Patent Publication Number: US-6990427-B2

Title: Gain factor and position determination system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 09/892,153, filed Jun. 26, 2001 now U.S. Pat. No. 6,625,563. The content of the prior application is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This invention relates to systems that use magnetic fields to determine an object&#39;s location and orientation, and system gain factor. 
     BACKGROUND 
     As is known in the art, systems may use magnetic field measurements to indirectly determine the location and orientation of an object. These systems are useful, for example, in the medical field, because they are able to accurately locate an object in a patient&#39;s body with only minimal intrusion into the body. The intrusion involves placing a small probe near the object to be located. The three-dimensional location and orientation of the probe is then determined from the effect that the probe&#39;s location and orientation have on magnetic field measurements. 
     The probe may be either a source or a sensor of a magnetic field. If the probe is a source, sensors exterior to the body measure the field produced by the probe. If the probe is a sensor, magnetic sources exterior to the body produce the fields being measured. 
     Determining a probe&#39;s location and orientation from magnetic field measurements is not straight forward because the measured magnetic fields are nonlinear functions of the location and orientation. To determine the probe&#39;s location and orientation from the measured magnetic field values, the probe&#39;s location and orientation are first presumed or “guessed” to be at a predicted location and orientation. An iterative process is used to compare values of the magnetic field at the guessed probe location and orientation with the measured field values. If the magnetic field values at a guessed location and orientation are close to the measured values, the guessed location and orientation are presumed to accurately represent the actual location and orientation of the probe. 
     The iterative process uses a physical model for the probe&#39;s environment. The physical model specifies the location and orientation of each field source. From the specified locations and orientations, laws of electrodynamics determine the field values. 
     As the probe and its positioning system are physical systems, they are susceptible to various external influences (e.g., stray magnetic fields, field absorbing materials being positioned proximate the field generators and/or sensors, etc.) that affect the gain of the system. Additionally, these physical devices have various engineering tolerances (e.g., cable resistance, probe gain, input impedance, etc.) that also affect overall system gain. Accordingly, each time a component of the system is replaced, the system must be manually recalibrated. 
     SUMMARY 
     According to an aspect of this invention, a system for determining the position, orientation and system gain factor of a probe includes magnetic field sources and at least one magnetic field sensor, such that a combination of a magnetic field sensor and a magnetic field source generates a unique measured magnetic field value. The system also includes a probe whose position and orientation affect the unique measured magnetic field values. A processor, coupled to receive these unique measured magnetic field values, iteratively processes measured magnetic field values to determine a system gain factor indicative of the gain of the probe and location factors indicative of the position and orientation of the probe. The number of unique measured magnetic field values generated must be at least equal to the sum of the number of factors calculated. 
     One or more of the following features may also be included. The iterative process is configured to determine a function of the differences between the measured magnetic field values and a plurality of predicted magnetic field values. The processor includes a calculated location process for calculating the predicted magnetic field values, in that the calculated location process guesses an initial gain, position and orientation for the probe, and then calculates the predicted magnetic field values based on a physical model and the initial gain, position and orientation. The initial position and orientation may be a predetermined or randomly selected fixed point. 
     The processor includes an optimization function for determining an extremum indicative of the differences between the measured magnetic field values and the predicted magnetic field values. The optimization function is a least squares sum function. The processor includes a repositioning process for adjusting the initial gain, position and orientation of the probe in response to the extremum being in a predefined range of unacceptable values, which is indicative of an unacceptable level of difference between the measured magnetic field values and the plurality of predicted magnetic field values. The location factors may include spatial, spherical, and/or rotational coordinates. 
     According to a further aspect of this invention, a method for determining the position, orientation and system gain factor of a three-dimensional object includes positioning a plurality of magnetic field sources proximate the three-dimensional object and positioning at least one magnetic field sensor in a fixed spatial relationship with that three-dimensional object. A combination of a magnetic field sensor and a magnetic field source generates a unique measured magnetic field value. Further, the position and orientation of the three-dimensional object affects these unique measured magnetic field values. The method determines a system gain factor indicative of the gain of the three-dimensional object and a plurality of location factors indicative of the position and orientation of the three-dimensional object. The number of unique measured magnetic field values generated must be at least equal to the sum of the number of factors calculated. 
     One or more of the following features may also be included. The step of determining a system gain factor and a plurality of location factors includes determining a function of the differences between the measured magnetic field values and a plurality of predicted magnetic field values. The step of determining a system gain factor and a plurality of location factors includes guessing an initial gain, position and orientation for the three-dimensional object and calculating the predicted magnetic field values based on a physical model and the initial gain, position and orientation. The step of determining a system gain factor and a plurality of location factors includes determining an extremum indicative of the differences between the measured magnetic field values and the predicted magnetic field values. The step of determining a system gain factor and a plurality of location factors includes adjusting the initial gain, position, and orientation of the three-dimensional object in response to the extremum being in a predefined range of unacceptable values, which is indicative of an unacceptable level of difference between the measured magnetic field values and the plurality of predicted magnetic field values. 
     While the system and method described above includes a plurality of magnetic field sources and at least one magnetic field sensor, the system can also include a plurality of magnetic field sensors and at least one magnetic field source. Further, while the system and method described above were said to include a probe, that probe can actually be any three-dimensional object, such as a hollow tube (e.g., a biopsy needle). 
     The advantages of the above aspects of the invention are numerous. As this system automatically calculates the system gain factor for the probe or three-dimensional object being utilized, device gain calibration is automated. Therefore, the need for tedious and time-consuming manual gain recalibration is eliminated. Additionally, as this calibration process is automated, the system components (e.g., probes, sensors, leads, etc.) can be quickly and easily swapped and the system reconfigured without the need for manual gain recalibration. This, in turn, streamlines and simplifies the reconfiguration process. Additionally, as the system automatically and continuously determines the system gain factor, the system can be physically moved without fear of external influences mandating manual gain recalibration. 
     The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic representation of a system that uses magnetic measurements to find a probe&#39;s system gain factor, location, and orientation; 
         FIG. 2  is a perspective view of the system of  FIG. 1 ; 
         FIG. 3  is a side view of an alternate system that uses magnetic measurements to find a probe&#39;s gain, location, and orientation; 
         FIG. 4  is a flow chart for a process that iteratively guesses the gain, location, and orientation of a probe from measured magnetic field values; 
         FIG. 5  is a flow chart for a process that determines whether the best guess of the gain, location, and orientation of a probe is reliable; 
         FIG. 6  is a flow chart for a process that evaluates an error or optimization function at global and local extrema; 
         FIG. 7  is a flow chart for a process that determines extrema values of the error or optimization function that correspond to the presence of distortions; and 
         FIG. 8  shows a computer that finds a probe&#39;s gain, location, and orientation from measurements of magnetic fields. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     Referring to  FIGS. 1 and 2 , there is shown a schematic representation of a system  10  that uses measurements of magnetic fields to find the location, orientation and system gain factor of a moveable probe  12 . The moveable probe  12  is located inside a volume  14  (e.g., a body of a medical patient). System  10  also includes a plurality of field sources  16   1-n  (e.g., small induction coils) that are located outside of volume  14 . Field sources  16   1-n  are driven by a field-generating module  22  (e.g., an alternating or direct current source). Please note that while seven field sources are shown, this is for illustrative purposes only and is not intended to be a limitation of the invention. 
       FIG. 2  is a side view of system  10  that shows the three-dimensional orientation and location of field sources  16   1-n  and probe  12 . Each field source  16   1-n  is either: a surface-mount field source  17  located on a surface  18  of a regular tetrahedron  24 ; or an edge-mount field source  19  located on an edge  20  of a regular tetrahedron  24 . The field sources  16   1-n  are typically oriented so that their internal magnetic moments “m” are either perpendicular to the surfaces  18  of tetrahedron  24  or parallel to the edges  20  of tetrahedron  24 . Probe  12  is located outside of tetrahedron  24  and has an orientation defined by a normal direction “n” to a sensor  13  that measures local magnetic field values. Sensor  13  may include a simple coil, several coils, a Hall sensor, or a flux gate sensor and may measure a magnetic field flux or magnetic field differential. Note that while system  10  is shown to include a single tetrahedron  24  having a maximum of four surface-mount field sources  17  and six edge-mount field sources  19 , this is for illustrative purposes only and is not intended to be a limitation of the invention, as the positioning of these field sources  16   1-n  can be adjusted and reconfigured as known by those skilled in the art. For example, a pair of tetrahedrons  24  utilizing only edge-mount field sources  19  can be utilized. This configuration allows for a maximum of twelve distinct field sources. 
     Each source  16   1-n  may also include single or multiple field coils. For a source  16   1-n  with a single coil, the magnetic field in the volume  14  can be approximated by a dipole field. For a source  16   1-n  with several coils, the magnetic field in the volume  14  may be a higher multipole field. In one embodiment, each source  16   1-n  uses two identical coils whose normal vectors are anti-parallel. Such a source produces a magnetic quadrapole field in volume  14 . A quadrapole field has larger spatial variations than a dipole field and thus, may be more convenient for locating probe  12 . 
     Other embodiments may use field sources  16   1-n  that primarily generate higher magnetic multipole fields. Further, other embodiments may use a different numbers of field sources  16   1-n  or locate and orient the field sources  16   1-n  differently. 
     Referring to  FIGS. 1 and 2 , magnetic fields from sources  16   1-n  induce electromotive forces (EMF&#39;s) in internal sensor coil  13  of probe  12 . An electronics module  26  connected to probe  12  measures the EMF&#39;s. The measured EMF&#39;s represent the measured local values of magnetic fields at the probe&#39;s location and orientation in space  14 . Electronics module  26  also can identify the individual source  16   1-n  that produces each measured EMF. 
     In one embodiment, measurement timing information is used to identify the source  16   1-n  producing a measured field. In this embodiment, field-generating module  22  temporally multiplexes power to the different field sources  16   1-n  and relays timing information to the electronics module  26 . 
     In another embodiment, the field generating module  22  drives each field source  16   1-n  at a different frequency. To identify the particular source  16   1-n  of a measured field, electronics module  26  or computer  28  decomposes measured EMF&#39;s from the probe&#39;s coil  13  into frequency components. These frequency components of the measured fields are then matched to individual field sources  16   1-n . 
     In either embodiment, electronics module  26  outputs several measured magnetic fields B 1-n   measured  corresponding to the individual field measurements performed. It is important to note that there are several hardware configurations that can generate these field measurements. For example, if eight distinct field measurements are desired, system  10  can be configured so that eight field sources  16   1-n  are utilized in conjunction with a probe  12  incorporating one sensor coil  13 . In this configuration sensor coil  13  would measure the field generated by each of the eight field sources  16   1-n , resulting in eight distinct field measurements. 
     Alternatively, a probe  12  could be constructed that incorporates multiple sensor coils  13 . For example, if a probe  12  was constructed that includes two sensor coils  13  (configuration not shown), this configuration would double the number of individual field measurements achievable by that probe (using the equivalent number of field sources  16   1-n ). Specifically, if probe  12  includes two sensor coils  13 , each coil could independently measure the strength of the magnetic field generated by a single field source. Therefore, if (as stated above) eight distinct field measurements are desired and a probe  12  is utilized that includes two sensor coils  13 , only four field sources  16   1-n  would be required, as each coil  13  could independently measure the field generated by each of the four field sources, thus resulting in eight distinct field measurements. 
     These measured magnetic field values B 1-n   measured  depend on the system gain factor of probe  12  and the three-dimensional location and the orientation of the probe&#39;s coil  13 . Please note that the lower case “n” is used to denote the number of measured magnetic fields (except where it denotes normal vectors in the various figures). 
     As stated above, the number of field sources  16   1-n  and sensor coils  13  incorporated into and utilized by system  10  varies depending on the number of factors to be determined by the system. Specifically, system  10  will determine the system gain factor of probe  12 . Additionally, system  10  will also determine the position and orientation of probe  12 . As the position and orientation of probe  12  is described by specifying up to six degrees of freedom (i.e., x-axis position, y-axis position, z-axis position, roll, pitch, and yaw) for probe  12 , the maximum number of position factors that system  10  will calculate is six. Therefore, the maximum number of factors (both positional and gain) that system  10  calculates is seven. Thus, the number of distinct field measurements required to determine these factors is one greater than the number of factors being determined. Accordingly, if system  10  is determining the system gain factor plus six positional factors (i.e., degrees of freedom), a total of seven calculated factors need to be determined. This would require eight distinct field measurements. As stated above, this can be achieved utilizing a probe  12  incorporating a single sensor coil  13  and eight field sources  16   1-n . Alternatively, this could be achieved by utilizing a probe  12  incorporating eight sensor coils  13  (if physically possible) and only one field source  16   1-n . Accordingly, the important issue is the number of distinct field measurements made and not the specific number of field source  16   1-n  or sensor coils  13  employed. 
     Similarly, if system  10  is determining the system gain factor plus five positional factors (i.e., five degrees of freedom), a total of six calculated factors need to be determined. Again, as above, this can be accomplished utilizing a variety of configurations. 
     As will be described below, the use of a number of distinct field measurements that is greater than the number of factors being calculated allows for the determination of the quality of the guesses used during an iterative process. If this quality determination is not required (or desired), the specific number of distinct field measurement required would be equal to the number of factors being calculated. 
     Further, when employing multiple field sensors, it is important to realize that there is a gain factor associated with each sensor. Accordingly, for the example stated above concerning the determination of six degrees of freedom, since at least two non-coaxial sensor coils are required to determine six degrees of freedom, there are at least two system gain factors (one for each sensor coil). Therefore, when calculating the six degrees of freedom and system gain factor of a probe utilizing two non-coaxial sensor coils, the system gain factor actually consists of two components, namely a gain factor for each sensor within the probe. Accordingly, the total number of calculated factors is eight (six positional, the gain factor for the first field sensor, and the gain factor for the second field sensor) and, therefore, the number of distinct field measurements required is nine (if the quality determination is required or desired). 
     Electronics module  26  sends the measured field values to computer  28 . Computer  28  uses the measured magnetic field values to determine the probe&#39;s system gain factor and location/orientation by comparing the measured magnetic field values to magnetic field values from a physical model, as will be described below in greater detail. 
     The physical model is a set of physical equations that determine values of magnetic fluxes measured by probe  12  as a function of several parameters. The parameters include: the position, orientation, and magnetic moments of field sources  16   1-n ; the location, orientation, and sensitivity of probe  12 ; and characteristics of electronics module  26 . A vector (x, y, z) and a pair of angles (φ, θ) specify the three-dimensional location and orientation of sensor coil  13  of probe  12 . If the probe  12  has multiple non-colinear coils, the parameters may include an additional angular parameter (ψ) that defines a rotational aspect of the probe  12 . Note that this factor (i.e., the sixth degree of freedom) can only be calculated by utilizing a probe having a second coil on a different axis (non-coaxial), as multiple coils about the same axis would not allow system  10  to sense probe rotation about that axis. 
     As is known by those skilled in the art, the physical model may describe each source as a magnetic multipole so that the fields measured by sensor coil  13  are the associated multipole fields (e.g., dipole or quadrapole). The multipole field values depend on the system gain and the location, orientation, and magnetic moment “m” of each source  16   1-n . The measured values of the magnetic flux depend on the location, size, orientation and gain of sensor coil  13  with respect to field sources  16   1-n . 
     The physical model is also based on underlying assumptions about the environment near the volume  14 . For example, the model assumes preselected values for the location and orientation of each field source  16   1-n  and the absence of other sources or field distorting objects. The presence of field distorting objects  30 ,  32  (e.g., conductors or new field sources) may invalidate the model&#39;s predictions for field values. However, the negative effects of constant background fields are eliminated, as sensing coil  13  only measures time varying magnetic fields. Alternatively, if static field measurements are desired, a flux gate sensor or hall effect sensor (as is known in the art) can be utilized, as they allow for measurement of static (or constant) magnetic fields. 
       FIG. 3  shows another system  40  that uses magnetic measurements to find the system gain factor and location/orientation of a moveable probe  42 . In system  40 , the roles of the field sensors and sources are interchanged. The movable probe  42 , which is located inside an observation volume  44 , is a source of a magnetic field and external field sensors  46   1-n  measure the magnetic field produced by probe  42 . Probe  42  connects to a field-generating module  51  (e.g., a voltage source). As above, these field sensors  16   1-n , which are located on either the edges or surfaces of a tetrahedron  41 , measure either magnetic fields or magnetic field gradients through induced EMF&#39;s. Each sensor  46   1-n  may have one or more magnetic field sensors oriented to measure fields in various directions. Each sensor  46   1-n  has an orientation “p” fixed by the orientation of its one or more internal magnetic field sensors. 
     Please note that, as stated above, the location and orientation of each sensor, as well as the number of sensors  46   1-n  utilized, may vary depending on the specific application and the number of factors (i.e., position/orientation and system gain) being determined. 
     An electronics module  52  monitors EMF&#39;s from the various field sensors  46   1-n  to determine the individual magnetic field values. These measured magnetic field values are then sent to a computer  54 , which calculates the system gain factor and location/orientation of the probe  42  from these measured magnetic field values. 
     Referring to  FIGS. 1–3 , both systems  10 ,  40  measure a set of magnetic fluxes to obtain a set of measured magnetic field values B 1-n   measured , such that “n” is greater than the number of factors (i.e., position and system gain) being calculated. 
     This set of measured field values B 1-n   measured , which are obtained from measured magnetic fluxes, also has a non-linear dependence on the three-dimensional location/orientation of the probe and a linear dependence on the system gain factor. As stated above, the probe&#39;s location and orientation are defined by a vector (x, y, z) and at least a pair of azimuthal and polar angles (φ, θ), respectively. Further, the system gain factor of probe  12  is defined by a gain coefficient (g). By using a physical model for the “measured” field dependencies, the systems  10 ,  40  can iteratively determine the probe&#39;s gain factor, location, and orientation from the associated set of measured field values B 1-n   measured . 
     The physical model describes a preselected magnetic environment in the region of the field sensor[s] (i.e., the volumes  14  and  44  shown in  FIGS. 1 and 3  respectively). The preselected magnetic environment may or may not include contributions from nearby conducting objects (i.e., objects  30  and  32 ). If the preselected environment is different from the actual environment, the model may predict incorrect magnetic field values; otherwise the predictions are correct. The actual environment may be different due to the presence of field distorting objects  30 ,  32 . Field distorting objects  30 ,  32  include conducting objects that support eddy currents (e.g., a pair of surgical scissors, ferromagnetic materials, and active sources of magnetic fields). The presence of such objects can invalidate magnetic determinations of the probe&#39;s gain, location, and orientation. 
     The iterative process may also yield incorrect probe gain, location, and orientation because of hardware or software failures in modules  22 ,  26 ,  51 ,  52  or computers  28 ,  54 . 
     The presence of distorting conditions may not be evident to users of systems  10 ,  40 . The users may be unskilled with respect to physical basis for the magnetic location systems (e.g., the users may be medical doctors). To avoid errors by unskilled users, each system  10 ,  40  detects and warns users about the presence of potentially measurement distorting conditions (e.g., by flashing messages on a video monitor or through audio alert signals). 
     Please note that while probe  12 ,  42  is stated as being a probe, this is only intended to ease in the explanation of the subject invention and is for illustrative purposes only. Probe  12  can be various other devices known in the art (e.g., a catheter, an endoscope, biopsy needles, body-mounted position sensors, etc.). 
       FIG. 4  shows a flow chart for an iterative process  60  that uses the measured magnetic field values B 16   1-n   measured  to determine the gain, location, and orientation of either probe  12  of  FIGS. 1–2  or probe  42  of  FIG. 3 . 
     Process  60  receives  62  an initial guess for the probe&#39;s system gain factor, location and orientation. This initial guess can be predefined in the process, user definable, or randomly selected. The initial guess is a preselected point of the (x, y, z, φ, θ) parameter space that defines the location and orientation of the probe and a preselected system gain factor (g). The initial guess is the first accepted guess for the probe&#39;s gain, location, and orientation. From the last accepted guess, the process makes a new guess  64  for the probe&#39;s location, orientation, and gain. Naturally, while the initial preselected point (x, y, z, φ, θ) is shown to include five degrees of freedom, this is for illustrative purposes only and is not intended to be a limitation of the invention. Specifically, if greater or fewer degrees of freedom are desired, the preselected point (x, y, z, φ, θ) will have greater or fewer variables respectively. 
     Each new guess of the probe&#39;s gain, location, and orientation is found from the last accepted guess by any of a variety of procedures including the Levenberg-Marquardt process, a log-likelihood function, a neural network, simulated annealing, a genetic algorithm, a simplex process, or other processes known to those skilled in the art 
     The Levenberg-Marquardt process is an iterative process used to find a best match between a set of measurements and a set of values obtained from preselected nonlinear model equations. The Levenberg-Marquardt process is described in:  Numerical Recipes in C: the Art of Scientific Computing , by W.H. Press et al., Cambridge University Press 1992 and is incorporated herein by reference. 
     In Levenberg-Marquardt process, the model equations are the set of physical equations B 1-n   predicted  (x, y, φ, θ, g), which define the magnetic field values B 1-n   predicted  in terms of the probe&#39;s location, orientation, and gain (x, y, z, φ, θ, g). The model equations come from the physical laws of electrodynamics. In one embodiment, the model equations may describe the magnetic field of each field source as a magnetic dipole or as a magnetic quadrupole. 
     The Levenberg-Marquardt procedure iteratively tries to find a best match between the measured magnetic field values B 1-n   measured  and the magnetic field values B 1-n   predicted  predicted from the physical model equations. The Nth accepted guess for a match is associated with the probe gain, location, and orientation coordinates (x N , y N , z N , φ N , θ N , g N ). From these coordinates and the physical model equations, the Levenberg-Marquardt process generates an (N+1) th  guess that specifies the associated gain, location, and orientation coordinates (x N+ , y N+1 , z N+1 ; φ N+1 , θ N+1 , g N+1 ) of the probe. The Levenberg-Marquardt equation for the (N+1) th  guess utilizes the values of the fields B 1-n   predicted  and derivatives of the fields B 1-n   predicted  evaluated at the value of the N th  accepted guess for a match. The Levenberg-Marquardt process provides new guesses that rapidly produce the best match between measured field values B 1-n   measured  and predicted field values B 1-n   predicted  which are obtained from the non-linear model equations. Please note that the lower case “n” is used to denote the number of measured magnetic fields (e.g., B 1-n   measured ) and the upper case “N” is used to denote the specific guess processed by the Levenberg-Marquardt procedure (e.g., (N+1 th )). 
     The process  60  evaluates the quality of each new guess for the probe&#39;s gain, location, and orientation. To determine the quality of this guess, process  60  calculates  66  new magnetic field values which correspond to the new guess for the probe gain, location and orientation (i.e., B 1-n   predicted (new) =B 1-n   predicted (x N+1 , y N+1 , z N+1 ; φ N+1 , θ N+1 , g N+1 ) for the (N+1) th  guess. Using both the calculated (i.e., B 1-n   predicted ) and the measured (i.e., B 1-n   measured ) magnetic field values, process  60  evaluates  68  an optimization function. The optimization function is also referred to as an error function, because the optimization function is sensitive to differences between measured (i.e., B 1-n   measured ) and calculated (i.e., B 1-n   predicted ) field values. A global extremum of the optimization function defines the “best” guess for the location and orientation of the probe. 
     One embodiment uses a least-squares sum (i.e., χ 2 ) as the optimization function. In general, these functions have both minima and maxima extrema. However, the extrema of the least-squares sum that we are interested in are the minima. The value of the least-squares sum χ 2 (N) for the magnetic field associated with the N th  guess has the form:
 
χ 2 ( N )=Σ 1-n   [B   1-n   measured   −B   1-n   predicted ) x   N   , y   N , φ N , θ N , g N )] 2 /σ 1-n   2 .
 
     The sum goes over the “1-n” members in the set of measured field values (i.e., B 1-n   measured ) that are obtained for a single probe location and orientation. The term σ 1-n  represents uncertainties associated with the measurement of B 1-n   measured . 
     Process  60  determines  70  whether the value of the optimization function for the new guess is closer to a value at an extremum than the value for the last accepted guess. For the least-squares sum, since the extrema are minima, the new value is closer to a minimum if χ 2 (N+1)&lt;χ 2 (N). If the value of the optimization function for the new guess is closer to an extremum, process  60  accepts  72  the new guess for the gain, location, and orientation of the probe. If the value of the optimization function for the new guess is farther from an extremum (e.g., χ 2 (N+1)&gt;χ 2 (N)), process  60  rejects  74  the new guess. After accepting  72  the new guess, process  60  determines  75  if the difference between the optimization function for the old and new guesses is less than an acceptable threshold (e.g., 0.01). If it is less than this threshold, the probe&#39;s gain, location, and orientation are reported  77 . If the new guess is rejected  74  or if the difference between the optimization function for the old and new guesses is not less than an acceptable threshold, process  60  increments  76  a counter for the number of iterations performed. Process  60  then checks  79  to see if the incrementation counter is greater than the maximum number of iterations specified. If it is, process  60  then reports  77  the probe&#39;s gain, location, and orientation. If the number of iterations performed is not greater than the maximum number of iterations specified, process  60  loops back  78  to find a new and better guess of the probe&#39;s gain, location, and orientation. 
     Process  60  outputs the last accepted guess for the probe&#39;s gain, location, and orientation and a count specifying the number of iterations performed. In some embodiments, process  60  performs a preselected number of iterative loops  78  to find a better guess before reporting the accepted guess for the probe&#39;s gain, location, and orientation. This produces reported guesses that are closer to values associated with extremum of the optimization function. 
       FIG. 5  is a flow chart for a process  80  that uses magnetic field measurements to determine a probe&#39;s gain, location, and orientation. Process  80  provides an initial guess  82  for the probe&#39;s gain, location, and orientation. The initial guess of the probe&#39;s gain, location, and orientation (x, y, z, φ, θ, g) may include either a preselected fixed point or a randomly selected point in the (x, y, z, φ, θ) space. For the selected initial guess, process  80  performs  84  iterative process  60  (of  FIG. 4 ) to obtain a better guess for the probe&#39;s gain, location, and orientation. The better guess is based on the selected initial guess and the measured magnetic field values. Process  80  may perform several iterative loops of process  60  to obtain a better guess, which is closer to an extremum of the optimization function used in process  60 . The optimization process  60  provides a value for the optimization function (e.g., the χ 2  function) and the loop count (which indicates the number of iterations performed to obtain the better guess). 
     The value of the optimization function provides data indicative of the reliability of the better guess of the probe&#39;s gain, location, and orientation. Random measurement errors cause the value of the optimization function to fall on a probabilistic distribution function whose form is independent of the physical model for the magnetic field measurements. For the least-squares sum, the probabilistic distribution function is known as the χ 2 -distribution. Systematic measurement errors also affect the value of the optimization function. 
     The extrema of the optimization function can be maxima or minima and can fall into several classes. An extremum may be local or global extremum. Local and global extrema are distinguished by the associated values of the optimization function. For the least-squares sum, the value of the optimization function at a global minimum is smaller than the value of the function at a local minimum. Thus, global and local minima are associated with respective low and high values of the least-squares sum. 
     An extremum may also correspond to a situation in which measurements of magnetic fields are either distorted or undistorted. For the least squares sum, values of the optimization function at global minima for undistorted measurements are smaller than values of the optimization function at global minima for distorted measurements. Also, values of the optimization function at global minima for distorted measurements are smaller than values of the optimization function at local minima. 
     Thus, values of the optimization function at extrema carry information about the quality of the estimates of a probe&#39;s gain, location, and orientation obtained through process  60 . The information enables determining whether random or systematic errors are present. Values of the least-squares sum at extrema are typically ordered. The lowest values correspond to global minima in the absence of distortions to field measurements. Intermediate values correspond to global minima in the presence of distortions to field measurements. The highest values correspond to false or local minima for which estimates of the probe&#39;s gain, location, and position are not reliable. 
     Distortions may occur during generation of magnetic fields, measurement of magnetic fields, acquisition of field measurements, or processing of field measurements. The distortions to the generation of magnetic fields may occur due to a failure of a field source  16   1-n , probe  42 , or field-generating module  22  or  51 . The distortion of magnetic field measurements may result from the presence of conductors or ferromagnetic materials in the monitored space, which distort the time-varying magnetic fields. Distortion during the acquisition or processing of magnetic field measurements may result from hardware or software failures (e.g., in electronics modules  26 ,  52  or computers  28 ,  54 ). 
     Prior to performing process  80 , a calibration is performed to classify extrema of the optimization function. The calibration classifies extrema of the optimization function into three or more sets (S i ). One set (S G-ND ) corresponds to real global extrema of the optimization function for which field measurements and field measurement processing is not distorted. Another set (S L ) corresponds to false or local extrema of the optimization function. A third set (S G-D ) corresponds to real global extrema of the optimization function for which either field measurements or field measurement processing is distorted. 
     New sets may be formed from the sets (S G-ND , S L , and S G-D ) by set intersection and union operations. One set (S ND ) includes values of the optimization function that are only associated with extrema of the function for which field measurements and measurement processing are not distorted. This set (S ND ) is defined as S G-ND −(S L ∪S G-D ). Another set (S D ) includes values of the optimization function that are only associated with global extrema of the function for which field measurements or field measurement processing is distorted. This set (S D ) is defined as S G-D -(S L ∪S G-ND ). Another set (S L0 ) includes values of the optimization function that are only associated with false or local extrema of the function. This set (S L0 ) is defined as S L -(S G-ND ∪S G-D ). Finally, a set (S ND-D ) includes values of the optimization function that are only associated with global extrema of the function. For values in S ND-D , the field measurements and field measurement processing may or may not be distorted. S ND-D  is defined as S G-ND ∪S G-D . In various embodiments, some of the above-described sets (S i ) may be empty. 
     Referring again to  FIG. 5 , process  80  uses the calibrated classification of values of the optimization function to classify extrema found with iterative process  60 . Process  80  determines  86  whether the value of the optimization function at each extremum corresponds only to a global minimum without distortion (i.e., whether the value belongs to S G-ND ). If the value belongs to set S G-ND , process  80  registers  88  the associated “better” guess for the probe&#39;s gain, location, and orientation as the probe&#39;s gain, location, and orientation. For example, the “better” guess for the location/orientation coordinates and the gain (x, y, z, φ, θ, g) may be displayed on a computer screen for a user to view as the final estimate of the gain, location, and orientation of the probe. Further, process  80  determines  87  if the system gain factor is within an acceptable range. If so, process  80  stops. If not, process  80  provides  93  a warning to the user that the system gain factor is out of range and, therefore, the probe&#39;s operating environment has changed. 
     Additionally, process  80  determines  90  whether the value of the optimization function for the “better” guess corresponds to a global extremum in the presence of a distortion (i.e., whether the value belongs to S G-D ). If the value belongs to set S G-D , process  80  provides  92  a warning to the user and also registers  88  the new guess for the probe&#39;s gain, location, and orientation for the viewer to see. For example, the warning may be an audio signal or a flashing signal on a computer display for a user to hear or view. 
     Further, process  80  also determines  94  whether the value of the optimization function corresponds to a local extremum (i.e., whether the value belongs to S L ). If the value belongs to S L , process  80  determines  96  whether the loop count (LC) is greater than a preselected timeout value (LC max ). If LC&gt;LC max , process  80  generates 98 a timeout warning. If LC≦LC max , process  80  loops back  99  to generate a better new guess for the probe&#39;s gain, location, and orientation (i.e., process  80  ignores the current new guess). In the loop back  99 , process  80  selects a new initial guess for the probe&#39;s gain, location, and orientation (e.g., by randomly selecting a new gain (g) and a new point (x, y, z, φ, θ) in the probe&#39;s coordinate space). Other processes for selecting the new initial guess so that the process  60  subsequently produces a better guess for a “global” extremum are known to persons of skill in the art. 
     In some embodiments, process  80  tries to obtain a better guess for the gain, location, and position of the probe after producing a warning that a distortion is present. For example, if the number of field measurements is greater than the number of parameters plus one, process  80  may produce a better guess by discarding one of the measured field values B 1-n   measured  and repeating process  80 . If the distortion affects only the discarded field value, discarding the distorted value will produce a better estimate of the probe&#39;s gain, location, and orientation. One field measurement may be distorted because of the presence of a conductor near one field sensor or because of a hardware failure in one sensor. 
     Some embodiments of process  80  handle overlapping extrema values, which belong to more than one of the sets of S L , S G-ND , and S G-D , differently. For extrema values in both S L  and S G-D , process  80  may provide  92  a warning, indicate  88  the guessed probe location and orientation, and try to find a non-overlapping extrema value by repeating steps  82  and  84  for a new initial guess of the probe&#39;s gain, location, and orientation. For extrema values belonging to the set S L –S L0 , the process may generate a warning that identifies the extrema value as overlapping and then reselect an initial guess for the probe&#39;s gain, location, and orientation and re-execute process  60  to try to find a value not belonging to S L –S L0 . Of course, overlapping subsets such as S L –S L0  may also be empty. 
     It is important to note that the system gain factor can also be used as a means for detecting measurement distortion. The basis for this is the assumption that the system gain factor should remain essentially constant and stay within a defined range (which is typically determined during system calibration). Deviations from this range are indicative of a change in the probe&#39;s environment or in the system itself. This system gain factor range (SGFR) has to be chosen so that it can accommodate normal system gain factor variations for different probe positions and orientations throughout the operating volume. This range may also take into account gain variations caused by manufacturing tolerances and environmental factors (e.g., temperature variations, the presence of conductive objects, etc.). 
     If uniform damping of the magnetic field(s) (as sensed by the magnetic field sensors) occurs due to the presence of conductive objects within the operating volume, this uniform damping is automatically compensated for when the system gain factor is determined. Further, this compensation occurs without any loss in the positional and/or orientation accuracy of the system. 
     Accordingly, this automated uniform damping compensation allows for the determination of the probe&#39;s position/orientation within metallic tubes (e.g., a biopsy needle with a field sensor in its stylet). This allows for the tracking of the tip of a biopsy needle as it travels through the human body. This is an important advantage, as biopsy needles tend to bend and/or flex when passing through the body and, accordingly, the tip&#39;s position cannot be accurately interpolated. These advantages extend to other metallic tube objects, such as endoscopes, brachytherapy applicators etc. 
     The system can determine whether the probe is inside of a metallic tube by defining the SGFR such that system gain factor values for sensors within metallic tubes are not included in this range.  FIG. 6  is a flow chart for a calibration process  100  that finds values of the optimization function at extrema to define the membership of sets S G-ND  and S L . If iterative process  60  (of  FIG. 4 ) generates a real global extremum, the probe&#39;s gain, location, and orientation found by process  60  correlate closely to the actual gain, location, and orientation of the probe. If iterative process  60  generates a false or local extremum of the optimization function, the probe&#39;s gain, location, and orientation found by process  60  do not correlate closely to the actual gain, location, and orientation of the probe. 
     To perform this calibration, process  100  positions  102  the probe at a selected location and orientation. Further, an initial gain is selected for the probe. The initial gain is based on an accepted range of gain values for a properly functioning probe. During calibration, the probe mounts on a mechanical positioning frame (not shown) that positions the probe at the selected location and orientation. The mechanical positioning frame is made of materials that do not distort magnetic fields and provides a separate measurement of the selected actual location and orientation of the probe. The separate measurements may be optical measurements or mechanical measurements. Process  100  measures  104  the magnetic field values that correspond to the selected probe location and orientation. 
     Process  100  selects  106  an initial guess of the gain, location and position of the probe for optimization process  60 . From the measured field values and the initial guess, process  100  performs  108  iterative optimization procedure  60  to obtain a better-guess value of the probe&#39;s gain, location and orientation. The optimization procedure  60  also provides a value for the optimization function that corresponds to the better guess for the probe gain, location and orientation and is a value of the optimization function at an extremum. 
     Process  100  compares  110  the better-guess and actual coordinates of the probe&#39;s gain, location and orientation to determine whether both coordinates are in close proximity to each other. The better guess (x N , y N , z N , φ N , θ N , g) and actual values (x, y, z, φ, θ, g) of the probe coordinates are close if the values are within a preselected range of each other in a component-by-component fashion. If the better-guess and actual coordinates are close, the process  100  labels  112  the corresponding value of the optimization function as a value belonging to S G-ND . If the better-guess and actual probe coordinates are not close, process  100  labels  114  the corresponding value of the optimization function as a value belonging to S L . 
     To classify values of the optimization function at each extremum, process  100  loops back  116  and repeats steps  106 - 114  for other initial guesses of the probe&#39;s gain, location and orientation. These repetitions for different initial guesses cover the whole space (x, y, z, φ, θ, g) of possible probe coordinates representatively (e.g., by randomly selecting points in the (x, y, z, φ, θ, g) space). 
     Process  100  also repeats the classification of values of the optimization function at extrema for other selections of the actual probe gain, location and orientation. The repetitions for other actual probe gain, locations and orientations cover a representative portion of the parameter space (x, y, z, φ, θ, g) representatively (e.g., with randomly selected points). The representative portion may be a portion of the entire space (x, y, z, φ, θ, g) that is related to other portions of the space by symmetry rotations. 
     These repetitions may generate different extrema values of the optimization function that belong to S G-ND  and/or S L . For the least-squares sum, the optimization function has smaller values at global minima (i.e., in the presence or absence of measurement distortions) than at local minima. 
       FIG. 7  is a flow chart for a calibration process  120  that finds values of the optimization function belonging to S G-D . The values of S G-D  correspond to extrema of the optimization function that occur when distortions affect the iteration process  60  (of  FIG. 4 ). Process  120  may be performed separately for each type of distortion that can affect either magnetic field measurements or the processing of magnetic field measurements. The distortions may result from nearby conducting or ferrous objects, nearby field sources, sensor hardware failures, field source hardware/software failures, and/or software measurement processing failures. 
     Process  120  physically sets up  122  a selected type of distortion for the system. For example, the setting up of a distortion may include placing a pair of conducting scissors inside the monitored volume or causing a hardware failure in the electronics module. After setting up the distortion condition, process  120  positions  124  the probe with the mechanical positioning frame and receives the value of the probe&#39;s actual location and orientation. Further, an initial gain is selected for the probe. The initial gain is based on an accepted range of gain values for a properly functioning probe. The process also measures  126  the magnetic field values that depend on the probe&#39;s actual gain, location and orientation. Process  120  also selects  128  an initial guess for the gain, location and orientation of the probe. 
     From the measured field values and selected initial guess, process  120  utilizes  130  the iterative process  60  to obtain a better guess for the probe&#39;s gain, location and orientation. Iterative process  60  returns an associated extrema value of the optimization function that corresponds to each better guess. Process  120  determines  132  whether the new value is better than other extrema values of the optimization function, which were generated from different initial guesses for the probe&#39;s gain, location and position. For the least-squares sum, the best extrema value is the minimum value. 
     If the new value is better than values associated with earlier accepted guesses, the process  120  labels  134  the new value as a value of the optimization function at a global extremum (i.e., as a member of S G-D ). Values of the optimization function that belong to S G-D  indicate the presence of distortion. If the new value is not better than earlier values of the optimization function associated with accepted guesses, process  120  labels  136  the new value as a value that corresponds to a false or local extremum. After classifying the extrema value, process  120  loops back  138 ,  140  to repeat the search for values of the optimization function at other extrema by selecting a different initial guess for the probe&#39;s gain, location and orientation. The best extrema value for various initial guesses of the probe&#39;s gain, location and orientation provides a value in S G-D . 
     The process also repeats the search for values of the optimization function in S G-D  for different actual gains, locations and orientations of the probe. For each actual gain, orientation and location, an extrema value of the optimization function in S G-D  may be generated. Similarly, different positions of a distorting object (e.g., objects  30  and  32  of  FIG. 1 ) may generate different extrema values of the optimization function, which belong to S G-D . 
     In some embodiments, the extrema values of the optimization function for different types of distortion are distinguishable. Distinguishable extrema values fall in different ranges. In such embodiments, calibration process  120  is performed separately for the different types of distortion to obtain ranges of extrema values of the optimization function for each separate type of distortion. Process  80  (of  FIG. 5 ) uses the extrema values to classify the type of distortion, e.g., hardware failure, software failure, or nearby conducting object. 
       FIG. 8  shows a computer  142  that determines the gain, location, and orientation of a probe from measurements of magnetic fields and indicates the presence of distortions to the determinations. Computer  142  may be an embodiment for computer  28  of  FIG. 1  or computer  54  of  FIG. 3 . 
     Computer  142  receives data on measured magnetic field values from a line  144  that connects to an output of an electronics module  146 . The module  146  may be module  26  ( FIG. 1 ) or module  52  ( FIG. 3 ). Computer  142  processes the data according to processes  60  ( FIG. 4) and 80  ( FIG. 5 ) to determine a probe&#39;s gain, location, and orientation and the presence or absence of distortion. Computer  142  displays the results of the determinations on a screen  148 . Computer  142  has a data storage drive  154  (e.g., a hard disk or optical drive) for storing the above-described executable programs/processes and the data generated therefrom. 
     A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.