Electromagnetic Tracker

• US 20070299623A1
• Filed: 11/16/2005
• Published: 12/27/2007
• Est. Priority Date: 11/21/2004
• Status: Active Grant

• Current Assignee: Elbit Systems Limited
• Original Assignee: Elbit Systems Limited
• Inventors: Gandelsman, Mark, Kornblau, Giora
• Granted Patent: US 7,542,869 B2
• Time in Patent Office: Days
• US Class Current: 702/95
• CPC Class Codes: G01D 5/22 differentially influencing two coils
• CPC Class Codes: G06F 3/0346 with detection of the device orientation or free movement in a 3D space, e.g. 3D mice, 6-DOF [six degrees of freedom] pointers using gyroscopes, accelerometers or tilt-sensors

Abstract

Apparatus for adaptively tracking the position of an object in a volume of interest, the apparatus including at least one transmitter, at least one sensor assembly, and a tracking processor, the transmitter being coupled with the volume of interest, for transmitting a multiple axis, time variant, electromagnetic field through the volume of interest, the sensor assembly including at least three sensors, the sensor assembly being coupled with the object, each of the three sensors respectively measuring a respective component of the electromagnetic field, the tracking processor being coupled with the transmitter and the sensor assembly, wherein the tracking processor produces and adapts a mathematical field model describing the electromagnetic field, the tracking processor further produces and adapts a mathematical sensing model, for compensating the effect of the translational and rotational velocity of each of the sensors, wherein the tracking processor estimates the position of the object from the measured respective components of the electromagnetic field, the field model and from the sensing model.

Claims

1. Apparatus, for adaptively tracking the position of an object in a volume of interest, the apparatus comprising:

at least one transmitter, coupled with said volume of interest, for transmitting a multiple axis, time variant, electromagnetic field through said volume of interest;

at least one sensor assembly, said at least one sensor assembly including at least three sensors, said at least three sensors arranged in a fixed configuration at different predetermined locations and orientations, said at least one sensor assembly being coupled with said object, each of said at least three sensors respectively measuring a respective component of said electromagnetic field; and

a tracking processor, coupled with said at least one transmitter and said at least one sensor assembly;

wherein said tracking processor produces and adapts a mathematical field model describing said electromagnetic field, said mathematical field model is at least based on said multiple axis, time variant, electromagnetic field, said fixed configuration of said at least three sensors and said measured respective components of said electromagnetic field;

wherein said tracking processor further produces and adapts a mathematical sensing model, for compensating the effect of the translational and rotational velocity of each of said at least three sensors;

wherein said tracking processor estimates said position of said object from said measured respective components of said electromagnetic field, said field model and said sensing model;

wherein said tracking processor stores calibration parameters associated with said at least one sensor assembly; and

wherein said position of said object includes the physical location of said object and the orientation of said object.

2. The apparatus according to claim 1, further comprising:

a transmitter interface, coupled with said processor, for producing a first digital representation of a signal;

at least one digital to analog converter, coupled with said transmitter interface, for converting said first digital representation of a signal into at least one analog signal; and

an amplifier, coupled with said at least one transmitter and with said at least one digital to analog converter, for amplifying said at least one analog signal and providing each of the amplified at least one analog signal to a respective one of said at least one transmitter.

3. The apparatus according to claim 2, wherein said first digital representation of a signal includes measurements of current flowing in said at least one transmitter.

4. The apparatus according to claim 3, wherein said at least one transmitter synchronizes the measuring of said measurements of current flowing with the measuring of said respective components of said electromagnetic field.

5. The apparatus according to claim 2, wherein each said at least one analog signal is respective of at least one spatial axis.

6. The apparatus according to claim 1, further comprising:

at least three respective analog to digital converters, one for each of said at least three sensors, for converting each said measurement of a respective component of said electromagnetic field into a respective second digital representation of a signal; and

a sensor interface, coupled with said at least three respective analog to digital converters and with said processor.

7. The apparatus according to claim 6, further comprising:

at least one respective multiplexer, for each of said at least three respective analog to digital converters, for coupling said at least three respective analog to digital converters with said sensor interface.

8. The apparatus according to claim 1, wherein said tracking processor comprises:

a position processor, for determining the position of said at least three sensors;

a magnetic field model generator, coupled with said position processor, for generating said mathematical field model; and

a magnetic flux to magnetic field converter, coupled with said magnetic field model generator and with said position processor, for partially transforming said measured respective components of said electromagnetic field into a measure of the amplitude components of said electromagnetic field.

9. The apparatus according to claims 8, wherein said tracking processor further comprises a storage unit, coupled with said magnetic flux to magnetic field converter, for storing said calibration parameters associated with said at least one sensor assembly and said measured respective components of said electromagnetic field.

10. The apparatus according to claim 8, wherein said tracking processor further comprises a sensor motion effect compensator, coupled with said magnetic flux to magnetic field converter and with said position processor, for compensating the effect of the translational and rotational velocity of each of said at least three sensors.

11. The apparatus according to claim 10, wherein said tracking processor further comprises a grade assignment module, coupled with said position processor, for assigning grades to the estimated position of said at least three sensors.

12. The apparatus according to claim 8, wherein said tracking processor further comprises a model accuracy evaluator, coupled with said position processor, for evaluating the accuracy to which said calibration parameters are known and the accuracy to which said mathematical field model estimates said measure of the amplitude components of said electromagnetic field by said at least three sensors.

13. The apparatus according to claim 8, wherein said tracking processor further comprises a parameters adaptation module coupled with said position processor, for adapting said calibration parameters and the parameters defining said mathematical field model and said mathematical sensing model.

14. The apparatus according to claim 13, wherein said tracking processor further comprises an adaptation accuracy evaluator, coupled with said parameter adaptation module, for evaluating the accuracy of an adapted mathematical field model and an adapted mathematical sensing model.

15. The apparatus according to claim 8, wherein said tracking processor further comprises a model comparer module, coupled with said position processor, for comparing said mathematical field model and said mathematical sensing model with an adapted mathematical field model and an adapted mathematical sensing model.

16. The apparatus according to claim 1, wherein said mathematical field model comprises at least one of:

a harmonic expansion function describing said electromagnetic field;

an analytic relation describing said electromagnetic field;

at least one parameter set describing said electromagnetic field;

a matrix function for estimating amplitude components of said electromagnetic field;

a model reference frame coordinate system between said object and said volume of interest;

a sensor reference frame coordinate system between said at least three sensors and said at least one sensor assembly; and

a relationship between said model reference frame coordinate system and said sensor reference frame coordinate system.

17. The apparatus according to claim 16, wherein said at least one parameter set is selected from the list consisting of:

a coordinate relationship between said at least one transmitter and said at least three sensors;

at least one expansion center for each of said mathematical field model and said mathematical sensing model;

at least one expansion coefficient for each of said mathematical field model and said mathematical sensing model.

18. The apparatus according to claim 1, wherein said respective components of said electromagnetic field are related to the flux of said electromagnetic field.

19. The apparatus according to claim 16, wherein said matrix function for estimating comprises estimating said amplitude components from an observation point within each of said at least three sensors.

20. The apparatus according to claim 19, wherein said observation point is the magnetic center of each of said at least three sensors.

21. The apparatus according to claim 16, wherein said relationship comprises:

at least three respective radius vectors, from the origin of said sensor reference frame to an observation point in each of said at least three sensors;

at least one rotation matrix, for relating the orientation of said sensor reference frame to the orientation of said model reference frame; and

at least one vector, for relating the location of the origin of said sensor reference frame relative to said model reference frame.

22. The apparatus according to claim 16, wherein said calibration parameters are selected from the list consisting of:

the orientation of each of said at least three sensors with respect to said sensor reference frame;

at least three respective radius vectors, from the origin of said sensor reference frame to an observation point in each of said at least three sensors;

the gain characteristics of each of said at least one sensor assembly;

parameters relating to the electronic components of said at least one sensor assembly; and

the known error characteristics of said calibration parameters.

23. The apparatus according to claim 10, wherein said measured respective components of said electromagnetic field are expected to follow a mathematical periodic function of time, wherein said sensor motion effect compensator uses said measured respective components of said electromagnetic field to estimate an amplitude and a phase of said mathematical periodic function of time.

24. The apparatus according to claim 1, wherein said measured respective components of said electromagnetic field are expected to follow a mathematical periodic function of time, wherein said mathematical sensing model comprises:

a mathematical definition of at least one of an amplitude and a phase of said mathematical periodic function of time, as a function of time.

25. The apparatus according to claim 24, wherein said at least one function of time is expressed mathematically as at least one expansion function, wherein at least one expansion parameter of said at least one function of time is estimated each time said measured respective components of said electromagnetic field are acquired.

26. The apparatus according to claim 25, wherein said tracking processor estimates said at least one expansion parameter by minimizing the deviation between said measured respective components of said electromagnetic field and said mathematical periodic function of time.

27. The apparatus according to claim 24, wherein the number of expansion parameters of said at least one function of time depends on at least one of:

a predetermined time period wherein said measured respective components of said electromagnetic field are measured;

the typical velocity and acceleration of said object; and

mathematical field gradients of said mathematical field model.

28. The apparatus according to claim 27, wherein said number of said expansion parameters is fixed.

29. The apparatus according to claim 27, wherein said tracking processor adapts said mathematical sensing model by varying said number of said expansion parameters.

30. The apparatus according to claim 29, wherein said varying by said tracking processor depends on a figure of merit.

31. The apparatus according to claim 8, wherein said tracking processor performs said partial transformation, by expanding an expansion function, for each respective component of said electromagnetic field, and by expanding at least one of an amplitude and a phase of a mathematical periodic function of time, as at least one function of time, in terms of a basic harmonic function.

32. The apparatus according to claim 31, wherein said basic harmonic function comprises expansion coefficients, wherein said expansion coefficients relate said respective measured components of said electromagnetic field to said mathematical field model and to mathematical field gradients of said mathematical field model.

33. The apparatus according to claim 32, wherein said tracking processor modifies and adapts said expansion coefficients.

34. The apparatus according to claim 31, wherein the number of expansion terms of said basic harmonic function depends on at least one of:

the approximate size of said at least three sensors; and

an estimation of the gradients of said mathematical field model.

35. The apparatus according to claim 34, wherein said number of expansion terms is fixed.

36. The apparatus according to claim 34, wherein said mathematical field model is adapted by said tracking processor by varying said number of expansion terms.

37. The apparatus according to claim 36, wherein said varying by said position processor and said magnetic flux to magnetic field converter depends on a figure of merit.

38. The apparatus according to claim 8, wherein said magnetic flux to magnetic field converter transforms the remaining portion of said transformation by extrapolating the position of said at least three sensors, and estimating the mathematical field gradients of said basic harmonic function at said extrapolated position.

39. The apparatus according to claim 38, wherein said extrapolation is based upon an assumption, wherein said assumption is selected from the list consisting of:

a fixed translational and rotational velocity of said at least three sensors in a predetermined time period; and

a fixed translational and rotational velocity of said at least three sensors between the center of two predetermined time periods.

40. The apparatus according to claim 8, wherein said magnetic flux to magnetic field converter and said position processor, transform the remaining portion of said transformation by iteratively estimating said amplitude components of said electromagnetic field, based on a model of said at least three sensors as volumeless point-like sensors, estimating the position of said at least three sensors, and estimating the mathematical gradient terms of said basic harmonic function.

41. The apparatus according to claim 8, wherein said position processor transforms the remaining portion of said transformation by minimizing the deviation between said respective measured components of said electromagnetic field compensated for by a sensor motion effect compensator, and respective components of said electromagnetic field estimated from said mathematical field model.

42. The apparatus according to claim 41, wherein said position processor determines the position of said at least three sensors, thereby determining the position of said object, based on said mathematical field model, by minimizing the deviation between estimates of said amplitude components based on said mathematical field model and estimates of said amplitude components estimated from said remaining portion of said transformation.

43. The apparatus according to claim 8, wherein said position processor determines a figure of merit,

wherein said figure of merit is defined as the normalized residual error of the minimization of the deviation between estimates of said amplitude components based on said mathematical field model and estimates of said amplitude components estimated from a remaining portion of said transformation,

wherein said mathematical field model comprises:

at least one parameter set describing said electromagnetic field;

a matrix function for estimating said amplitude components of said electromagnetic field; and

a relationship between a model reference frame coordinate system and a sensor reference frame coordinate system,

wherein said relationship comprises;

at least three respective radius vectors, from the origin of said sensor reference frame to an observation point within each of said at least three sensors;

at least one rotation matrix, for relating the orientation of said sensor reference frame to the orientation of said model reference frame; and

at least one vector, for relating the location of the origin of said sensor reference frame to said model reference frame.

wherein said figure of merit is defined mathematically as

$\mathrm{FOM}=\sqrt{\frac{1}{N_f<br><br>N_c}<br><br>\underset{m=1}{\overset{N_f}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{k=1}{\overset{N_c}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{<br><br>B_{\mathrm{mk}}^{\mathrm{\alpha <br><br>}}-{\mathrm{\Phi <br><br>}}_{\mathrm{mk}}^{\mathrm{\alpha <br><br>}}<br><br>\left({\mathrm{\theta <br><br>}}_{11},\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>},{\mathrm{\theta <br><br>}}_{{\mathrm{SN}}_f},P^{*},O^{*},{\stackrel{\to <br><br>}{r}}_1,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>},{\stackrel{\to <br><br>}{r}}_{N_c}\right)<br><br>}^2}{{<br><br>B_{\mathrm{mk}}^{\mathrm{\alpha <br><br>}}<br><br>}^2}}$

wherein N_f is defined as the total number of analog signals generated by said at least one transmitter, N_c is defined as the total number of said at least three sensors, B_mk^α

is defined as the estimated amplitude components of said electromagnetic field at frequency m in sensor k, and Φ

_mk^α

(θ

₁₁, . . . , θ

_SNf, P*,O*,,{right arrow over (r)}₁, . . . , {right arrow over (r)}_Nc) is said matrix function, wherein θ

₁₁, . . . , θ

_SNf is defined as said at least one parameter set, P* is defined as the estimated location of said object, O* is defined as the estimated orientation of said object, and {right arrow over (r)}₁, . . . , {right arrow over (r)}_Nc is defined as said radius vectors.

44. The apparatus according to claim 8, wherein said tracking processor further comprises a grade assignment module, coupled with said position processor,

wherein said grade assignment module groups together said respective measured components of said electromagnetic field compensated for by a sensor motion effect compensator and said estimated position of said object, based on said mathematical field model, into at least one point.

45. The apparatus according to claim 44, wherein said grade assignment module assigns said at least one point at least one grade,

wherein said at least one grade depends on at least one factor selected from the list consisting of:

a figure of merit of said at least one point;

the position of said at least one point in said volume of interest; and

grades assigned to previous points;

wherein each of said at least one factor has a relative weight.

46. The apparatus according to claim 45, wherein said grade assignment module lowers the value of said at least one grade, over time.

47. The apparatus according to claim 8, wherein said tracking processor further comprises a model accuracy evaluator, coupled with said position processor,

wherein said model accuracy evaluator evaluates the accuracy to which said calibration parameters are known and the accuracy to which said mathematical field model estimates said amplitude components of said electromagnetic field estimated by said at least three sensors.

48. The apparatus according to claim 47, wherein said determination of the accuracy depends on at least one of:

a figure of merit for accumulated measurements of said measured respective components of said electromagnetic field;

the accuracy of said apparatus achieved so far;

the desired accuracy of said apparatus;

the mathematical observability of at least one parameter set, said at least one parameter set describing said electromagnetic field; and

said calibration parameters.

49. The apparatus according to claim 8, wherein said tracking processor further comprises a parameters adaptation module coupled with said position processor and with said magnetic field model generator,

wherein said parameters adaptation module adapts at least one of:

at least one parameter set describing said electromagnetic field;

said calibration parameters; and

the expansion parameters of at least one function of time expressed as an expansion function,

wherein at least one of an amplitude and a phase of a mathematical periodic function of time is expressed as said at least one function of time,

by minimizing at least one of;

the deviation between estimates of said amplitude based on said mathematical field model and values of said amplitude estimated from a basic harmonic function; and

the deviation between said measured respective components of said electromagnetic field, compensated by said mathematical periodic function of time, and estimates of said respective components of said electromagnetic field based on said mathematical field model.

50. The apparatus according to claim 49, wherein said tracking processor further comprises an adaptation accuracy evaluator coupled with said position processor and with said parameters adaptation module,

wherein said adaptation accuracy evaluator evaluates the accuracy to which said mathematical field model estimates the amplitude of said electromagnetic field estimated by said at least three sensors and the accuracy in said calibration parameters, after said minimizing.

51. The apparatus according to claim 50, wherein said adaptation accuracy evaluator evaluates said accuracy by computing a figure of merit for each said measured respective components, of said electromagnetic field, used in said minimizing.

52. Method, for adaptively tracking the position of an object in a volume of interest, comprising the procedures of:

transmitting a multiple axis, time variant, electromagnetic field through said volume of interest;

measuring a respective component of said electromagnetic field, in at least one sensor assembly, said at least one sensor assembly including at least three sensors, said at least three sensors arranged in a fixed configuration at different predetermined locations and orientations;

producing a mathematical field model describing said electromagnetic field, said field model based on said multiple axis, time variant, electromagnetic field, said fixed configuration of said at least three sensors and said measured respective components of said electromagnetic field;

producing a mathematical sensing model, for compensating the effect of the translational and rotational velocity of each of said at least three sensors; and

determining said position of said object, from said measured respective components of said electromagnetic field, said field model and said sensing model,

wherein said position of said object includes the physical location of said object and the orientation of said object.

53. The method according to claim 52, wherein said mathematical field model comprises at least one of:

a harmonic expansion function describing said electromagnetic field;

an analytic relation describing said electromagnetic field;

at least one parameter set describing said electromagnetic field;

a matrix function for estimating amplitude components of said electromagnetic field;

a model reference frame coordinate system between said object and said volume of interest;

a sensor reference frame coordinate system between said at least three sensors and said at least one sensor assembly; and

a relationship between said model reference frame coordinate system and said sensor reference frame coordinate system.

54. The method according to claim 52, wherein said respective components of said electromagnetic field are related to the flux of said electromagnetic field.

55. The method according to claim 53, wherein said matrix function for estimating comprises estimating said amplitude components from an observation point within each of said at least three sensors.

56. The method according to claim 53, wherein said relationship comprises:

at least three respective radius vectors, from the origin of said sensor reference frame to an observation point in each of said at least three sensors;

at least one rotation matrix, for relating the orientation of said sensor reference frame to the orientation of said model reference frame; and

at least one vector, for relating the location of the origin of said sensor reference frame relative to said model reference frame.

57. The method according to claim 52, further comprising the procedure of storing calibration parameters associated with said at least three sensors.

58. The method according to claim 57, wherein said calibration parameters are selected from the list consisting of:

the orientation of each of said at least three sensors with respect to a sensor reference frame;

at least three respective radius vectors, from the origin of said sensor reference frame to an observation point in each of said at least three sensors;

the gain characteristics of each of said at least one sensor assembly;

parameters relating to the electronic components of said at least one sensor assembly; and

the known error characteristics of said calibration parameters.

59. The method according to claim 52, wherein said mathematical field model is constructed as a function selected from the list consisting of:

a linear function; and

a non-linear function.

60. The method according to claim 52, further comprising the procedure of storing an expansion function for each respective component of said electromagnetic field.

61. The method according to claim 52, further comprising the procedure of estimating an amplitude and a phase of a mathematical periodic function of time associated with said measured respective components of said electromagnetic field.

62. The method according to claim 52, wherein said measured respective components of said electromagnetic field are expected to follow a mathematical periodic function of time, wherein said mathematical sensing model comprises:

a mathematical definition of at least one of said amplitude and said phase of said mathematical period function of time, as a function of time.

63. The method according to claim 62, wherein said at least one function of time is expressed mathematically as at least one expansion function, wherein at least one expansion parameter of said at least one function of time is estimated each time said measured respective components of said electromagnetic field are acquired.

64. The method according to claim 63, further comprising the procedure of estimating said at least one expansion parameter by minimizing the deviation between said measured respective components of said electromagnetic field and said mathematical periodic function of time.

65. The method according to claim 63, wherein the number of expansion parameters of said at least one function of time depends on at least one of:

a predetermined time period wherein said measured respective components of said electromagnetic field are measured;

the typical velocity and acceleration of said object; and

mathematical field gradients of said mathematical field model.

66. The method according to claim 65, wherein said number of said expansion parameters is fixed.

67. The method according to claim 65, further comprising the procedure of adapting said mathematical sensing model by varying said number of said expansion parameters.

68. The method according to claim 67, wherein said procedure of varying depends on a figure of merit.

69. The method according to claim 52, further comprising the procedure of partially transformation said measured respective components of said electromagnetic field into a partial estimate of the amplitude components of said electromagnetic field, by expanding an expansion function, for each respective component of said electromagnetic field, and by expanding at least one of an amplitude and a phase of a mathematical periodic function of time, as at least one function of time, in terms of a basic harmonic function.

70. The method according to claim 69, wherein said basic harmonic function comprises at least one expansion coefficient, wherein said at least one expansion coefficient relates said respective measured components of said electromagnetic field to said mathematical field model and to mathematical field gradients of said mathematical field model.

71. The method according to claim 70, further comprising the procedure of adapting said expansion coefficients.

72. The method according to claim 69, wherein the number of expansion terms of said basic harmonic function depends on at least one of:

the approximate size of said at least three sensors; and

an estimation of the gradients of said mathematical field model.

73. The method according to claim 72, wherein said number of expansion terms is fixed.

74. The method according to claim 72, further comprising the procedure of adapting said mathematical field model by varying said number of expansion terms.

75. The method according to claim 74, wherein said procedure of varying depends on a figure of merit.

76. The method according to claim 69, further comprising the procedure of transforming said respective partial estimates of said amplitude components of said electromagnetic field into full respective estimates of said amplitude components of said electromagnetic field, by extrapolating the position of said at least three sensors, and estimating the mathematical field gradients of said basic harmonic function at said extrapolated position.

77. The method according to claim 76, wherein said extrapolation is based upon an assumption, wherein said assumption is selected from the list consisting of:

a fixed translational and rotational velocity of said at least three sensors in a predetermined time period; and

a fixed translational and rotational velocity of said at least three sensors between the center of two predetermined time periods.

78. The method according to claim 69, further comprising the procedure of transforming said respective partial estimates of said amplitude components of said electromagnetic field into full respective estimates of said amplitude components of said electromagnetic field, by iteratively estimating said amplitude components of said electromagnetic field, based on a model of said at least three sensors as volumeless point-like sensors, estimating the position of said at least three sensors, and estimating the mathematical gradient terms of said basic harmonic function.

79. The method according to claim 69, further comprising the procedure of transforming said respective partial estimates of said amplitude components of said electromagnetic field into full respective estimates of said amplitude components of said electromagnetic field, by minimizing the deviation between compensated respective measured components of said electromagnetic field, and respective components of said electromagnetic field estimated from said mathematical field model.

80. The method according to claim 79, further comprising the procedure of determining the position of said at least three sensors, thereby determining the position of said object, based on said mathematical field model, by minimizing the deviation between estimates of said amplitude components based on said mathematical field model and estimates of said amplitude components estimated from said procedure of transforming said respective partial estimates of said amplitude components.

81. The method according to claim 52, further comprising the procedure of assigning a grade to each said estimated position of said object.

82. The method according to claim 52, further comprising the procedure of grouping together said respective measured components of said electromagnetic field, compensated for by said mathematical sensing model, and said estimated position of said object, based on said mathematical field model, into at least one point.

83. The method according to claim 82, further comprising the procedure of assigning at least one grade to said at least one point,

wherein said at least one grade depends on at least one factor selected from the list consisting of:

a figure of merit of said at least one point;

the position of said at least one point in said volume of interest; and

grades assigned to previous points;

wherein each of said at least one factor has a relative weight.

84. The method according to claim 83, further comprising the procedure of lowering the value of said at least one grade, over time.

85. The method according to claim 52, further comprising the procedure of evaluating the accuracy to which calibration parameters, associated with said at least three sensors, are known and the accuracy to which said mathematical field model estimates said amplitude components of said electromagnetic field estimated by said at least three sensors.

86. The method according to claim 85, wherein said procedure of evaluating the accuracy depends on at least one of:

a figure of merit for accumulated measurements of said measured respective components of said electromagnetic field;

the accuracy achieved so far;

the desired accuracy;

the mathematical observability of at least one parameter set, said at least one parameter set describing said electromagnetic field; and

said calibration parameters.

87. The method according to claim 52, further comprising the procedure of determining a figure of merit for each said estimated position of said object.

88. The method according to claim 52, further comprising the procedure of adaptively modifying at least one of:

said mathematical field model; and

said mathematical sensing model.

89. The method according to claim 52, further comprising the procedure of adapting at least one of:

at least one parameter set describing said electromagnetic field;

at least one calibration parameter, associated with said at least three sensors; and

the expansion parameters of at least one function of time expressed as an expansion function,

wherein at least one of an amplitude and a phase of a mathematical periodic function of time is expressed as said at least one function of time,

by minimizing at least one of;

the deviation between estimates of amplitude components of said electromagnetic field based on said mathematical field model and values of said amplitude components estimated from a basic harmonic function; and

the deviation between said measured respective components of said electromagnetic field, compensated by said mathematical periodic function of time, and estimates of said respective components of said electromagnetic field based on said mathematical field model.

90. The method according to claim 89, wherein said procedure of minimizing includes at least one sub-procedure selected from the list consisting of:

minimizing said deviations by excluding non-observable parameters from said minimizations;

minimizing said deviations by considering said non-observable parameters as constants; and

minimizing said deviations under at least one mathematical constraint.

91. The method according to claim 89, further comprising the procedure of evaluating the accuracy to which said mathematical field model estimates the amplitude components of said electromagnetic field estimated by said at least three sensors and the accuracy in said calibration parameters, after said minimizing.

92. The method according to claim 91, wherein said procedure of evaluating comprises computing a figure of merit for each said measured respective component, of said electromagnetic field, used in said minimizing.

93. The method according to claim 52, further comprising the procedure of determining an accuracy value for parameters defining said mathematical field model, said mathematical sensing model and calibration parameters associated with said at least three sensors.

94. The method according to claim 52, further comprising the procedure of determining an accuracy for at least one of:

an adapted model of said mathematical field model; and

an adapted model of said mathematical sensing model.

95. The method according to claim 52, further comprising the procedure of adding an expansion center to at least one of:

said mathematical field model; and

said mathematical sensing model.

96. The method according to claim 52, further comprising the procedure of comparing at least one of:

an adapted model of said mathematical field model; and

an adapted model of said mathematical sensing model,

with at least a respective one of;

said mathematical field model; and

said mathematical sensing model,

said procedure of comparing being performed on a competitive basis, for a predetermined amount of time.

97. (canceled)

98. (canceled)