Electromagnetic tracking method and system

Provided is an electromagnetic tracking system, comprising a coil arrangement comprising a first coil configured to generate a first magnetic field and a second coil configured to generate a second magnetic field and a drive unit configured to provide a first drive current to the first coil and to provide a second drive current to the second coil, wherein the first drive current and the second drive current are at about the same frequency, wherein the frequency is below 60 Hz, and wherein the first electromagnetic field and the second magnetic field are generated out of phase. Also provided is a method of electromagnetic tracking comprising generating a first electromagnetic field at a frequency, generating a second electromagnetic field at about the frequency, wherein the frequency is below 60 Hz and wherein the first electromagnetic field and the second magnetic field are generated out of phase, sensing the first electromagnetic field and the second electromagnetic field and processing a waveform indicative of a combination of the sensed first electromagnetic field and the sensed second electromagnetic field.

BACKGROUND

This disclosure relates generally to tracking systems that use magnetic fields to determine the position and orientation of an object, such as systems used for tracking instruments and devices during surgical interventions and other medical procedures. More particularly, this disclosure relates to a system and method of tracking including a coil transmitter having two coils operating at about the same frequency.

Tracking systems have been used in various industries and applications to provide position information relating to objects. For example, electromagnetic tracking may be useful in aviation applications, motion sensing applications, and medical applications. In medical applications, tracking systems have been used to provide an operator (e.g., a physician) with information to assist in the precise and rapid positioning of a medical device located in or near a patient's body. In general, an image may be displayed on a monitor to provide positioning information to an operator. The image may include a visualization of the patient's anatomy with an icon on the image representing the device. As the device is positioned with respect to the patient's body, the displayed image is updated to reflect the correct device coordinates. The base image of the patient's anatomy may be generated either prior to, or during, the medical procedure. For example, any suitable medical imaging technique, such as X-ray, computed tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), and ultrasound, may be utilized to provide the base image displayed during tracking. The combination of the base image and the representation of the tracked device provide positioning information that allows a medical practitioner to manipulate a device to a desired position and/or associate information gathered to a precise location.

To determine device location, tracking systems may utilize a method of electromagnetic (EM) field generation and detection. Using this method, at least one magnetic field is generated from one or more EM sensors (e.g., EM field generators or transmitters), and the magnetic fields are detected by one or more complementary EM sensors (e.g., EM receivers). In such a system the EM field may be detected by measuring the mutual inductance between the EM sensors and the complementary EM sensors. The measured values may then be processed to resolve a position and/or orientation of the EM sensors relative to one another. For example, an electromagnetic tracking system may include an EM sensor mounted at the operative end of a device and a complementary EM sensor fixed in a known position. When the EM sensor generates a magnetic field, a voltage indicative of the mutual inductance may be induced across the complementary EM sensor. The signal may be sensed and transmitted to a processor for processing. Processing may then use the measured voltage signal indicative of mutual inductance to determine the position and orientation of the EM sensors relative to one another (e.g., the X, Y and Z coordinates, as well as the roll, pitch and yaw angles).

Generally electromagnetic tracking systems contain EM sensors that include an array of one or more EM transmitter coils and an array of one or more EM receiver coils. Preferably, the mutual inductance between the two coils may be measured without inaccuracies. However, when measuring the mutual inductance between the transmitter and receiver coils, electrically conductive materials in the vicinity of the transmitters and receivers may distort the electromagnetic fields generated by the transmitter. For example, a nearby metal instrument may create distortions in the magnetic field. These distortions may lead to inaccuracies in tracking position and orientation.

As an additional consideration, electromagnetic tracking systems may be limited by the number of degrees of freedom they are able to track. In general, the number of degrees of freedom that an electromagnetic tracking system is able to track and resolve depends on the number of receiving and transmitting coils in the system. For example, a system consisting of a single transmitting coil and multiple receiver coils may be tracked in only five degrees of freedom. As will be appreciated, this is because a dipole coil is uniform about its axis and, therefore, processing cannot resolve the rotational orientation of the coil transmitter.

Accordingly, there is a desire to provide an electromagnetic field tracking system, wherein EM sensors are configured to limit the impact of magnetic field distortions. There is also a desire to provide a system configured to track in six degrees of freedom.

BRIEF DESCRIPTION

In accordance with an aspect, provided is an electromagnetic tracking system, comprising a coil arrangement comprising a first coil configured to generate a first magnetic field and a second coil configured to generate a second magnetic field and a drive unit configured to provide a first drive current to the first coil and to provide a second drive current to the second coil, wherein the first drive current and the second drive current are at about the same frequency, wherein the frequency is below 60 Hz, and wherein the first electromagnetic field and the second magnetic field are generated out of phase.

In accordance with another aspect, provided is a method for electromagnetic tracking, comprising driving a first current across a first coil to generate a first magnetic field, driving a second current across a second coil to generate a second magnetic field, wherein the first magnetic field and the second magnetic field are at about same frequency, wherein the frequency is below 60 Hz, and wherein the first magnetic field is out of phase with the second magnetic field, sensing the first magnetic field and the second magnetic field with at least one electromagnetic receiver and processing the sensed first magnetic field and the sensed second magnetic field.

In accordance with yet another aspect, provided is a method of electromagnetic tracking comprising generating a first electromagnetic field at a frequency, generating a second electromagnetic field at about the frequency, wherein the frequency is below 60 Hz and wherein the first electromagnetic field and the second magnetic field are generated out of phase, sensing the first electromagnetic field and the second electromagnetic field and processing a waveform indicative of a combination of the sensed first electromagnetic field and the sensed second electromagnetic field.

DETAILED DESCRIPTION

Referring now toFIG. 1, a tracking system10in accordance with an embodiment of the present technique is illustrated. The tracking system10may generally include multiple tracking components. As depicted, the tracking components may include a transmitter12, at least one receiver14, a drive unit15, a processor16and a user interface18.

In the tracking system10, the transmitter12may include a conductive coil that provides an electromagnetic field when a current is passed across the coil. In certain embodiments, the transmitter12may include a single dipole coil. For example, the transmitter12may include a single dipole coil that is about 8 mm long and about 1.7 mm in diameter, with 7700 turns of American Wire Gauge (AWG) wire formed around a ferromagnetic core that is about 8 mm long and about 0.5 mm in diameter. When a current is provided across a single dipole coil, a single magnetic field may be generated with a magnitude moment vector along its “axis.” Those of ordinary skill in the art will appreciate that multiple transmitting coils may be used in coordination to generate multiple magnetic fields. For example, the transmitter12may be formed from three co-located orthogonal quasi-dipole coils (i.e., a coil-trio). When a coil-trio is energized, each coil may generate a magnetic field. As a result, three magnetic fields may be generated with magnitude vectors that are co-located and orthogonal to one another.

Complementary to the transmitter12, the system10may also include at least one receiver14that is configured to “receive” (i.e., sense) the magnetic field(s) generated by the transmitter12. When a current is applied to the transmitter12, the magnetic field generated by a coil of the transmitter12may induce a voltage into a coil of each of the at least one receiver14. The induced voltage may be indicative of the mutual inductance between the two coils. Thus, the induced voltage across the coil of each of the at least one receiver14may be sensed and processed to determine the mutual inductance (Lm) between the transmitter12and each of the at least one receiver14.

Similar to the transmitter12, the at least one receiver14may employ a single dipole coil or multiple coils (e.g., a coil trio). For example, the system10may include an electromagnetic tracking system configured with industry-standard coil architecture (ISCA). ISCA type coils are defined as three approximately collocated, approximately orthogonal, and approximately dipole coils. An ISCA configuration includes a three-axis dipole coil transmitter and a three-axis dipole coil at least one receiver14. In such a configuration, the coils of the transmitter12and the coils of the at least one receiver14are configured such that the three coils exhibit the same effective area, are oriented orthogonally one another, and are centered at the same point. Using this configuration, nine parameter measurements may be obtained (i.e., a measurement between each transmitting coil and each receiving coil). From the nine parameter measurements, processing may determine position and orientation information for each coil of the transmitter12with respect to each coil of the at least one receiver14. If either of the transmitter14or receivers12is in a known position, processing may also resolve position and orientation relative to the known position.

As mentioned previously, the system10may further include a drive unit15. In accordance with certain implementations of the present technique, the drive unit15may be configured to provide a drive current via cable17to each coil of the transmitter12. By way of example, a drive current may be supplied by the drive unit15to energize a coil of a transmitter12and, thereby, generate a magnetic field that is sensed by the at least one receiver14. The drive current may include a periodic waveform with a given frequency (e.g., a sine wave). In turn, the current across the coil will generate a magnetic field at the same frequency as the drive current. For example, electromagnetic tracking systems generally may be supplied with sine wave current waveforms with frequencies between 8 kHz and 40 kHz and, thus, generate magnetic fields with frequencies between 8 kHz and 40 kHz.

The system10further may include a processor16. In the illustrated embodiment, the magnetic fields sensed by the at least one receiver14may be output via cable19to the processor16for processing. The processor16may include, for example, a digital signal processor, a CPU, or the like. The processor may process received signals to track the orientation and position of a device. For example, the at least one receivers14will produce output signals that are to the mutual inductance between a transmitter12and the at least one receiver14. The processor16may use use ratios of the mutual inductance measurements to triangulate the position of an transmitter12relative to the at least one receiver14. When the fields generated include multiple frequencies, processing may be able to determine the magnetic field frequency from the signal sensed by the at least one receiver14. Thus, the frequency of a magnetic field may be useful to distinguish magnetic fields when multiple magnetic fields are sensed by a single receiving coil. For example, when driving a transmitter (such as transmitter12) having a single dipole coil, a single drive current of a given frequency may be sufficient to identify the magnetic field. This is true because only a single transmitting coil is generating a magnetic field. However, when a transmitter (such as transmitter12) includes multiple coils (e.g., a coil trio), each of the at least one receiver14may sense multiple magnetic fields simultaneously. The result may be a single signal from each of the at least one receiver14that is transmitted to the processor16. So that the subsequent processing can more easily identify each of the magnetic fields, the frequency of each of the generated magnetic fields may be varied. By identifying each magnetic field, processing may be able to isolate the signal between each respective transmitting and receiving coil and, thereby, determine the relative position and/or orientation of each of the coils. For example, if each coil of the transmitter12is provided a current waveform of a different frequency, processing may identify each magnetic field. Thus, the processor16may implement any suitable algorithm(s) to establish the position and orientation of the transmitter12relative to the at least one receiver14. For example, the processor16may use the ratios of mutual inductance between each coil of the at least one receiver14and each coil of the transmitter12to triangulate the position of the coils. The processor16may use these relative positions to resolve a position and orientation of the transmitter12.

As illustrated, system10may also include a user interface18. For example, the system10may include a monitor to display the determined position and orientation of a tracked object. As will be appreciated, the user interface18may include additional devices to facilitate the exchange of data between the system10and the user. For example, the user interface18may include a keyboard, mouse, printers or other peripherals. While the processor16and the user interface18may be separate devices, in certain embodiments, the processor16and the user interface18may be provided as a single unit.

Although electromagnetic tracking may be employed as described above, other concerns may exist. For example, electrically conductive materials in the vicinity of the transmitter12and the at least one receiver14may distort the magnetic field. This is because electromagnetic fields may induce eddy currents into conductors, resulting in distortions of the electromagnetic fields. Therefore, the presence of conductive objects may lead to inaccurate magnetic field measurements (e.g., mutual inductance measurements) and, thus, inaccurate tracking. Although some mapping techniques are known to compensate for these distortions, they may not be sufficient or practical in all instances. Therefore, it is desirable to understand the source of these distortions and provide techniques to reduce their effects.

Distortions from conductive objects may be present because eddy currents created in a conductive object prevents a magnetic field from penetrating through the “skin” of the electrically conductive object. For example, the electrically conductive material may be characterized by the material parameter “skin depth”. The “skin depth” represents the penetration of the magnetic field into the conductive object. “Skin depth” may be defined as:

skindepth=2ω*μ*ρ
where:ω=angular frequency=2π*FF=Frequencyμ=magnetic permeability of the materialρ=electrical resistivity of the material
Thus:

skindepth=1F⁢1π*μ*ρ
Accordingly, the skin depth is inversely proportional to the square root of the frequency of the magnetic field. As will be appreciated, as the skin depth increases, distortions to the magnetic field are reduced. Thus, at a lower frequency, the magnetic field will penetrate more of the conductive object, leading to less distortion of the magnetic field.

In light of this phenomenon, the magnetic field frequency may be reduced to increase the skin depth and, thereby, decrease the distortions caused by conductive objects that are near the transmitter12and/or the at least one receiver14. For example, pulsed-DC (called “direct-current”) systems may include lower frequency (e.g., 400 Hz) magnetic fields to reduce distortions. However, for highly electrically conductive materials such as copper and aluminum, these frequencies may not be low enough to make the skin depth large compared to the object and, thus, significant distortions remain. Therefore, it may be desirable to generate magnetic fields at even lower frequencies. However, lowering the frequency results in additional concerns. For instance, at frequencies near the power line frequency (50 or 60 Hz) or its harmonics, there may be interference with the magnetic fields generated at low frequencies. For example, the power line may generate a magnetic field at 50 or 60 Hz that induces additional eddy currents into conductive objects. Further, the power line magnetic field may be inadvertently sensed by the at least one receiver14. Thus, two concerns remain prevalent: distortions due to electrically conductive objects and distortions due to the electromagnetic fields of power lines.

One solution may include generating magnetic fields at frequencies below the power line frequency to increase skin depth and to reduce distortions from the electromagnetic fields of power lines. For example, a magnetic field may be generated at approximately half the utility-power frequency. This permits centering a selective filter at a passband between 0 Hz (direct current D.C.) and the power frequency of 60 Hz. Thus, the interference and distortions caused by the power line may be reduced.

Although lower frequencies provide advantages in reducing distortions, other issues may arise due to the low frequency. For example, one concern includes an increase in the amount of time required to detect and measure the magnetic field. As will be appreciated, when sampling a waveform (e.g., sine wave), samples may be taken over several periods to provide for an accurate representation of the waveform. As the frequency of a waveform is reduced, the period increases and, therefore, the time required to accurately sample the waveform increases. This is also true in sampling the waveform that is sensed by a receiving coil. Therefore, as the frequency of the magnetic field is lowered to resist distortions, the sample time may increase. For example, the transmitter12may generate a magnetic field at 25.44 Hz, and the corresponding signal induced across the at least one receiver14being measured at a period of 118 ms. Although this may be a suitable rate for some applications, it may still result in slower processing and, thus, slower tracking.

The concern of increased sampling time may be more prevalent as the number of transmitters12is increased. This is true because an increased number of samples must be taken at the slower sample rate. Thus, as the number of transmitting coils is increased to generate multiple magnetic fields, the sample time may increase. As will be appreciated (and discussed above), the number of coils, and, therefore, the sample time, may be dependent on the number of degrees of freedom to be tracked (e.g., more coils may allow resolution of more degrees of freedom). For example, if a transmitter (such as transmitter12) having a single coil is used, it may be small enough to be approximated as a dipole coil and, thus, generate a magnetic field that is substantially symmetrical about the axis of the coil. Being symmetrical about an axis may prevent processing from distinguishing the roll orientation about the axis because the magnetic field does not change as the coil rotates. Thus, tracking a single dipole coil does not allow for resolution of all six degrees of freedom. If only five degrees of freedom are needed, the single coil and the corresponding sample rate of the single waveform may be used. However, if six degrees of freedom are desired, the transmitter12may include a second coil with an orientation that is different from the first transmitter coil. In such a configuration, the “roll” of the transmitter12may be tracked. As discussed above, this may be accomplished by driving each coil with current waveforms of differing frequencies. When a second coil is added to the transmitter12, the measurement time increases significantly, as a second frequency must also be sensed and processed. Thus, tracking multiple coils of a transmitter12that is being driven at a low frequency may reduce electromagnetic distortions from conductive objects, but lead to unacceptably long measurement times.

In light of the above considerations and concerns, a system is needed that reduces the effects of distortions, can provide tracking in all six degrees of freedom, and has reduced measurement times. Provided is a system that includes a two-coil transmitter in an arrangement that allows that allows tracking in all six degrees of freedom. Further provided is a system in which the two coils operate at the same low frequency to reduce sampling rates. Such a system provides for tracking that is resistant to distortions, can be tracked in all six degrees of freedom, and has reduced measurement times.

To reduce the effects of magnetic field distorting objects, an embodiment may include the transmitter14generating magnetic fields that are at about the same low frequency. In addition, the system10may generate the magnetic fields below 60 Hz to further reduce distortions cause by the power line. The issues mentioned above, regarding reduced sample rates and tracking in six degrees of freedom may be addressed in the following discussion of the transmitter14and the method for tracking the transmitter. For example, an embodiment may include operating two coils of a transmitter14at the same frequency while shifting the phase and gain of each field to identify them. Further, as will be explained, an embodiment may include an arrangement of the coils of the transmitter14that are resistant to distortions.

To allow for tracking in six degrees of freedom (including “roll”), an embodiment may include a transmitter14that includes two coils. However, when implementing a two coil transmitter12, the mutual inductance cross coupling between the two coils of the transmitter12permits the current in the first coil of the transmitter12to induce voltage in the second coil of the transmitter12(i.e., similar to induced current into a receiver coil). The result is a current flow in the second coil that is the same frequency as the current driven across the first coil. This unwanted current makes distinguishing two transmitter coils difficult, as the induced current in the second coil to the transmitter12may result in a magnetic field being produced from both coils with the same frequency and phase. To minimize the mutual inductance between the two coils of the transmitter12a technique of tilting the coils may be employed.

Turning now toFIG. 2, depicted is a transmitter12including a first coil20and a second coil22that are tilted, for example, to minimize the mutual inductance between the two coils. In one embodiment, the center of the first coil20and the center of the second coil22may be separated by a separation distance24. For example, the separation distance may be approximately 4 cm. Further, in one embodiment, the arrangement may include the first coil20and second coil22tilted at the same orientation relative to the separation vector28running from the center of the first coil20to the center of the second coil22. For example, as depicted inFIGS. 2 and 3, the first coil20may be titled at a tilt angle26from the separation vector28. As illustrated, the separation vector28may run along the axis of an untilted first coil30and to the axis of an untilted second coil32if the axis of the two coils were aligned. In the illustrated embodiment, the first coil20and the second coil22may have a first magnitude vector40and a second magnitude vector42, respectively, when drive currents are supplied to the coils.

In an exemplary embodiment, the tilt angle26may be set to provide for reduced cross coupling as described above. For example, the tilt angle26may be approximately 54.7 degrees. In this embodiment, the mutual inductance cross coupling between the two coils is minimized and, thus, the interference due to each of the coils may be reduced. As will be appreciated by those of ordinary skill, the tilt angle26may be varied to accommodate numerous applications. For example, where the mutual inductance cross coupling is not a concern, the tilt angle26may range from 0 to 90 degrees to allow for the resolution of a roll orientation parameter. Or in other embodiments, a tilt angle26may be employed to minimize distortions of a specific system.

To arrange the first coil20and the second coil22at the tilt angle26, the transmitter12having two coils may be rigidly supported. For example, the transmitter12may be enclosed in a housing that provides for mounting of the first coil20and the second coil22.

Turning now toFIG. 4, an illustration of the transmitter12ofFIGS. 2 and 3mounted in an instrument is provided, in accordance with aspects of the present technique. In the illustrated embodiment, the transmitter12includes the first coil20and the second coil22and is enclosed in a housing34. As illustrated, the housing34may take the form of an enclosure coupled to the body36of the instrument38. For example, as depicted, the transmitter12may be mounted in the operative end of the instrument38. As will be appreciated by a person of ordinary skill in the art, the present technique may include coupling the transmitter12to various instruments38tracked during medical procedures. For example, the instrument38may include a catheter, a drill, a guide wire, an endoscope, a laparoscope, a biopsy needle, an ablation device or other similar devices.

As discussed previously, in a multi-coil transmitter (such as transmitter12having first coil20and second coil22) processing may be employed to track each coil. To accomplish this, processing may need to distinguish each of the magnetic fields sensed by the at least one receiver14. Thus, an embodiment may include drive currents supplied to each of the first coil20and the second coil22. For example, each drive current may include an identifying characteristic to allow processing to distinguish which coil of the transmitter12is generating each of the sensed magnetic fields. In one embodiment, providing a current to induce a magnetic field may include driving both the first coil20and the second coil22at the same frequency, but out of phase. For example, the first coil20may be driven by a sine waveform current and the second coil22may be driven by a cosine waveform current. In this embodiment, the two current waveforms may have the same frequency with a phase offset of approximately ninety degrees. As will be appreciated by those skilled in the art, the waveforms driving the first coil20and the second coil22may include a phase offset that is not ninety degrees, but is suitable to allow processing to differentiate between the generated waveforms.

Although offsetting the phases of the waveforms provided to each coil of the transmitter12may provide for distinguishing the first coil20and the second coil22, to aid in processing (as discussed in further detail below) it may be necessary to provide an additional distinguishing characteristic to each of the respective waveforms. This may be accomplished by increasing or decreasing the strength of the magnetic fields relative to one another. The strength of the magnetic field may be characterized by the magnitude of the magnetic field moment vector. The magnitude of the magnetic field moment vector may be increased or decreased by varying the amplitude of the drive current waveform. For example, the first coil20may be driven by a current waveform with a first amplitude and the second coil22may be driven by a current waveform of a second amplitude. In one embodiment, a modest ratio (e.g., 2:1 or less) of the first magnitude vector40to the second magnitude vector42(seeFIGS. 2 and 3) could be used to distinguish the two magnetic fields and, thus, allow processing to distinguish the first coil20and the second coil22. As will be appreciated by those of ordinary skill in the art, the ratio of the magnitude vectors may be varied to accommodate specific applications. For example, a larger ratio may be desirable in a system configured to detect and process signals of significantly different magnitudes or a smaller ratio may be desired for a system configured to detect and process signals of similar magnitudes.

As will be appreciated, EM tracking may be accomplished with a variety of configurations and combinations of the transmitter12and the at least one receiver14. For example, the transmitter12may be configured to be used as a “wired” device or a “wireless” device. In an embodiment including a wired transmitter, the transmitter12may be electrically coupled to the processor20and, thus, coupled to the at least one receiver14. In a wired configuration, the measured phases of the waveforms driving the first coil20and the second coil22may be known. For example, the source of the drive current waveforms may be embedded in the processor20. Therefore, the processor20may “know” the phase that is driving the first coil20and the second coil22and, thus, may parse out each signal indicative of the given phases and frequencies from the combined signal sensed and transmitted by a receiver coil. With each of the phases identified and associated with each coil of the transmitter12, the processor may implement any suitable algorithm(s) to establish the position and orientation of the transmitter12relative to the at least one receiver14. For example, the processor may use the ratios of mutual inductance between each of the at least one receiver14and each coil of the transmitter12to triangulate the position of the first coil20and the second coil22. The processor may use these relative positions to resolve a position and orientation of the transmitter12.

Although the phase of the waveforms driving the first coil20and the second coil22may be “known” in an embodiment where the transmitter12is wired, an embodiment including a wireless transmitter12may not have a “known” phase of the waveforms. For example, in an embodiment as depicted inFIG. 5, a wireless transmitter12may be driven by an independent current source that is coupled to the transmitter12and/or the instrument38. In an embodiment, the current source may include an oscillator44. In a configuration, the oscillator44may generate each of the current waveforms independent from the processor20(i.e., the processor does not have feedback or control relating to the phase of the two currents). For example, the transmitter12may be a standalone device that is generating magnetic fields independent of the processor16. Thus, the processor16must incorporate additional considerations in processing to resolve the position and orientation of the transmitter12(e.g., identify the phases of the current waveforms generated across the first coil20and second coil22of the transmitter12).

Processing in a “wireless” tracking system may include initial approximations and iterations to resolve a seed guess of position and orientation including the roll of the transmitter12. An embodiment of processing may include: estimating a position and orientation (not including roll) from a combined signal, performing fitting algorithms to determine the two phases of the waveforms, determining two coil positions based on the waveforms at the given phases, identifying each respective coil based on the EM field magnitude, and finally resolving a position and orientation “seed guess” (including roll) based on the position of the two coils.

To determine an initial position estimate, processing may consider the combined signals sensed by the receiving coils. For example, an embodiment may include a transmitter12that includes a first coil20and second coil22with a separation distance24that is small compared to the tracking area of the at least one receiver14. In this configuration, the mutual inductance sensed across each of the at least one receiver14may include a waveform indicative of a linear combination of the magnetic field mutual inductance generated by the first coil20and the second coil22. This combined waveform may take on characteristics of a single coil generating a magnetic field from an average position with an averaged phase. Thus, processing may consider the received signal as a single waveform based on the addition of the signals generated by the first coil20and the second coil22. As will be appreciated, any suitable from electromagnetic tracking processing may be used to estimate an averaged position and orientation based on this assumption. For example, processing may include triangulating the position of the transmitter12relative to the positions of the at least one receiver14. In an embodiment where the first coil20and the second coil22have the same orientation (as discussed previously), an initial approximation of orientation (without roll) may yield an orientation (without roll) for both the first coil20and the second coil22. As will be appreciated, the lack of a “roll” degree of freedom is because the averaged signal approximates the position of a single dipole coil, and therefore the “roll” orientation may not be resolved (as discussed previously). The “roll” orientation may be resolved in subsequent processing discussed below.

Further, the “combined waveform” sensed may provide for processing to determine an averaged phase. For discussion purposes, this phase may be referred to as the “seed phase” used as a starting point for subsequent processing. Given the averaged position, orientation and seed phase determined from the combined waveform, the processor20may continue processing to reach a “final seed guess” of position and orientation.

Although the “seed phase” may be determined from the combined waveform, the actual phase of each of the two magnetic fields may remain unknown at this point. An embodiment of processing may include an iterative approach to resolve the phases of the waveforms generated by first coil20and second coil22of the transmitter12. For example, a suitable “Goodness-of-fit” calculation may be processed over a range of phases to identify the phases of the two waveforms that make up the combined waveform. The Goodness-of-fit (Gf) may include a dimensionless measure of the discrepancies between the modeled mutual inductance Lmodel(which are functions of position estimates Rmodeland orientation estimate Omodel), and the measured mutual inductance Lmeas(for one transmitter coil and two receiver coils):

Gf=∑r=12⁢(Lmodel-Lmeas)r2∑r=12⁢(Lmeas)r2
When Gfis small, the remaining errors may be small, and thus the errors in R model and Omodelare small. If Gfis high, then the approximate characteristics of the system are not correct. In light of these considerations, the iterative steps of determining the phases of the waveforms generated by the first and second coils, may include varying the phase in processing to estimate a position and orientation and using the Goodness-of-fit for refitting based in the new position and orientation at the varied phase. Initially, the combined phase may yield a poor goodness-of-fit, due to the sum of the transmitter coils not being representative of a dipole coil. The phase of the combined waveform may be varied in processing until the contribution from one coil is nulled. For example, the phase of the signal extracted in processing may be varied across a range of phases until the goodness of fit calculated indicates relatively small errors at two phases. These two “good fits” may indicate the two phases of the waveforms generated across one of the transmitter coils.

Next, the position and orientation of one coil may be determined by extracting the waveform of a first phase, and then fitting a position and orientation of one coil of the transmitter12relative to the one of the at least one receiver14using any suitable algorithm. Similarly, a waveform of the second phase may be extracted to fit the position and orientation of the other coil of the transmitter12relative to the one of the at least one receiver14using any suitable algorithm. At this point of processing, the position and orientation of the two coils may be known, although it is not known which is the position of the first coil20and which is the position of the second coil22.

Additional considerations may be needed to identify the first coil20and the second coil22to fully resolve all six degrees of freedom (including roll). In one embodiment, the magnetic moments of each of the coils may be distinguished by the relative gain of each magnetic field. For example, as discussed previously, the magnetic moment of the first coil20and the second coil22may be of differing magnitudes (e.g., a ratio of 2:1). Thus, processing may include distinguishing the waveform at the first phase from the waveform at the second phase by comparing the amplitude of the waveforms received. For example, if waveform generated by the first coil20is a 25 Hz cosine waveform with an amplitude that is twice the amplitude of a 25 Hz sine wave waveform generated by the second coil22, then processing may isolate each phase and amplitude to associate the two calculated positions to the first coil20and a calculated position of the second coil22. Once the location of each coil has been established, orientation (including roll) may be resolved by processing using any suitable algorithm. For example, processing may include triangulating the position of each coil to determine the X, Y, Z, pitch, yaw, and roll of the transmitter12relative to the at least one receiver14. Thus, tracking may be accomplished in six degrees of freedom using a low frequency drive current.