Electromagnetic 3D tracking system

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

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

6DOF tracking system block diagram

An electromagnetic 3D tracking system (EM 3D tracking system) is a type of 3D tracking system for handheld devices and head-mounted displays that uses the strength of electromagnets to determine objects' position and orientation. Electromagnetic tracking systems have the highest speed and accuracy of all types of 3D tracking systems in many indoor environments. EM tracking can be used for 6DOF tracking and 5DOF tracking.

Electromagnetic tracking was the first type of 3D tracking used for virtual reality systems.

Examples of electromagnetic tracking systems are the 3D Guidance systems from Ascension and the Razer Hydra. Magnetic tracking was engineered into the Magic Leap 1 for its controller.

AC EM tracking can work without much interference with a headset if the headset is small enough.

EM tracking preserves high frequency transients in movement, like a flick of a finger.

There is a base station and a receiver. The base station generates the magnetic field, and the receiver senses it.

Electromagnetic tracking systems typically use a transmitter that has three coils, one for each X, Y, and Z direction. An example of a transmitter or receiver in this architecture is the Polhemus TX2. Alternatively, trihedral sources can be used.

EM tracking requires that there generally not be any metal objects in the tracking area; Metal objects cause jitter and drift. Metal objects must be at least a foot or two away from a tracking area. This is due to eddy current based distortion.

Principle of operation

Each coil is oriented along the X, Y, or Z axes. A total of nine signal measurements are made: each receiver coil receives a signal from each of the three receiver coils. That's 9 measurements per sensor in total needed for each "frame" of data.

There are two main types of EM 3D tracking that have been commercialized: AC electromagnetic tracking and DC electromagnetic tracking. AC was the first, which was popularized by Polhemus. Then, DC was popularized by Ascension as an alternative to AC.

History

Electromagnetic tracking was first commercialized by Polhemus. Then, another company was founded: Ascension, which was founded by two former Polhemus employees.

Before the year 2000, EM trackers were generally limited by the amount of compute, because computers were not powerful enough to run all the calculations.

Companies

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

Commercial systems

• Polhemus Viper
• AMFITRACK

Types

• AC magnetic tracking (Polhemus)
• Pulsed DC magnetic tracking (Invented by Ascension)

Components

In classical systems, there is a system electronics unit (SEU). It is a box that sources and sensors plug into.

There must be an analog to digital converter (ADC), magnet wire (enameled wire), and a microcontroller.

A basic 6DOF electromagnetic tracker can contain the parts shown in this block diagram, though there are many variations.

6DOF electromagnetic tracking systems were developed by Peter Traneus Anderson.

• https://web.archive.org/web/20151002101401/http://home.comcast.net/~traneus/dry_emtrackertricoil.htm is an example of a breadboard 6DOF tracker.

A transmitter typically contains three colocated orthogonal coils. The coils can be approximated as magnetic dipoles. A receiver contains three colocated orthogonal coils. the coils are approximated as dipoles.

• [PLUME project - Scroll down to see photo of hand-building a transmitter coil trio.]

• Media:Dry_elphel_model_1_rcvr_coils.jpg Photo of crude handmade receiver coil trio using [Sonion] T 20 AG telecoils. Each coil is ten millimeters long.

Update rate

From a user interface perspective, 240Hz update rate is generally sufficient if using magnetic tracking with no filtering.

Measurements

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)

• 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 converts HFluxPerIMeasured to estimated receiver position and orientation, using direct-solution algorithm in Raab's 1981 paper or iterative solution in Raab et. al.'s 1979 paper.

• 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, describes closed-form algorithm for concentric-dipole coil trios. Position is calculated first, directly in cartesian coordinates. Orientation is then calculated.

• Frederick H. Raab, "Remote Object Position Locater", expired U.S. Patent 4,054,881. Describes frequency-multiplexed hardware.

• 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. 5, September 1979, pages 709-718, 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.

• Berthold K. P. Horn, "Closed-form solution of absolute orientation using unit quaternions", Journal of the Optical Society of America A, volume 4, April, 1987, pages 629-642, has algorithm for converting from orthonormal rotation matrices to quaternions. Note error: r[2][1] on page 641 is incorrect, while r[2][1] on page 643 is correct.

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

• The software which calculates position and orientation from HFluxPerI measurements, is an example of realtime embedded computational electromagnetics.

• Needed HFluxPerI measurement accuracy can be calculated by a sensitivity analysis.

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, due to the fact that receiver at position = (Xo,Yo,Zo) and receiver at position = (-Xo,-Yo,-Zo) show identical HFluxPerIMeasured for identical orientations. This ambiguity can be resolved by using additional transmitter or receiver coils spaced away from the colocated transmitter or receiver coils.

• The receiver is normally kept on one side of the transmitter, to avoid the hemisphere ambiguity.

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

Signal to noise ratio

• The electromagnetics results in the signal-to-noise ratio in the five angles being 3.4 times worse than the HFluxPerIMeasured 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_Calculation details calculating signal-to-noise ratio (SNR) from accuracy requirements.

Electronics

• Data-acquisition electronics measures the currents in the three transmitter coils, and measures the voltages induced in the three receiver coils.

• Receiver coil signals can be measured simultaneously or sequentially. Simultaneous measurements improve signal-to-noise ratio.

• Many designs used one operating frequency, driving the transmitter coils sequentially. Use of one frequency simplifies handling frequency-dependent effects.

• Multiple-frequency designs drive the three transmitter coils simultaneously, with sinewaves at three distinct frequencies. This improves signal-to-noise ratio by lengthening measurement time.

• Operating frequencies are typically 30 Hz to 15000 Hz. 1000 Hz, 1300 Hz, and 1600 Hz are a good starting point. Higher frequencies give higher induced voltages. Lower frequencies reduce error-causing eddy-current effects.

• The transmitter coils are usually series tuned with capacitors.

• The transmitter-coil currents must be measured. The currents vary slowly due to coil heating, so currents can be measured periodically.

• Some designs use DC pulses to drive the transmitter coils, instead of AC frequencies. This simplifies driver design, but makes receiver signal recovery more difficult. DC pulse-driven transmitter coils must be driven sequentially.

Analog-to-digital converters

Dynamic range is a consideration. Analog to digital converters (ADCs) that have 24-bit resolution, those originally meant for audio, have enough dynamic range.

An electronics setup that has six ADCs can measure three transmitter-coil currents and three receiver-coil voltages continually and simultaneously. Add three more ADCs for each additional receiver coil trio.

A four-ADC electronics can use one channel to measure the currents periodically over time (The currents change slowly as the transmitter coils warm up.), and three channels to measure the three voltages continually and simultaneously.

A two-ADC system can measure currents sequentially with one ADC and voltages sequentially with the other ADC.

A single-ADC electronic system can measure the currents and voltages sequentially.

Papers

• C. L. Dolph, "A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level," Proc. IRE, Vol. 35, pp. 335-348, June, 1946. The original Dolph-Chebyshev window article. This window is capable of 140 dB rejection of out-of-band signals.

• The window in Figure 10 of Albert Nuttall's paper exhibits sidelobe peak, four DFT bins from the central peak, 91 dB down from the central peak (The window and its first through fifth derivatives are all continuous for all t, giving 42 dB/octave rolloff of the sidelobes) and is (for symmetrical limits |t|<=L/2, and zero for all t outside the limits):

w(t) = (1/L)(10/32 + 15/32 cos(2pi t/L) + 6/32 cos(4pi t/L) + 1/32 cos(6pi t/L))

• U.S. Patent 4,109,199 describes the use of a calibration coil in the receiver to calibrate the gains of the electronics.

• More elaborate algorithms provide higher accuracy at the expense of much more computation. by modeling the non-dipole and/or non-concentric parts of the coils. Expired U.S. Patent 5,307,072 is an early example.

• 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-testing methods using a known-flat nonmagnetic surface (such as a granite surface plate).

• A 6DOF tracker using four-coil printed-circuit transmitter and receiver (optimized for academic originality) is discussed in: Peter Traneus Anderson, "A Source of Accurately Calculable Quasi-Static Magnetic Fields", dissertation presented to the Faculty of the Graduate College of the University of Vermont, October 2001, stored here as three files: Media:AndersonPeterDissertation.pdf is the main body. Media:AndersonPeterDissertationReadme.pdf contains copyright license, additional comments, and four figures that are blank in the main body. Media:AndersonPeterDissertationFig14r1.jpg is the color original photo of two of the figures. Expired U.S. Patent 1,172,017 discloses a direct-conversion radio receiver. Peter intended to include this reference as reference 16 in his dissertation, but was unable to find the patent number before Google Patents existed, so made do with existing indirect reference 16.

• A 6DOF tracker using two transmitter coils (instead of three) can be built; Frederick Raab calls this two-state excitation in his 1981 paper. Two-state trackers are severely limited, as they cannot track near the axis of the missing transmitter coil and cannot track near the plane of the two existing transmitter coils.

References

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