6DOF Electromagnetic Tracker Construction HOWTO - Revision history

Traneus: Added patent reference and improved equation formatting

2017-11-12T22:27:40Z

Added patent reference and improved equation formatting

Traneus at 18:01, 12 January 2017

2017-01-12T18:01:25Z

Traneus at 20:58, 9 January 2017

2017-01-09T20:58:35Z

Traneus at 21:12, 20 May 2016

2016-05-20T21:12:32Z

Traneus at 21:07, 20 May 2016

2016-05-20T21:07:05Z

Traneus at 01:37, 25 February 2016

2016-02-25T01:37:20Z

Traneus at 20:29, 10 February 2016

2016-02-10T20:29:28Z

Traneus at 20:14, 10 February 2016

2016-02-10T20:14:50Z

Traneus at 04:05, 23 January 2016

2016-01-23T04:05:27Z

Traneus at 04:01, 23 January 2016

2016-01-23T04:01:13Z

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 * 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.
-* Albert H. Nuttall, "Some Windows with Very Good Sidelobe Behavior", IEEE Transactions on Acoustics, Speech, and Signal Processing 29 (1) 84-91, February 1981, doi:10.1109/TASSP.1981.1163506, "U.S. Government work not subject to U.S. copyright". The window in Figure 10 of this paper is (for symmetrical limits |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)), and is zero for all t outside the L/2 limits. The sidelobe peak four DFT bins from the central peak is 91 dB down from the central peak. This window function and its first through fifth derivatives are all continuous for all t, giving 42 dB/octave rolloff of sidelobes.
+* Albert H. Nuttall, "Some Windows with Very Good Sidelobe Behavior", IEEE Transactions on Acoustics, Speech, and Signal Processing 29 (1) 84-91, February 1981, doi:10.1109/TASSP.1981.1163506, "U.S. Government work not subject to U.S. copyright". The window in Figure 10 of this 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):
 * Expired U.S. Patent 4,109,199 describes the use of a calibration coil in the receiver to calibrate the gains of the electronics.
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 * 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.
+* 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 [[6DOF_Two_State_Electromagnetic_Trackers|two-state excitation]] in his 1981 paper referenced above.
+* A 6DOF tracker using two transmitter coils (instead of three) can be built; Frederick Raab calls this [[6DOF_Two_State_Electromagnetic_Trackers|two-state excitation]] in his 1981 paper referenced above. 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.

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 * 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. Useful for sensitivity analyses.
+* 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.
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 * 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.
 * There is an inherent hemisphere ambiguity, since 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.

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 * Accuracy is poor for lined-up pose: receiver positioned on a transmitter-coil axis, with receiver oriented to make receiver-coil axes parallel with transmitter-coil axes. Some of the first-order partial derivatives go to zero in these cases, causing the position-and-orientation solution to separate into four separate partial solutions.
-* Poses with poor tracking accuracy, should be good for coil characterization. Coil-characterization poses should be chosen based on electromagnetic theory, rather than on mechanical measurements. Use receiver positions close to transmitter, based on boundary-condition principles of EM theory. Receiver positions on both sides of transmitter (even if only one side is used in operation), are necessary to distinguish transmitter gain from transmitter nonconcentricity.
+* Poses with poor tracking accuracy, should be good for coil characterization. Coil-characterization poses should be chosen based on electromagnetic theory, rather than on mechanical measurements. Use receiver positions close to transmitter, based on boundary-condition principles of EM theory. Receiver positions on both sides of transmitter (even if only one side is used in operation), are necessary to distinguish transmitter gain from transmitter nonconcentricity. [[EM_Tracker_Coil_Characterization]] has further discussion.
 * The poor-accuracy poses can be reduced, by replacing the three-orthogonal-coil receiver with a receiver comprising four colocated coils (the transmitter remains three orthogonal coils). The four receiver coils point in the directions of the vertices of a regular tetrahedron. When the four-coil receiver is positioned on a transmitter-coil axis, with one receiver coil oriented parallel to a transmitter-coil axis, the remaining three receiver coils' axes cannot be parallel to transmitter-coil axes.

← Older revision		Revision as of 21:12, 20 May 2016
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	* 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.		* 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.

−	* A 6DOF tracker using two transmitter coils (instead of three) can be built; Frederick Raab calls this "two-state excitation" in his 1981 paper referenced above.	+	* A 6DOF tracker using two transmitter coils (instead of three) can be built; Frederick Raab calls this [[6DOF_Two_State_Electromagnetic_Trackers\|two-state excitation]] in his 1981 paper referenced above.

← Older revision		Revision as of 21:07, 20 May 2016
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	* 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.		* 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.
		+
		+	* A 6DOF tracker using two transmitter coils (instead of three) can be built; Frederick Raab calls this "two-state excitation" in his 1981 paper referenced above.

← Older revision		Revision as of 01:37, 25 February 2016
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−	A basic 6DOF (six degrees of freedom: three of position and three of orientation) electromagnetic tracker can contain the parts shown in this block diagram, though there are many variations: [[File:6DOF_tracker_block_diagram.png]]	+	A basic 6DOF (six degrees of freedom: three of position and three of orientation) electromagnetic tracker can contain the parts shown in this block diagram, though there are many variations. [[File:6DOF_tracker_block_diagram.png]]
		+
		+	* https://web.archive.org/web/20151002101401/http://home.comcast.net/~traneus/dry_emtrackertricoil.htm is an example of a breadboard 6DOF tracker.

	* Transmitter contains three colocated orthogonal coils. The coils are approximated as magnetic dipoles.		* Transmitter contains three colocated orthogonal coils. The coils are approximated as magnetic dipoles.

← Older revision		Revision as of 20:29, 10 February 2016
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−	A basic 6DOF (six degrees of freedom: three of position and three of orientation) electromagnetic tracker ~~contains~~ the ~~following~~ parts:	+	A basic 6DOF (six degrees of freedom: three of position and three of orientation) electromagnetic tracker can contain the parts shown in this block diagram, though there are many variations: [[File:6DOF_tracker_block_diagram.png]]

	* Transmitter contains three colocated orthogonal coils. The coils are approximated as magnetic dipoles.		* Transmitter contains three colocated orthogonal coils. The coils are approximated as magnetic dipoles.

← Older revision		Revision as of 20:14, 10 February 2016
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	* [[Media:EM_tracker_classic_coil_trio.jpg]] Photo of classic coil trio used as transmitter or receiver. The three coils are wound on a black plastic cube about one centimeter on a side.		* [[Media:EM_tracker_classic_coil_trio.jpg]] Photo of classic coil trio used as transmitter or receiver. The three coils are wound on a black plastic cube about one centimeter on a side.
−
−	* [[http://www.coilcraft.com/maine_scientific/transfrm.html One vendor's photo of a coil trio.]]

	* [[http://rose.eu.org/2014/tag/plume Scroll down to see photo of hand-building a transmitter coil trio.]]		* [[http://rose.eu.org/2014/tag/plume Scroll down to see photo of hand-building a transmitter coil trio.]]

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 * Algorithm software converts HFluxPerIMeasured to estimated receiver position and orientation, using direct-solution algorithm in Raab's 1981 paper or iterative solution in Raab etal'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. See also Raab's expired U.S. Patent 4,054,881 for hardware discussion.
+* 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, 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. Useful for sensitivity analyses.