Systems and methods for compensating for large moving objects in magnetic-tracking environments

1. A method of magnetic tracking in a tracking volume in the presence of movable magnetic-field distorter, comprising:

generating a magnetic field capable of being sensed by a magnetic-field sensor when the magnetic-field sensor is located in the tracking volume;

obtaining first magnetic-field data regarding the magnetic field via the magnetic-field sensor while the magnetic-field sensor is in the tracking volume;

calculating, within a machine, position and orientation of the magnetic-field sensor as a function of the first magnetic-field data and a difference between a first set of data items and a second set of data items, wherein the first set of data items results from second magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is present in the tracking volume, and the second set of data items results from third magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is not present in the tracking volume; and

outputting from the machine information that is a function of the position and orientation of the magnetic-field sensor.

2. A method according to claim 1 , wherein the data items of the first and second sets are position and orientation solutions calculated using a position-and-orientation algorithm.

3. A method according to claim 2 , further comprising manipulating algorithmically the position and orientation solutions.

4. A method according to claim 1 , wherein the data items of the first and second sets are magnetic-field measurements.

5. A method according to claim 4 , further comprising manipulating algorithmically the magnetic-field measurements.

6. A method according to claim 1 , further comprising interpolating the first and second sets of data items.

7. A method according to claim 1 , wherein said calculating of position and orientation includes:

rotating the first magnetic-field data by a matrix A 0 to obtain rotated first magnetic-field data having zero orientation;

rotating the second magnetic-field data by a matrix Ac to obtain zero orientation;

backing out a range R 0 from the rotated first magnetic-field data;

backing out a range Rc from the rotated second magnetic-field data;

obtaining matrix components V 0 from range R 0 ;

obtaining matrix components Vc from range Rc;

determining a difference matrix dV between matrix components V 0 and Vc;

collecting, via the magnetic-field sensor, real-time sensor field data;

obtaining matrix V from the real-time sensor data;

obtaining rebuilt sensor field data by incorporating the difference matrix dV into matrix V;

multiplying the rebuilt sensor field data by A 0 t Ac t so as to obtain a corrected matrix;

calculating corrected position and orientation data for the magnetic-field sensor as a function of the corrected matrix; and

outputting from the machine information that is a function of the corrected position and orientation data.

8. A method according to claim 1 , wherein said calculating of position and orientation includes:

determining, via the magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data R 1 regarding the magnetic-field sensor at a particular location within the tracking volume;

determining, via the magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data S 1 regarding the magnetic-field sensor at the particular location;

calculating a best-fit transformation matrix T that converts S 1 into R 1 ;

collecting, via the magnetic-field sensor, real-time position and orientation data for location within the tracking volume;

applying the best-fit transformation matrix T to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

9. A method according to claim 1 , wherein said calculating of position and orientation includes:

determining, via at least one magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data sets R 1 . . . Rn corresponding to differing locations of the at least one magnetic-field sensor within the tracking volume;

determining, via the at least one magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data sets S 1 . . . Sn corresponding to the differing locations;

calculating a best-fit transformation matrices T 1 . . . Tn that convert corresponding respective ones of R 1 . . . Rn into corresponding respective ones of S 1 . . . Sn;

forming an interpolation function ƒ from best-fit transformation matrices T 1 . . . Tn;

collecting, via the at least one magnetic-field sensor, real-time position and orientation data;

applying the interpolation function ƒ to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

10. A method according to claim 1 , wherein said calculating of position and orientation includes:

(a) collecting, with the magnetic-field distorter at a known distorter location within the tracking volume, measured magnetic-field data from one or more sensors placed at known sensor locations and orientations within the tracking volume;

(b) calculating expected magnetic-field data expected at each of the known sensor positions and orientations;

(c) determining a difference dF between the measured magnetic-field data and the expected magnetic-field data;

(d) fitting the difference dF and the measured positions and orientations to a dipole model so as to determine dipole parameters;

(e) calculating a magnetic-field contribution M from the dipole model;

(f) determining if |M−dF| is less than a tolerance; and

(g) if |M−dF| is less than the tolerance, save the dipole parameters.

11. A method according to claim 10 , further comprising, if |M−dF| is not less than the tolerance:

(h) calculating a new dF=M−dF;

(i) repeating steps (d) through (h) using the new dF until |M−dF| is less than the tolerance.

12. A method according to claim 11 , further comprising repeating steps (a) through (i) multiple times for differing distorter locations.

13. A method according to claim 10 , further comprising:

(j) collecting real-time magnetic-field data S 3 from the at least one magnetic-field sensor;

(k) obtaining real-time distorter location and orientation parameters;

(l) determining a dipole contribution D as a function of the real-time distorter location and orientation parameters;

(m) calculating corrected real-time magnetic-field data as a function of the real-time magnetic-field data S 3 and the dipole contribution D;

(n) calculating corrected position and orientation using the corrected real-time magnetic-field data; and

(o) outputting from the machine information that is a function of the corrected position and orientation data.

14. A method according to claim 13 , further comprising prior to step (o):

(p) determining if the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled;

(q) if one, the other, or both, of the corrected position and orientation data has not settled and/or if the corrected real-time magnetic-field data has settled, repeating steps (l) through (n) and (p); and

(r) if one, the other, or both, of the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled, proceeding to step (o).

15. A method according to claim 1 , wherein said calculating of position and orientation includes:

measuring first magnetic-field components within the tracking volume without the magnetic-field distorter present in the tracking volume;

extracting scalar magnetic potentials g j , from the first magnetic-field components;

measuring second magnetic-field components within the tracking volume with the magnetic-field distorter present in the tracking volume;

extracting induced moments p k from the second magnetic-field components;

determining gradient and scattering matrices s k,j from the scalar magnetic potentials and the induced moments p k ;

determine a distorter position and orientation of the magnetic-field distorter;

evaluating and rotating the gradient and scattering matrices as a function of the distorter position and orientation so as to obtain rotated gradient and scattering matrices;

computing multipole moments as a function of the rotated gradient and scattering matrices;

calculating a scattered field as a function of the multipole moments; and

transforming the scattered field to a desired coordinate frame so as to obtain transformed scattered field.

16. A method according to claim 15 , further comprising:

(a) collecting real-time magnetic-field data from the magnetic-field sensor;

(b) summing the real-time magnetic-field data with a magnetic-field corrections so as to obtain corrected magnetic-field data;

(c) determining corrected real-time position and orientation data as a function of the corrected magnetic-field data;

(d) outputting information as a function of the corrected real-time position and orientation data;

(e) determining the magnetic-field corrections as a function of the transformed scattered field and the corrected real-time position and orientation data; and

(f) repeating steps (a) through (e).

17. A method according to claim 16 , further comprising low-pass filtering the magnetic-field corrections prior to step (b).

18. A method according to claim 15 , wherein said determining of the gradient and scattering matrices s k,j from the scalar magnetic potentials g j , and the induced moments p k includes solving the following equation for s k,j :

p

k

=

∑

j

=

1

J

⁢

s

k

,

j

⁢

g

j

⁡

(

x

,

y

,

z

)

.

19. A system for magnetic tracking in a tracking volume in the presence of movable magnetic-field distorter, comprising:

a magnetic-field sensor;

a magnetic field generator for generating a magnetic field capable of being sensed by said magnetic-field sensor when said magnetic-field sensor is located in the tracking volume; and

means for:

collecting first magnetic-field data regarding the magnetic field via said magnetic-field sensor while said magnetic-field sensor is in the tracking volume; and

calculating position and orientation, of said magnetic-field sensor as a function of the first magnetic-field data and a difference between a first set of data items and a second set of data items, wherein the first set of data items results from second magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is present in the tracking volume, and the second set of data items results from third magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is not present in the tracking volume.

20. A system according to claim 19 , wherein the data items of the first and second sets are position and orientation solutions calculated using a position-and-orientation algorithm.

21. A system according to claim 20 , wherein said means is further for manipulating algorithmically the position and orientation solutions.

22. A system according to claim 19 , wherein the data items of the first and second sets are magnetic-field measurements.

23. A system according to claim 22 , wherein said means is further for manipulating algorithmically the magnetic-field measurements.

24. A system according to claim 19 , wherein said means is further for interpolating the first and second sets of data items.

25. A system according to claim 19 , wherein said means is further for:

rotating the first magnetic-field data by a matrix A 0 to obtain rotated first magnetic-field data having zero orientation;

rotating the second magnetic-field data by a matrix Ac to obtain zero orientation;

backing out a range R 0 from the rotated first magnetic-field data;

backing out a range Rc from the rotated second magnetic-field data;

obtaining matrix components V 0 from range R 0 ;

obtaining matrix components Vc from range Rc;

determining a difference matrix dV between matrix components V 0 and Vc;

collecting, via the magnetic-field sensor, real-time sensor field data;

obtaining matrix V from the real-time sensor data;

obtaining rebuilt sensor field data by incorporating the difference matrix dV into matrix V;

multiplying the rebuilt sensor field data by A 0 t Ac t so as to obtain a corrected matrix;

calculating corrected position and orientation data for the magnetic-field sensor as a function of the corrected matrix; and

outputting from the machine information that is a function of the corrected position and orientation data.

26. A system according to claim 1 , wherein said means is further for:

determining, via the magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data R 1 regarding the magnetic-field sensor at a particular location within the tracking volume;

determining, via the magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data S 1 regarding the magnetic-field sensor at the particular location;

calculating a best-fit transformation matrix T that converts S 1 into R 1 ;

collecting, via the magnetic-field sensor, real-time position and orientation data for location within the tracking volume;

applying the best-fit transformation matrix T to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

27. A system according to claim 1 , wherein said means is further for:

determining, via at least one magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data sets R 1 . . . Rn corresponding to differing locations of the at least one magnetic-field sensor within the tracking volume;

determining, via the at least one magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data sets S 1 . . . Sn corresponding to the differing locations;

calculating a best-fit transformation matrices T 1 . . . Tn that convert corresponding respective ones of R 1 . . . Rn into corresponding respective ones of S 1 . . . Sn;

forming an interpolation function ƒ from best-fit transformation matrices T 1 . . . Tn;

collecting, via the at least one magnetic-field sensor, real-time position and orientation data;

applying the interpolation function ƒ to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

28. A system according to claim 1 , wherein said means is further for:

(a) collecting, with the magnetic-field distorter at a known distorter location within the tracking volume, measured magnetic-field data from one or more sensors placed at known sensor locations and orientations within the tracking volume;

(b) calculating expected magnetic-field data expected at each of the known sensor positions and orientations;

(c) determining a difference dF between the measured magnetic-field data and the expected magnetic-field data;

(d) fitting the difference dF and the measured positions and orientations to a dipole model so as to determine dipole parameters;

(e) calculating a magnetic-field contribution M from the dipole model;

(f) determining if |M−dF| is less than a tolerance; and

(g) if |M−dF| is less than the tolerance, save the dipole parameters.

29. A system according to claim 10 , wherein said means is further for, if |M−dF| is not less than the tolerance:

(h) calculating a new dF=M−dF;

(i) repeating functions (d) through (h) using the new dF until |M−dF| is less than the tolerance.

30. A system according to claim 11 , wherein said means is further for repeating functions (a) through (i) multiple times for differing distorter locations.

31. A system according to claim 10 , wherein said means is further for:

(j) collecting real-time magnetic-field data S 3 from the at least one magnetic-field sensor;

(k) obtaining real-time distorter location and orientation parameters;

(l) determining a dipole contribution D as a function of the real-time distorter location and orientation parameters;

(m) calculating corrected real-time magnetic-field data as a function of the real-time magnetic-field data S 3 and the dipole contribution D;

(n) calculating corrected position and orientation using the corrected real-time magnetic-field data; and

(o) outputting from the machine information that is a function of the corrected position and orientation data.

32. A system according to claim 13 , wherein said means is further for, prior to function (o):

(p) determining if the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled;

(q) if one, the other, or both, of the corrected position and orientation data has not settled and/or if the corrected real-time magnetic-field data has settled, repeating functions (l) through (n) and (p); and

(r) if one, the other, or both, of the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled, proceeding to function (o).

33. A system according to claim 1 , wherein said means is further for:

measuring first magnetic-field components within the tracking volume without the magnetic-field distorter present in the tracking volume;

extracting scalar magnetic potentials g j , from the first magnetic-field components;

measuring second magnetic-field components within the tracking volume with the magnetic-field distorter present in the tracking volume;

extracting induced moments p k from the second magnetic-field components;

determining gradient and scattering matrices s k,j from the scalar magnetic potentials g j , and the induced moments p k ;

determine a distorter position and orientation of the magnetic-field distorter;

evaluating and rotating the gradient and scattering matrices as a function of the distorter position and orientation so as to obtain rotated gradient and scattering matrices;

computing multipole moments as a function of the rotated gradient and scattering matrices;

calculating a scattered field as a function of the multipole moments; and

transforming the scattered field to a desired coordinate frame so as to obtain transformed scattered field.

34. A system according to claim 15 , wherein said means is further for:

(a) collecting real-time magnetic-field data from the magnetic-field sensor;

(b) summing the real-time magnetic-field data with a magnetic-field corrections so as to obtain corrected magnetic-field data;

(c) determining corrected real-time position and orientation data as a function of the corrected magnetic-field data;

(d) outputting information as a function of the corrected real-time position and orientation data;

(e) determining the magnetic-field corrections as a function of the transformed scattered field and the corrected real-time position and orientation data; and

(f) repeating functions (a) through (e).

35. A system according to claim 16 , wherein said means is further for low-pass filtering the magnetic-field corrections prior to function (b).

36. A system according to claim 15 , wherein said means is further for determining the gradient and scattering matrices s k,j from the scalar magnetic potentials g j , and the induced moments p k by solving the following equation for s k,j :

p

k

=

∑

j

=

1

J

⁢

s

k

,

j

⁢

g

j

⁡

(

x

,

y

,

z

)

.

37. A computer-readable medium containing computer-executable instructions for use in performing a method of magnetic tracking in a tracking volume in the presence of movable magnetic-field distorter, said computer-executable instructions comprising:

a first set of computer-executable instructions for obtaining first magnetic-field data regarding the magnetic field via the magnetic-field sensor while the magnetic-field sensor is in the tracking volume;

a second set of computer-executable instructions for calculating position and orientation of the magnetic-field sensor as a function of the first magnetic-field data and a difference between a first set of data items and a second set of data items, wherein the first set of data items results from second magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is present in the tracking volume, and the second set of data items results from third magnetic-field data collected from the tracking volume when the movable magnetic-field distorter is not present in the tracking volume; and

a third set of computer-executable instructions for outputting from a machine information that is a function of the position and orientation of the magnetic-field sensor.

38. A computer-readable medium according to claim 37 , wherein the data items of the first and second sets are position and orientation solutions calculated using a position-and-orientation algorithm.

39. A computer-readable medium according to claim 38 , further comprising computer-executable instructions for manipulating algorithmically the position and orientation solutions.

40. A computer-readable medium according to claim 37 , wherein the data items of the first and second sets are magnetic-field measurements.

41. A computer-readable medium according to claim 40 , further comprising computer-executable instructions for manipulating algorithmically the magnetic-field measurements.

42. A computer-readable medium according to claim 37 , further comprising computer-executable instructions for interpolating the first and second sets of data items.

43. A computer-readable medium according to claim 37 , wherein said computer-executable instructions for calculating of position and orientation include computer-executable instructions for:

rotating the first magnetic-field data by a matrix A 0 to obtain rotated first magnetic-field data having zero orientation;

rotating the second magnetic-field data by a matrix Ac to obtain zero orientation;

backing out a range R 0 from the rotated first magnetic-field data;

backing out a range Rc from the rotated second magnetic-field data;

obtaining matrix components V 0 from range R 0 ;

obtaining matrix components Vc from range Rc;

determining a difference matrix dV between matrix components V 0 and Vc;

collecting, via the magnetic-field sensor, real-time sensor field data;

obtaining matrix V from the real-time sensor data;

obtaining rebuilt sensor field data by incorporating the difference matrix dV into matrix V;

multiplying the rebuilt sensor field data by A 0 t Ac t so as to obtain a corrected matrix;

calculating corrected position and orientation data for the magnetic-field sensor as a function of the corrected matrix; and

outputting from the machine information that is a function of the corrected position and orientation data.

44. A computer-readable medium according to claim 37 , wherein said computer-executable instructions for calculating of position and orientation include computer-executable instructions for:

determining, via the magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data R 1 regarding the magnetic-field sensor at a particular location within the tracking volume;

determining, via the magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data S 1 regarding the magnetic-field sensor at the particular location;

calculating a best-fit transformation matrix T that converts S 1 into R 1 ;

collecting, via the magnetic-field sensor, real-time position and orientation data for location within the tracking volume;

applying the best-fit transformation matrix T to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

45. A computer-readable medium according to claim 37 , wherein said computer-executable instructions for calculating of position and orientation include computer-executable instructions for:

determining, via at least one magnetic-field sensor with the magnetic-field distorter present in the tracking volume, position and orientation data sets R 1 . . . Rn corresponding to differing locations of the at least one magnetic-field sensor within the tracking volume;

determining, via the at least one magnetic-field sensor with the magnetic-field distorter removed from the tracking volume, position and orientation data sets S 1 . . . Sn corresponding to the differing locations;

calculating a best-fit transformation matrices T 1 . . . Tn that convert corresponding respective ones of R 1 . . . Rn into corresponding respective ones of S 1 . . . Sn;

forming an interpolation function ƒ from best-fit transformation matrices T 1 . . . Tn;

collecting, via the at least one magnetic-field sensor, real-time position and orientation data;

applying the interpolation function ƒ to the real-time position and orientation data so as to obtain corrected position and orientation data; and

outputting from the machine information that is a function of the corrected position and orientation data.

46. A computer-readable medium according to claim 37 , wherein said computer-executable instructions for calculating of position and orientation include computer-executable instructions for:

(a) collecting, with the magnetic-field distorter at a known distorter location within the tracking volume, measured magnetic-field data from one or more sensors placed at known sensor locations and orientations within the tracking volume;

(b) calculating expected magnetic-field data expected at each of the known sensor positions and orientations;

(c) determining a difference dF between the measured magnetic-field data and the expected magnetic-field data;

(d) fitting the difference dF and the measured positions and orientations to a dipole model so as to determine dipole parameters;

(e) calculating a magnetic-field contribution M from the dipole model;

(f) determining if |M−dF| is less than a tolerance; and

(g) if |M−dF| is less than the tolerance, save the dipole parameters.

47. A computer-readable medium according to claim 46 , further comprising computer-executable instructions for, if |M−dF| is not less than the tolerance:

(h) calculating a new dF=M−dF;

(i) repeating steps (d) through (h) using the new dF until |M−dF| is less than the tolerance.

48. A computer-readable medium according to claim 47 , further comprising computer-executable instructions for repeating steps (a) through (i) multiple times for differing distorter locations.

49. A computer-readable medium according to claim 46 , further comprising computer-executable instructions for:

(j) collecting real-time magnetic-field data S 3 from the at least one magnetic-field sensor;

(k) obtaining real-time distorter location and orientation parameters;

(l) determining a dipole contribution D as a function of the real-time distorter location and orientation parameters;

(m) calculating corrected real-time magnetic-field data as a function of the real-time magnetic-field data S 3 and the dipole contribution D;

(n) calculating corrected position and orientation using the corrected real-time magnetic-field data; and

(o) outputting from the machine information that is a function of the corrected position and orientation data.

50. A computer-readable medium according to claim 49 , further comprising computer-executable instructions for, prior to step (o):

(p) determining if the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled;

(q) if one, the other, or both, of the corrected position and orientation data has not settled and/or if the corrected real-time magnetic-field data has settled, repeating steps (l) through (n) and (p); and

(r) if one, the other, or both, of the corrected position and orientation data has settled and/or if the corrected real-time magnetic-field data has settled, proceeding to step (o).

51. A computer-readable medium according to claim 37 , wherein said computer-executable instructions for calculating of position and orientation include computer-executable instructions for:

measuring first magnetic-field components within the tracking volume without the magnetic-field distorter present in the tracking volume;

extracting scalar magnetic potentials g j , from the first magnetic-field components;

measuring second magnetic-field components within the tracking volume with the magnetic-field distorter present in the tracking volume;

extracting induced moments p k from the second magnetic-field components;

determining gradient and scattering matrices S k,j from the scalar magnetic potentials g j , and the induced moments p k ;

determine a distorter position and orientation of the magnetic-field distorter;

evaluating and rotating the gradient and scattering matrices as a function of the distorter position and orientation so as to obtain rotated gradient and scattering matrices;

computing multipole moments as a function of the rotated gradient and scattering matrices;

calculating a scattered field as a function of the multipole moments; and

transforming the scattered field to a desired coordinate frame so as to obtain transformed scattered field.

52. A computer-readable medium according to claim 51 , further comprising computer-executable instructions for:

(a) collecting real-time magnetic-field data from the magnetic-field sensor;

(b) summing the real-time magnetic-field data with a magnetic-field corrections so as to obtain corrected magnetic-field data;

(c) determining corrected real-time position and orientation data as a function of the corrected magnetic-field data;

(d) outputting information as a function of the corrected real-time position and orientation data;

(e) determining the magnetic-field corrections as a function of the transformed scattered field and the corrected real-time position and orientation data; and

(f) repeating steps (a) through (e).

53. A computer-readable medium according to claim 52 , further comprising computer-executable instructions for low-pass filtering the magnetic-field corrections prior to step (b).

54. A computer-readable medium according to claim 51 , wherein said computer-executable instructions for determining of the gradient and scattering matrices s k,j from the scalar magnetic potentials g j , and the induced moments p k include computer-executable instructions for solving the following equation for s k,j :

p

k

=

∑

j

=

1

J

⁢

s

k

,

j

⁢

g

j

⁡

(

x

,

y

,

z

)

.