Abstract:
A system for estimating the position of an imaging capsule that examines the gastrointestinal tract of a user, including an imaging capsule for examining inside the user; and a recorder for communicating with the imaging capsule from outside the user. The imaging capsule includes a controller for controlling functionality of the imaging capsule, a transceiver for communication with the recorder and a coil for transmission of electromagnetic signals. The recorder includes a controller for controlling functionality of the recorder, a transceiver for communication with the imaging capsule and a coil for receiving electromagnetic signals from the coil of the imaging capsule. Wherein the recorder determines the location of the imaging capsule based on measurements of the amplitude of the electromagnetic signals transmitted by the coil in the imaging capsule.

Description:
RELATED APPLICATIONS 
       [0001]    The present application claims priority from U.S. Provisional application No. 61/831,163 filed on Jun. 5, 2013, 61/903,998 filed on Nov. 14, 2013 and 61/931,742 filed on Jan. 27, 2014 the disclosures of which are incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present disclosure relates generally to investigating the insides of a patient&#39;s colon using an intra-lumen capsule and more specifically to estimating the position of the capsule as it traverses the gastrointestinal tract. 
       BACKGROUND 
       [0003]    One method for examining the gastrointestinal tract for the existence of polyps and other clinically relevant features that may provide an indication regarding the potential of cancer is performed by swallowing an imaging capsule that will travel through the gastrointestinal (GI) tract and viewing the patient&#39;s situation internally. In a typical case the trip can take between 24-48 hours, after which the imaging capsule exits in the patient&#39;s feces. Typically the patient swallows a contrast agent to enhance the imaging ability of the imaging capsule. Then the patient swallows the imaging capsule to examine the gastrointestinal tract while flowing through the contrast agent. The imaging capsule typically includes a radiation source, for example including a radioisotope that emits X-rays or Gamma rays. The radiation is typically collimated to allow it to be controllably directed in a specific direction during the imaging process. In some cases the imaging capsule is designed to measure Compton back-scattering and/or X-ray florescence and wirelessly transmit the measurements (e.g. a count rate) to an external analysis device, for example a computer or other dedicated instruments. 
         [0004]    In a typical implementation a radio-opaque contrast agent is used so that a position with a polyp will have less contrast agent and will measure a larger back-scattering count to enhance accuracy of the measurements. Alternatively, other methods may be used to image the gastrointestinal tract. 
         [0005]    U.S. Pat. No. 7,787,926 to Kimchy, the disclosure of which is incorporated herein by reference, describes details related to the manufacture and use of such an imaging capsule. 
         [0006]    The use of the imaging capsule exposes the user to radiation, which is potentially harmful. Accordingly, it is of interest to limit the user&#39;s exposure to radiation when not necessary, for example by radiating only when required and blocking the release of radiation from the capsule when not required. The imaging capsule may be designed with a concealment mechanism that can be instructed to block radiation when not needed for scanning. Optionally, the concealment mechanism would normally be in the closed position, preventing radiation from exiting the capsule when it is not scanning. 
         [0007]    In a typical embodiment the imaging capsule can be instructed to selectively scan with radiation only when the capsule changes its position in the colon, since there is no need to repeatedly scan the same position. The use of selective scanning can also preserve energy, thus prolonging the life of the battery and/or enabling the use of a smaller size battery. 
         [0008]    It is thus desirable to continuously keep track of the position of the capsule so that the capsule can be instructed to radiate when the position changes or the capsule reaches specific locations of interest. Additionally, tracking the location of the capsule as it traverses through the gastrointestinal tract can help in forming an accurate three dimensional map to assist in locating and treating polyps or other obstructions that are detected. 
       SUMMARY 
       [0009]    An aspect of an embodiment of the disclosure relates to a system and method for estimating the position of an imaging capsule inside the body of a user. The system includes an imaging capsule that is swallowed by the user and a recorder that is positioned outside on the user&#39;s body, for example on the user&#39;s back or on a belt at the waist. The imaging capsule includes a controller to control functionality of the imaging capsule and a transceiver to communicate with the recorder to receive instructions or provide information. Additionally, the imaging capsule includes a coil to transmit an electromagnetic signal, for example having a low frequency. 
         [0010]    The recorder also includes a controller to control its functionality and a transceiver to communicate with the imaging capsule. Additionally, the recorder includes one or more coils to receive the electromagnetic signal transmitted by the imaging capsule. 
         [0011]    The controller of the recorder is programmed to analyze the amplitude of the received electromagnetic signal and determine the location of the imaging capsule based on the electromagnetic signal. 
         [0012]    In some embodiments of the disclosure, the coil in the imaging capsule may be a single dimension coil with windings in a single plane or it may have windings in two or three planes orthogonal to each other (2D or 3D). Likewise the coil in the recorder may have windings in a single plane or in two or three orthogonal planes. 
         [0013]    In an exemplary embodiment of the disclosure, the coil in the imaging capsule has a 3D coil and is designed to transmit simultaneously in three orthogonal directions in different frequencies. Alternatively, the coil in the imaging capsule may transmit sequentially in the three orthogonal directions. 
         [0014]    In an exemplary embodiment of the disclosure, the recorder has at least two 3D coils to receive the transmitted signals by the coil of the imaging capsule and determine the location of the imaging capsule based on the transmissions. 
         [0015]    In an exemplary embodiment of the disclosure, the imaging capsule and the recorder both include an accelerometer and a magnetometer that identify motion of the imaging capsule. Optionally, the readings of the accelerometer and magnetometer in the imaging capsule are transmitted to the recorder via the transceiver and compared to the readings of the accelerometer and magnetometer of the recorder to identify the spatial orientation of the imaging capsule. In an exemplary embodiment of the disclosure, the spatial orientation is used with the amplitude of the electromagnetic signal received by the coil of the recorder to determine the location of the imaging capsule relative to the recorder and the distance between them. 
         [0016]    There is thus provided according to an exemplary embodiment of the disclosure, a system for estimating the position of an imaging capsule that examines the gastrointestinal tract of a user, comprising: 
         [0017]    an imaging capsule for examining inside the user; and 
         [0018]    a recorder for communicating with the imaging capsule from outside the user; 
         [0019]    the imaging capsule, comprising:
       a controller for controlling functionality of the imaging capsule;   a transceiver for communication with the recorder;   a coil for transmission of electromagnetic signals, the recorder comprising:   a controller for controlling functionality of the recorder;   a transceiver for communication with the imaging capsule;   a coil for receiving electromagnetic signals from the coil of the imaging capsule;       
 
         [0026]    wherein the recorder determines the location of the imaging capsule based on measurements of the amplitude of the electromagnetic signals transmitted by the coil in the imaging capsule. 
         [0027]    In an exemplary embodiment of the disclosure, the coil in the imaging capsule is a 3D coil having windings in three orthogonal directions that transmit simultaneously in three different frequencies. Alternatively, the coil in the imaging capsule is a 3D coil having windings in three orthogonal directions that transmit sequentially. 
         [0028]    In an exemplary embodiment of the disclosure, the recorder comprises at least two 3D coils having windings in three orthogonal directions and determines the location of the imaging capsule by detecting a direction in which the amplitudes of the at least two 3D coils are in agreement. Optionally, the agreement takes into account the position difference between the at least two 3D coils. 
         [0029]    In an exemplary embodiment of the disclosure, the imaging capsule and the recorder both include a magnetometer and an accelerometer. Optionally, the imaging capsule uses the transceiver to communicate readings from the magnetometer and/or the accelerometer to the recorder. In an exemplary embodiment of the disclosure, the readings are communicated with a time stamp. Optionally, the recorder determines the spatial orientation of the imaging capsule based on the readings of the magnetometer and accelerometer received from the imaging capsule. In an exemplary embodiment of the disclosure, the recorder determines the location of the imaging capsule based on the determined spatial orientation and based on the transmissions of the coil of the imaging capsule. Optionally, the system further comprises a reference patch with similar elements as the imaging capsule; wherein the reference patch is attached to the body of the user and the recorder compares readings from the imaging capsule with readings from the reference patch to eliminate errors resulting from movements of the recorder. In an exemplary embodiment of the disclosure, the recorder uses an adaptive filter to improve the signal to noise ratio of the transmissions received from the coil of the imaging capsule. Optionally, the coil in the imaging capsule includes windings in a single plane. In an exemplary embodiment of the disclosure, the coil in the recorder is a 3D coil having windings in three orthogonal directions. 
         [0030]    There is thus further provided according to an exemplary embodiment of the disclosure, a method of estimating the position of an imaging capsule that examines the gastrointestinal tract of a user, comprising: 
         [0031]    swallowing an imaging capsule to examine inside the user; 
         [0032]    attaching a recorder for communicating with the imaging capsule outside on the body of the user; 
         [0033]    programming a controller in the imaging capsule to control functionality of the imaging capsule and a controller in the recorder to control functionality of the recorder; 
         [0034]    communicating information between the controller of the imaging capsule and the controller of the recorder using a transceiver in the imaging capsule and a transceiver in the recorder; 
         [0035]    transmitting electromagnetic signals from a coil in the imaging capsule; 
         [0036]    receiving the electromagnetic signals by a coil in the recorder; 
         [0037]    analyzing the amplitude of the electromagnetic signals transmitted by the coil to determine the location of the imaging capsule. 
         [0038]    In an exemplary embodiment of the disclosure, the coil in the imaging capsule is a 3D coil having windings in three orthogonal directions that transmit simultaneously in three different frequencies. Alternatively, the coil in the imaging capsule is a 3D coil having windings in three orthogonal directions that transmit sequentially. Optionally, the recorder comprises at least two 3D coils having windings in three orthogonal directions and determines the location of the imaging capsule by detecting a direction in which the amplitudes of the at least two 3D coils are in agreement. In an exemplary embodiment of the disclosure, the imaging capsule and the recorder both include a magnetometer and an accelerometer. Optionally, the imaging capsule uses the transceiver to communicate readings from the magnetometer and/or the accelerometer to the recorder. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0039]    The present disclosure will be understood and better appreciated from the following detailed description taken in conjunction with the drawings. Identical structures, elements or parts, which appear in more than one figure, are generally labeled with the same or similar number in all the figures in which they appear, wherein: 
           [0040]      FIG. 1  is a schematic illustration of a system for estimating the position of an imaging capsule inside the body of a user, according to an exemplary embodiment of the disclosure; 
           [0041]      FIG. 2  is a schematic illustration of an imaging capsule, according to an exemplary embodiment of the disclosure; 
           [0042]      FIG. 3  is a schematic illustration of a recorder, according to an exemplary embodiment of the disclosure; 
           [0043]      FIG. 4  is a schematic illustration of a reference patch for use with a system for estimating the position of an imaging capsule, according to an exemplary embodiment of the disclosure; 
           [0044]      FIG. 5  is a schematic illustration of an adaptive filter for improving the accuracy in estimating the position of an imaging capsule, according to an exemplary embodiment of the disclosure; 
           [0045]      FIG. 6  is a schematic illustration of magnetic fields transmitted and received by an imaging capsule and a recorder, according to an exemplary embodiment of the disclosure; and 
           [0046]      FIG. 7  is a schematic illustration of vectors representing magnetic fields transmitted and received by an imaging capsule and a recorder, according to an exemplary embodiment of the disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0047]      FIG. 1  is a schematic illustration of a system  100  for estimating the position of an imaging capsule  110  inside the body of a user. In an exemplary embodiment of the disclosure the user swallows imaging capsule  110 . The capsule enters the Gastro Intestinal tract and is especially useful in taking images and mapping the small intestine and colon  190 . In an exemplary embodiment of the disclosure, system  100  includes a recorder  120  to communicate  130  with imaging capsule  110  and record information provided by imaging capsule  110 . Optionally, the recorder is coupled to a strap or belt  180  to keep it fixated to the user&#39;s body in proximity to the small intestine and colon  190  as they are examined by imaging capsule  110 . The recorder may be positioned on the front of the user, the back of the user or in any selected position. Optionally, the position is selected empirically to provide optimal readings from transmissions provided by imaging capsule  110 . In an exemplary embodiment of the disclosure, recorder  120  analyzes transmissions from image capsule  110  to determine the spatial position of imaging capsule  110  relative to recorder  120 . 
         [0048]      FIG. 2  is a schematic illustration of imaging capsule  110 , according to an exemplary embodiment of the disclosure. Optionally, capsule  110  includes a coil  240  for transmitting a low frequency electromagnetic wave, for example at 1-50 Khz. Alternatively, the transmission of electromagnetic signal may be at approximately 7-14 MHz and the signal can then be used for both localization and data transmission, for example using a communication system on a chip such as NxH2180 manufactured by NXP Semiconductors from Eindhoven, The Netherlands 
         [0049]    With this implementation, the communication information will be extracted from the coil with a good signal to noise ratio (SNR). 
         [0050]    The transmissions are received by recorder  120  and their amplitudes are analyzed to determine the location of imaging capsule  110 . In some embodiments of the disclosure, the windings of coil  240  reside in a single plane. Alternatively, coil  240  may include windings in two or three orthogonal planes (a coil with windings in two orthogonal planes is referred to as a 2D coil and a coil with windings in three orthogonal planes is referred to as a 3D coil). Optionally, a 3D coil transmits in three orthogonal directions and uses more energy than a coil transmitting in a single plane. Accordingly, in some embodiments of the disclosure, imaging capsule  110  may be designed to use a single plane coil  240  to conserve power (e.g. provided by a battery  270 ), and to enable a relatively large coil that improves power efficiency. Whereas recorder  120  that is located outside the user&#39;s body may use a 3D coil since its power source can be larger and can easily be replaced if necessary. 
         [0051]    In an exemplary embodiment of the disclosure, imaging capsule  110  includes a magnetometer  230  that functions as a 3D geomagnetic sensor (e.g. MAG3110 manufactured by Freescale Semiconductors Ltd from Austin Tex.). Alternatively or additionally, imaging capsule  110  includes an accelerometer  220  that functions to sense changes in the position of imaging capsule  110 , for example in colon  190 . MMA7260QT manufactured by Freescale Semiconductors LTD is an example of a small sized accelerometer that can be incorporated into imaging capsule  110 . In some embodiments of the disclosure, a combined magnetometer and accelerometer can be used, for example FXOS8700CQ manufactured by Freescale Semiconductors LTD. 
         [0052]    In an exemplary embodiment of the disclosure, imaging capsule  110  includes a controller  250  and a transceiver  260  to control the functionality of imaging capsule  110  and communicate with recorder  120 . The controller  250  may include a processor and/or memory to receive and execute software instructions. Optionally, controller  250  can receive instructions via transceiver  260 , for example to start scanning and to stop scanning. Additionally, controller  250  can transmit images recorded by imaging capsule  110  and information regarding the spatial position of the imaging capsule  110 , for example the readings of the magnetometer  230  and/or the accelerometer  220 . Optionally, the information can notify recorder  120  regarding the orientation of imaging capsule  110  and coil  240  relative to the magnetic field and gravitational field of the earth. 
         [0053]      FIG. 3  is a schematic illustration of recorder  120 , according to an exemplary embodiment of the disclosure. Optionally, recorder  120  may include a controller  350 , a transceiver  360 , a magnetometer  330 , an accelerometer  320 , a power source  370  and one or more reception coils  340 . Optionally, the one or more reception coils  340  may be single plane coils or have windings in two or three orthogonal planes (a 2D coil or a 3D coil). In an exemplary embodiment of the disclosure, one or more reception coils  340  of recorder  120  interact with coil  240  of imaging capsule  110  by receiving the low frequency transmissions transmitted from the imaging capsule  110 . Optionally, analysis of the amplitude of the transmissions from imaging capsule  110  by a combination of reception coils  340  can be used to determine the direction and distance from recorder  120  so that the spatial location of the imaging capsule  110  can be calculated and the distance between the recorder  120  and the imaging capsule  110  can be determined. 
         [0054]    In an exemplary embodiment of the disclosure, readings from magnetometer  230  and/or accelerometer  220  are transmitted from imaging capsule  110  to recorder  120 . Optionally, recorder  120  compares the readings with the readings of magnetometer  330  and/or accelerometer  320  to determine the angular direction of imaging capsule  110  and coil  240  relative to the direction of recorder  120  and the one or more reception coils  340 . In an exemplary embodiment of the disclosure, the readings of magnetometer  230  and/or accelerometer  220  are transmitted with a timestamp from imaging capsule  110  to synchronize comparison of the readings of magnetometer  230  and/or accelerometer  220  with the readings of magnetometer  330  and/or accelerometer  320 . Optionally, the amplitudes measured by the one or more reception coils  340  from the transmissions of coil  240  with the angular direction determined from the readings of magnetometer  230  and/or accelerometer  220  are used to determine the spatial location of imaging capsule  110  relative to recorder  120 . 
         [0055]    In an exemplary embodiment of the disclosure, electromagnetic disturbances to the transmissions of coil  240  can be identified, for example by controller  350  of recorder  120  since the spatial angles of imaging capsule  110  are acquired by magnetometer  330  and/or accelerometer  320 . Optionally, in the case of an external magnetic or metallic disturbance the electromagnetic field will be disturbed differently then the constant earth magnetic field and/or the gravitational field. Therefore a sudden change in the amplitude of the transmissions from coil  240  without a matching change in the spatial orientation of the imaging capsule as recorded by the magnetometer  330  and/or accelerometer  320  can provide an indication regarding an electromagnetic disturbance that can be disregarded. In some embodiments of the disclosure, the coil amplitude will be processes only when movement of the imaging capsule  110  is detected. 
         [0056]    In an exemplary embodiment of the disclosure, the distance to the imaging capsule  110  is calculated using two or more reception coils  340  at recorder  120  without information from accelerometer  220  and/or magnetometer  230 . In an exemplary embodiment of the disclosure, the two or more reception coils may have windings in a single plane or may have windings in two or three orthogonal planes. In some embodiments of the disclosure at least one of the reception coils  340  is a 3D coil. Optionally, the position is determined by testing all possible directions for the imaging capsule  110  and selecting the direction for which the two or more reception coils  340  reach agreement for the calculated position of the imaging capsule  110 . Optionally, the agreement takes into account the position difference between the two or more reception coils  340  in recorder  120 . In an exemplary embodiment of the disclosure, one of the reception coils  340  may serve as a transmitter and receiver to provide transmissions to the other reception coils  340  so that the relative distance and angles between the reception coils  340  in the recorder  120  can be measured before calculating the distance to coil  240 . Alternatively, a separate transmitting reference coil is used and distance is calculated relative to that reference. 
         [0057]    In some embodiments of the disclosure, coil  240  in imaging capsule  110  is a 3D coil that transmits simultaneously in three different frequencies, or alternatively transmits with a single frequency but the windings of each orthogonal plane transmit sequentially so that the receiver can distinguish between the three transmissions. Optionally, a single planar reception coil  340  may be used to receive the transmissions and calculate the distance from recorder  120  and imaging capsule  110  at that moment. 
         [0058]    In an exemplary embodiment of the disclosure, recorder  120  includes an encasement  380  ( FIG. 3 ). Optionally, encasement  380  is coated with a high permeability material that shields the elements of recorder  120  from the influence of magnetic fields outside the body, for example such as MuMetal manufactured by The MuShield Company from Londonderry, N.H., USA. In an exemplary embodiment of the disclosure, the side facing the user&#39;s body is not coated so that it can receive transmissions from imaging capsule  110  from inside the user&#39;s body. Optionally, the effect of the shielding if any is calibrated by recorder  120  so that it is shielded from external electromagnetic interference. 
         [0059]      FIG. 4  is a schematic illustration of a reference patch  410  for use with system  100  for estimating the position of imaging capsule  110 . In an exemplary embodiment of the disclosure, reference patch  410  is small like imaging capsule  110  and includes similar elements, for example an accelerometer  420 , a magnetometer  430 , a coil  440 , a controller  450  and a transceiver  460 . Optionally, reference patch  410  is attached to the user, for example adhesively positioned on the user&#39;s back. The reference patch  410  serves as a stationary reference in contrast to imaging capsule  110  that dynamically moves through the user&#39;s gastro intestinal tract. Optionally, recorder  120  communicates with reference patch  410  and with imaging capsule  110 . 
         [0060]    In an exemplary embodiment of the disclosure, recorder  120  calculates the position of the imaging capsule  110  relative to reference patch  410  to reduce recording false movements resulting from movements of recorder  120  which is optionally, larger and bulkier than reference patch  410  and more susceptible to movements since it may be attached to belt  180  and not adhesively attached to the body of the user. In some embodiments of the disclosure, recorder  120  may be implemented in the form of reference patch  410  (e.g. in the form of a small patch attached to the user as shown in  FIG. 4 ) instead of in the form of recorder  120  as shown in  FIG. 1 , so that recorder  120  only needs to communicate with imaging capsule  110  and not with an additional reference patch. In some embodiments of the disclosure, reference patch  410  may also transmit signals from coil  440  to imaging capsule  110 , for example to test the communication range. 
         [0061]      FIG. 5  is a schematic illustration of an adaptive filter  500  for improving the accuracy in estimating the position of imaging capsule  110 . In an exemplary embodiment of the disclosure, recorder  120  uses an adaptive filter (e.g. in controller  350 ) to reduce noise and improve the signal to noise ratio (SNR) in the transmissions received from imaging capsule  110  (e.g. from the signals received by reception coils  340 ). Optionally, by estimating the noise in the environment while the imaging capsule  110  is not transmitting, adaptive filter  500  can be set to reduce the noise (assuming that the noise while imaging capsule  110  is transmitting is similar to the noise when it is not transmitting). In an exemplary embodiment of the disclosure, a signal received by recorder  120  from imaging capsule  110  (including noise) is fed into an input  540  of adaptive filter  500 . Optionally, the estimated noise measured while imaging capsule  110  is not transmitting is recorded and fed into a noise input  550 . A filter  510  accepts the signal from noise input  550  and prepares it for combining with the input signal to cancel out the noise from the input signal. A summator  520  combines the input signal with the processed noise and provides the combined signal to an output  560  as an output signal. Additionally, the output signal is provided as feedback via a signal to noise ratio controller  530  to filter  510  to improve processing of the input signal and maximize the signal to noise ratio. 
         [0062]    Following is a description of an exemplary closed form analytic solution to calculate the distance from recorder  120  to imaging capsule  110 , according to an exemplary embodiment of the disclosure. Optionally, in this calculation the spatial orientation of imaging capsule  110  relative to recorder  120  is known from the readings of accelerometer  220 , accelerometer,  320 , magnetometer  230 , magnetometer  330 , coil  240  with windings in one to three orthogonal planes and one reception coil  340  with windings in three orthogonal planes. 
         [0063]    Induction coil  240  generates a low-frequency magnetic field having the vector amplitude B=B x , B y , B z ) described by the magnetic dipole: 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                     = 
                     
                       β 
                        
                       
                         
                           
                             3 
                              
                             
                               ( 
                               
                                 n 
                                 , 
                                 
                                   r 
                                   ′ 
                                 
                               
                               ) 
                             
                              
                             r 
                           
                           - 
                           
                             
                               
                                  
                                 r 
                                  
                               
                               2 
                             
                              
                             n 
                           
                         
                         
                           
                              
                             r 
                              
                           
                           5 
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
         [0064]    Where n is the capsule coil normal vector (representing the transmission from coil  240 ) and r is the radius vector of the coil center. 
         [0065]    The amplitude induced on the i-th coil in the receiver is: 
         [0000]        V   i =α i ( B,n   i   t ), i= 1,2,3;  Equation (2)
 
         [0000]    where n i  is the i-th coil normal vector. 
         [0000]    
       
         
           
             β 
             = 
             
               
                 
                   μ 
                   0 
                 
                  
                 
                   I 
                   c 
                 
                  
                 
                   N 
                   c 
                 
                  
                 π 
                  
                 
                     
                 
                  
                 
                   a 
                   c 
                   2 
                 
               
               
                 4 
                  
                 
                     
                 
                  
                 π 
               
             
           
         
       
     
         [0000]    where μ 0 =4π 10 −7 Vs/(Am) is the magnetic permeability of vacuum, I c  is the electric current in the capsule coil, N c  is the number of capsule coil turns, a c  is the capsule coil effective radius, n=(n x , n y , n z ) is the capsule coil normal vector and r=(x−x 0 , y−y 0 , z−z 0 ) is the Cartesian distance vector between the observation point (x 0 , y 0 , z 0 ) and the capsule coil center (x, y, z). 
         [0000]      α i =2π fN   i   πa   i   2  
 
         [0000]    where f is the field frequency, N i  is the i-th coil number of turns, a i  is the i-th coil effective radius, n i =(n xi , n yi , n zi ) is the i-th coil normal vector, and B i  is the magnetic field at the i-th coil center. 
         [0066]    Now we go to calculate vector r from the known amplitude values and the coil normal vectors. First of all one can see that if r is a solution then −r is a solution as well. We can choose usually the proper solution from the physical issues and/or from the history of the tracking. 
         [0067]    By substituting equation (1) to (2) we obtain: 
         [0000]    
       
         
           
             
               V 
               i 
             
             = 
             
               
                 
                   α 
                   i 
                 
                 ( 
                 
                   
                     β 
                      
                     
                       
                         
                           3 
                            
                           
                             ( 
                             
                               n 
                               , 
                               
                                 r 
                                 t 
                               
                             
                             ) 
                           
                            
                           r 
                         
                         - 
                         
                           
                             
                                
                               r 
                                
                             
                             2 
                           
                            
                           n 
                         
                       
                       
                         
                            
                           r 
                            
                         
                         5 
                       
                     
                   
                   , 
                   
                     n 
                     i 
                     t 
                   
                 
                 ) 
               
               = 
               
                 
                   α 
                   i 
                 
                  
                 
                   β 
                    
                   
                     ( 
                     
                       
                         
                           
                             3 
                              
                             
                               ( 
                               
                                 n 
                                 , 
                                 
                                   ρ 
                                   t 
                                 
                               
                               ) 
                             
                              
                             ρ 
                           
                           - 
                           n 
                         
                         
                           
                              
                             r 
                              
                           
                           3 
                         
                       
                       , 
                       
                         n 
                         i 
                         t 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0068]    Here ρ is the normalized vector r. 
         [0069]    Accordingly: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     r 
                      
                   
                   3 
                 
                 
                   
                     α 
                     i 
                   
                    
                   β 
                 
               
                
               
                 V 
                 i 
               
             
             = 
             
               
                 n 
                  
                 
                   ( 
                   
                     
                       3 
                        
                       
                         ρ 
                         t 
                       
                        
                       ρ 
                     
                     - 
                     I 
                   
                   ) 
                 
               
                
               
                 n 
                 i 
                 t 
               
             
           
         
       
       
         
           Let 
         
       
       
         
           
             N 
             = 
             
               [ 
               
                 
                   
                     
                       n 
                       1 
                       t 
                     
                   
                   
                     
                       n 
                       2 
                       t 
                     
                   
                   
                     
                       n 
                       3 
                       t 
                     
                   
                 
               
               ] 
             
           
         
       
       
         
           
             V 
             = 
             
               
                 [ 
                 
                   
                     
                       
                         
                           V 
                           1 
                         
                         
                           α 
                           1 
                         
                       
                     
                     
                       
                         
                           V 
                           2 
                         
                         
                           α 
                           2 
                         
                       
                     
                     
                       
                         
                           V 
                           3 
                         
                         
                           α 
                           3 
                         
                       
                     
                   
                 
                 ] 
               
               = 
               BN 
             
           
         
       
     
         [0070]    Then we obtain: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     r 
                      
                   
                   3 
                 
                 β 
               
                
               V 
             
             = 
             
               
                 n 
                  
                 
                   ( 
                   
                     
                       3 
                        
                       
                         ρ 
                         t 
                       
                        
                       ρ 
                     
                     - 
                     I 
                   
                   ) 
                 
               
                
               N 
             
           
         
       
       
         
           
             
               
                 
                   
                      
                     r 
                      
                   
                   3 
                 
                 β 
               
                
               
                 VN 
                 
                   - 
                   1 
                 
               
             
             = 
             
               n 
                
               
                 ( 
                 
                   
                     3 
                      
                     
                       ρ 
                       t 
                     
                      
                     ρ 
                   
                   - 
                   I 
                 
                 ) 
               
             
           
         
       
     
         [0071]    Now we define (m) and receive equation (3) by substitution: 
         [0000]    
       
         
           
             
               
                 
                   
                     m 
                     = 
                     
                       
                         
                           1 
                           β 
                         
                          
                         
                           VN 
                           
                             - 
                             1 
                           
                         
                       
                       = 
                       
                         
                           1 
                           β 
                         
                          
                         B 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                            
                           r 
                            
                         
                         3 
                       
                        
                       m 
                     
                     = 
                     
                       n 
                        
                       
                         ( 
                         
                           
                             3 
                              
                             
                               ρ 
                               t 
                             
                              
                             ρ 
                           
                           - 
                           I 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0072]    Let us consider the special case as illustrated by  FIG. 6 , wherein the normal vector of the transmission by coil  240  ( n ) and the normal vector of the reception by coil  340  ( m ) are parallel (i.e. m↑↑n) and designated as (S) with 2 sub-cases (S1) and (S2) (parallel and anti-parallel). 
         [0073]    This means that the magnetic field B is parallel to the capsule direction n, B=kn. One can see from (1) above that: 
         [0000]    
       
         
           
             
               B 
               = 
               
                 kn 
                 = 
                 
                   β 
                    
                   
                     
                       
                         3 
                          
                         
                           ( 
                           
                             n 
                             , 
                             
                               r 
                               t 
                             
                           
                           ) 
                         
                          
                         r 
                       
                       - 
                       
                         
                           
                              
                             r 
                              
                           
                           2 
                         
                          
                         n 
                       
                     
                     
                       
                          
                         r 
                          
                       
                       5 
                     
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                 β 
                  
                 
                   
                     3 
                      
                     
                       ( 
                       
                         n 
                         , 
                         
                           r 
                           t 
                         
                       
                       ) 
                     
                      
                     ρ 
                   
                   
                     
                        
                       r 
                        
                     
                     3 
                   
                 
               
               = 
               
                 
                   k 
                   ~ 
                 
                  
                 n 
               
             
           
         
       
     
         [0074]    We represent 
         [0000]      ρ=τ n+φn   −   ,             n,n   −           =0
 
         [0075]    And obtain from this 
         [0000]    
       
         
           
             
               
                 
                   k 
                   ~ 
                 
                  
                 n 
               
               = 
               
                 β 
                  
                 
                   
                     3 
                      
                     
                       τ 
                        
                       
                         ( 
                         
                           
                             τ 
                              
                             
                                 
                             
                              
                             n 
                           
                           + 
                           
                             ϕ 
                              
                             
                                 
                             
                              
                             
                               n 
                               - 
                             
                           
                         
                         ) 
                       
                     
                   
                   
                     
                        
                       r 
                        
                     
                     3 
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                 τ 
                  
                 
                     
                 
                  
                 ϕ 
               
               = 
               0 
             
           
         
       
     
         [0076]    Thus the case (S) may be divided to two sub-cases: 
         [0000]      ρ=± n   (S1)
 
         [0000]                ρ, n             = 0( S 2)
 
         [0077]    For S1 the formula looks like this: 
         [0000]    
       
         
           
             B 
             = 
             
               
                 β 
                  
                 
                   
                     
                       3 
                        
                       ρ 
                     
                     - 
                     n 
                   
                   
                     
                        
                       r 
                        
                     
                     3 
                   
                 
               
               = 
               
                 β 
                  
                 
                   
                     2 
                      
                     n 
                   
                   
                     
                        
                       r 
                        
                     
                     3 
                   
                 
               
             
           
         
       
       
         
           
             r 
             = 
             
               
                 ± 
                 
                   
                     
                       2 
                        
                       β 
                     
                     
                        
                       B 
                        
                     
                   
                   3 
                 
               
                
               n 
             
           
         
       
     
         [0078]    And for S2 we get: 
         [0000]    
       
         
           
             
               B 
               = 
               
                 β 
                  
                 
                   
                     - 
                     n 
                   
                   
                     
                        
                       r 
                        
                     
                     3 
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                  
                 r 
                  
               
               = 
               
                 
                   r 
                   0 
                 
                 = 
                 
                   
                     β 
                     
                        
                       B 
                        
                     
                   
                   3 
                 
               
             
           
         
       
     
         [0079]    As shown in  FIG. 6  r 0  is the radius of the circle (O) with the center in the origin and oriented orthogonally to n. Then every point in O is the solution of (1). Accordingly the solution can be found by tracking the received amplitudes. 
         [0080]      FIG. 7  illustrates the normal vector of the transmission by coil  240  ( n ) and the normal vector of the reception by coil  340  ( m ) in the general case when they are not parallel. Accordingly, in the non non-special case (not S). We multiple both sides from the left by 
         [0000]    
       
      
       h=[m,n] 
      
     
         [0000]      | r|mh   t   =n (3ρ t   ρ−I ) h   t  
 
         [0000]      0=3γρ h   t  
 
         [0000]      Here 
         [0000]      γ= nρ   t =cos δ
 
         [0081]    We see that vector ρ is co-planar to the vectors n and m. 
         [0082]    Let μ be the normalized vector in the plane of m and n which is orthogonal to n. 
         [0083]    Let us multiply the equation (3) by n and by μ taking into account the following: 
         [0000]      ρμ t =±√{square root over (1−γ 2 )}=sin ε
 
         [0000]      Receiving equations (4): 
         [0000]      | r|   3   mn   t   =n (3ρ t   ρ−I ) n   t =3γ 2 −1=3 cos 2 δ−1  (4)
 
         [0000]      | r|   3   mμ   t   ==n (3ρ t   ρ−I )μ t =±3γ√{square root over (1−γ 2 )}=3 cos δ sin δ  (4)
 
         [0000]      For 
         [0000]      η= nm   t   =|m |cos ε
 
         [0000]      ξ= mμ   t   =|m |sin ε
 
         [0000]      (3γ 2 −1)ξ=±3γ√{square root over (1−γ 2 )}η  (5)
 
         [0084]    We take the square of the both sides of (5) and solve the bi-quadratic equation 
         [0000]        aγ   4   +bγ   2   +c= 0 
         [0000]        a= 9(ξ 2 +η 2 )=9 m   2  
 
         [0000]        b=− 6ξ 2 −9η 2 =−3 m   2 (2+cos 2 ε)
 
         [0000]        c=ξ   2   =m   2  sin 2 ε
 
         [0000]    with respect to γ. The discriminant 
         [0000]    
       
         
           
             
               
                 
                   D 
                   = 
                     
                    
                   
                     
                       b 
                       2 
                     
                     - 
                     
                       4 
                        
                       
                           
                       
                        
                       ac 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       m 
                       4 
                     
                      
                     
                       ( 
                       
                         
                           9 
                            
                           
                             
                               ( 
                               
                                 2 
                                 + 
                                 
                                   
                                     cos 
                                     2 
                                   
                                    
                                   ɛ 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         - 
                         
                           36 
                            
                           
                               
                           
                            
                           
                             sin 
                             2 
                           
                            
                           ɛ 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     9 
                      
                     
                       
                         m 
                         4 
                       
                        
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 2 
                                 + 
                                 
                                   
                                     cos 
                                     2 
                                   
                                    
                                   ɛ 
                                 
                               
                               ) 
                             
                             2 
                           
                           - 
                           
                             4 
                              
                             
                                 
                             
                              
                             
                               sin 
                               2 
                             
                              
                             ɛ 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     9 
                      
                     
                       
                         m 
                         4 
                       
                        
                       
                         ( 
                         
                           4 
                           + 
                           
                             4 
                              
                             
                                 
                             
                              
                             
                               cos 
                               2 
                             
                              
                             ɛ 
                           
                           + 
                           
                             
                               cos 
                               4 
                             
                              
                             ɛ 
                           
                           - 
                           
                             4 
                              
                             
                                 
                             
                              
                             
                               sin 
                               2 
                             
                              
                             ɛ 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       9 
                        
                       
                         
                           m 
                           4 
                         
                          
                         
                           ( 
                           
                             
                               8 
                                
                               
                                   
                               
                                
                               
                                 cos 
                                 2 
                               
                                
                               ɛ 
                             
                             + 
                             
                               
                                 cos 
                                 4 
                               
                                
                               ɛ 
                             
                           
                           ) 
                         
                       
                     
                     &gt; 
                     0 
                   
                 
               
             
           
         
       
     
         [0085]    Thus there are two real solutions for γ 2 :g 1  and g 2 . We can see from the Vieta formulas that 
         [0000]    
       
         
           
             
               
                 g 
                 1 
               
                
               
                 g 
                 2 
               
             
             = 
             
               
                 c 
                 a 
               
               = 
               
                 
                   
                     
                       sin 
                       2 
                     
                      
                     ɛ 
                   
                   9 
                 
                 ≤ 
                 
                   1 
                   9 
                 
               
             
           
         
       
       
         
           
             
               
                 g 
                 1 
               
               + 
               
                 g 
                 2 
               
             
             = 
             
               
                 - 
                 
                   b 
                   a 
                 
               
               = 
               
                 
                   - 
                   
                     
                       
                         - 
                         3 
                       
                        
                       
                         
                           m 
                           2 
                         
                          
                         
                           ( 
                           
                             2 
                             + 
                             
                               
                                 cos 
                                 2 
                               
                                
                               ɛ 
                             
                           
                           ) 
                         
                       
                     
                     
                       9 
                        
                       
                         m 
                         2 
                       
                     
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         2 
                         + 
                         
                           
                             cos 
                             2 
                           
                            
                           ɛ 
                         
                       
                       ) 
                     
                     3 
                   
                   ≥ 
                   
                     2 
                     3 
                   
                 
               
             
           
         
       
     
         [0086]    One can see from (5) as well that 0≦γ 2 ≦1. Finally 
         [0000]    
       
         
           
             0 
             ≤ 
             
               g 
               1 
             
             ≤ 
             
               1 
               3 
             
             ≤ 
             
               g 
               2 
             
             ≤ 
             1 
           
         
       
     
         [0087]    We can choose the solution g 1,2  for which the expression 
         [0000]    
       
         
           
             
               
                 
                   3 
                    
                   
                     g 
                     
                       1 
                       , 
                       2 
                     
                   
                 
                 - 
                 1 
               
               η 
             
             &gt; 
             0 
           
         
       
     
         [0088]    The case η=0 is of special interest. One can see that in this situation 
         [0000]    
       
         
           
             
               
                 g 
                 1 
               
               = 
               
                 
                   g 
                   2 
                 
                 = 
                 
                   1 
                   3 
                 
               
             
             , 
             
               ξ 
               = 
               
                 
                    
                   m 
                    
                 
                 . 
               
             
           
         
       
     
         [0089]    Finally we obtain from (4): 
         [0000]    
       
         
           
             
                
               r 
                
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               3 
                                
                               
                                 g 
                                 1 
                               
                             
                             - 
                             1 
                           
                           η 
                         
                         3 
                       
                       , 
                       
                         γ 
                         = 
                         
                           
                             g 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       η 
                       &lt; 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             2 
                           
                           
                              
                             m 
                              
                           
                         
                         3 
                       
                       , 
                       
                         γ 
                         = 
                         
                           1 
                           
                             3 
                           
                         
                       
                     
                   
                   
                     
                       η 
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               3 
                                
                               
                                 g 
                                 2 
                               
                             
                             - 
                             1 
                           
                           η 
                         
                         3 
                       
                       , 
                       
                         γ 
                         = 
                         
                           
                             g 
                             2 
                           
                         
                       
                     
                   
                   
                     
                       η 
                       &gt; 
                       0 
                     
                   
                 
               
             
           
         
       
     
         [0090]    The final step is 
         [0000]    
       
         
           
             ρ 
             = 
             
               
                 ± 
                 
                   1 
                   
                     3 
                      
                     γ 
                   
                 
               
                
               
                 ( 
                 
                   
                     
                       
                          
                         r 
                          
                       
                       3 
                     
                      
                     m 
                   
                   + 
                   n 
                 
                 ) 
               
             
           
         
       
     
         [0091]    Accordingly, the value of p provides us with the distance. 
         [0092]    Optionally, previous position data are used to solve ambiguity relating to special cases, for example using historical positions near the singularity. 
         [0093]    It should be appreciated that the above described methods and apparatus may be varied in many ways, including omitting or adding steps, changing the order of steps and the type of devices used. It should be appreciated that different features may be combined in different ways. In particular, not all the features shown above in a particular embodiment are necessary in every embodiment of the disclosure. Further combinations of the above features are also considered to be within the scope of some embodiments of the disclosure. It will also be appreciated by persons skilled in the art that the present disclosure is not limited to what has been particularly shown and described hereinabove.