is a box that the transmitters and sensors plug into.

History

Magnetic tracking was earliest used in Headsight for 3DOF rotation.

Electromagnetic tracking for navigation was described by Henry Kalmus in about 1962.

Then, electromagnetic tracking with 6DOF (SPASYN) was invented by Jack Kuipers and commercialized at Polhemus.

Magnetic tracking was developed for fighter jet pilot helmet tracking.

Jack Kuipers' invention involved the fact that in a nutating magnetic dipole field, the field strength remains constant only along the axis of nutation. This allows precise tracking of a remote object in 6DOF.

After Polhemus, another company was founded: Ascension, which was started by two former Polhemus employees to improve the technology.

Milestones

Milestones in the development of electromagnetic 3D tracking technology:

• 1960s: Bill Polhemus developed a magnetic tracker for head-mounted display uses at Harvard University. He developed it as a component of a Head Mounted Display system. He founded Polhemus Incorporated in 1970 while consulting for the military.
• 1970: The company Polhemus was founded to build a head-mounted aiming device for helicopter pilots
• 1986: Ascension was founded, which developed interference-free tracking
• 1988: Polhemus released the first commercial EM 3D device, the 3Space digitizer
• 1990s: Polhemus devices are used by motion capture artists and 3D animators including Disney and Pixar

Before the year 2000, EM trackers were limited by the speed of the computer.

Companies

• Ascension (Merged into NDI)
• Polhemus
• AmfiTrack
• NDI
• Sixense
• Radwave Technologies
• PREMO Group, a company in Spain that markets electromagnetic tracking parts, including coils. Premo's electromagnets are in some AmfiTrack products.
• Cedrat Technologies

6DOF electromagnetic tracking systems have been developed by Peter Traneus Anderson. An example of a breadboard 6DOF tracker is at https://web.archive.org/web/20151002101401/http://home.comcast.net/~traneus/dry_emtrackertricoil.htm.

Human-computer interaction factors

240Hz update rate is sufficient for head tracking and handheld controller tracking for room-scale virtual and augmented reality. Filtering such as kalman filtering makes no difference to this requirement. Under 240Hz is laggy for quick movements, like turning the head suddenly or making a sudden movement with the hand or wrist.

For desktop use, as low as 30Hz is acceptable for hand tracking, and as low as 60Hz is acceptable for head tracking.

Measured signals

Software running on a microcontroller takes measurements of the magnetic flux strength, and turns these into a position and orientation measurement. Measurements are taken the same way between AC and DC systems.

Three transmitter coils times three receiver coils gives nine coil-coupling measurements, expressable as a 3x3 signal matrix, HFluxPerIMeasured (Magnetic flux per current measured). The current should be the same, and known beforehand.

The needed accuracy in the HFluxPerI measurement can be determined by doing a sensitivity analysis.

Signal-to-noise ratio

For an AC system, the electromagnetics results in the signal-to-noise ratio (SNR) in the five angles being 3.4 times worse than the magnetic flux per current measured signal-to-noise ratio, due to interactions between position errors and orientation errors.

The electromagnetics results in the signal-to-noise ratio in range being 3 times better than the HFluxPerIMeasured signal-to-noise ratio, due to the inverse-cube law of dipole-dipole field coupling.

6DOF electromagnetic tracker signal-to-noise requirements details calculating signal-to-noise ratio from accuracy requirements.

Software algorithms

For each of the three coils in the sensor, there are three measurements: X, Y, and Z. It is known beforehand which is which, because the microcontroller knows the timing of the X, Y, and Z transmitter signals, and can pair each transitter signal with one measurement from the sensor.

The software algorithm has as its inputs a set of 9 magnetic flux strengths.

Each component of HFluxPerIMeasured is the magnetic flux through one receiver coil (due to magnetic field H from transmitter coil), divided by the current I in one transmitter coil. HFLuxPerIMeasured has units of meters, and is a geometrical property of the coils' sizes, shapes, number of turns, ferromagnetic core (if any), positions, and orientations. HFluxPerI coupling between two dipole coils.

Algorithm software running on a microcontroller calculates the sensor's position and orientation from HFluxPerIMeasured, using direct-solution algorithm (analytical method) in Raab's 1981 paper or iterative solution in Raab et. al.'s 1979 paper (numerical method).

Raab's 1981 paper describes closed-form algorithm for concentric-dipole coil trios. Position is calculated first, directly in cartesian coordinates. Orientation is then calculated.

The Raab, Blood, Steiner, Jones paper describes iterative algorithm for concentric-dipole coil trios, using small-angle approximation for changes in position and in orientation. Includes sensitivity matrix of magnetic couplings partial derivatives with respect to changes in position and orientation.

• File:Dry0097.c is a simulator program containing an implementation of Raab's algorithm.

Hemisphere ambiguity

There is an inherent hemisphere ambiguity, meaning that the system does not know if the tracked device is in a position in front of or behind the transmitting source. This is because a receiver at position = (Xo,Yo,Zo) and receiver at position = (-Xo,-Yo,-Zo) have identical HFluxPerI measurements if their orientations are identical.

The receiver is normally kept on one side of the transmitter, to avoid the hemisphere ambiguity. This ambiguity can be resolved by using additional transmitter or receiver coils spaced away from the colocated transmitter or receiver coils.

The transmitter field on the unused side of the transmitter can be eliminated by using a magnetic mirror: Reference U.S. patent 5,640,170, which references many older expired EM-tracker patents.

System development

A low cost magnetic tracking system can consist of the following steps in order, from a free-running AC source tuned to a specific frequency:

• Sense magnetic field
• Amplify voltage from the millivolt range to the volt range
• Run voltage through envelope detector
• Run output of envelope detector through voltage to frequency converter
• Count number of pulses in frame period and store in a register
• Send number of pulses to PC

Examples

A team of researchers used an ALT021-10E sensor in an EMT system.

Open-source electromagnetic trackers

Open source electromagnetic trackers are trackers that have designs publicly available. Contributions in this area have been made by Peter Traneus Anderson.

• https://github.com/traneus/emtrackers
• Plume
• Anser EMT

In one research paper by Gerald Pirkl and Paul Lukowicz, a transmitter generates a magnetic field at a certain resonant frequency, and the receiver is calibrated to the frequency. This constituted a magnetic resonant coupling-based system.

In a magnetically resonant system, the energy transmitted in the field decreases with 1/r^6. The range depends on the size of the transmitter coil, the number of windings, and the voltage. Pirkl and Lukowicz were able to get a 4m range (covers a diameter of 8m). However, a large range comes with the requirement of needing a large dynamic range at the receiver.

References

• "Electromagnetic Tracking System Market". https://www.statsndata.org/report/Electromagnetic-Tracking-System-Market-191994.

• Frederick H. Raab, Ernest B. Blood, Terry O. Steiner, Herbert R. Jones, "Magnetic Position and Orientation Tracking System", IEEE Transactions on Aerospace and Electronic systems, Vol. AES-15, No. 4, September 1979, pages 709-718. Iterative solution for 6DOF tracker. Includes sensitivity matrix of magnetic couplings partial derivatives with respect to position and orientation changes.

• Frederick H. Raab, "Quasi-Static Magnetic-Field Technique for Determining Position and Orientation", IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-19, No. 4, October 1981, pages 235-243. Direct solution for 6DOF tracker.

• Schroeder, Tobias (2015-06-12). "An accurate magnetic field solution for medical electromagnetic tracking coils at close range". Journal of Applied Physics (AIP Publishing) 117 (22). doi:10.1063/1.4922667.

• C.A. Nafis, V. Jensen, L. Beauregard, P.T. Anderson, "Method for estimating dynamic EM tracking accuracy of Surgical Navigation tools", SPIE Medical Imaging Proceedings, 2006. Reports low-cost accuracy-measuring techniques and results for various trackers.

• C. L. Dolph, "A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level," Proceedings of the IRE (now part of the IEEE), Vol. 35, pp. 335-348, June, 1946. The original Dolph-Chebyshev Fourier-transform window article. Dolph-Chebyshev window can give 140 dB rejection in the stopband.

• Albert H. Nuttall, "Some Windows with Very Good Sidelobe Behavior", IEEE Transactions on Acoustics, Speech, and Signal Processing 29 (1) 84-91, doi:10.1109/TASSP.1981.1163506, "U.S. Government work not subject to U.S. copyright", in particular Figure 10 window for -L/2 < t < L/2: w(t) = (1/L) (10/32 + 15/32 cos(2pi t/L) + 6/32 cos(4pi t/L) + 1/32 cos(6pi t/L)) has first sidelobe at -61 dB and 42 dB/octave sidelobe rolloff.

• Eugene Paperno, "Suppression of magnetic noise in the fundamental-mode orthogonal fluxgate", Elsevier, Sensors and Actuators A 116 (2004) 405-409. Picotesla noise in 20 mm long 1 mm diameter fluxgate magnetometer. To get low noise, the drive flux swings between saturation in one direction and zero flux. The usual noisy fluxgate drive flux swings between saturation in one direction and saturation in the other direction, to ease measurement down to DC.

• [| Nara etal, "Moore-Penrose generalized inverse of the gradient tensor in Euler's equation for locating a magnetic dipole"][| J. Appl. Phys. 115, 17E504 (2014)] on field-and-gradient single-coil 5DOF tracking closed-form algorithm.

• James M. Chappell, Samuel P. Drake, Cameron L. Seidel, Lachlan J. Gunn, Azhar Iqbal, Andrew Allison, Derek Abbott, "Geometric Algebra for Electrical and Electronic Engineers", Proceedings of the IEEE, Vol. 102, No. 9, September 2014, pages 1340 to 1363. Clifford algebra formulation of electromagnetics using vectors, bivectors, trivector.

• Anton Plotkin, Vladimir Kucher, Yoram Horen, and Eugene Paperno, "A New Calibration Procedure for Magnetic Tracking Systems", IEEE Transactions on Magnetics, Volume 44, Number 11, November 2008, Pages 4525 to 4528. In-system coil characterization using just receiver positions on the plane closest to the transmitter, which makes electromagnetic sense.