Determining positioning by measuring an oscillating magnetic field produced by non-orthogonal generators

Abstract

The invention relates to a method for determining at least one component of the positioning of a receiver (24) relative to a transmitter (22), the transmitter (22) comprising at least two magnetic generators (30, 32, 34), the method comprising the following steps: - measuring a resulting magnetic field; - demodulating the measurement signal so as to determine a plurality of candidate measurements; - applying, to each candidate measurement, a correction that aims to compensate for a directional orthogonality defect in the magnetic generators (30, 32, 34) so as to obtain a corresponding corrected measurement; - calculating a value representative of the likelihood that this candidate measurement reflects the actual contributions of each alternating magnetic field; - selecting a selected measurement corresponding to the highest likelihood; and - determining the at least one component of the positioning of the receiver (24).

Description

[0001] DESCRIPTION

[0002] TITLE: DETERMINATION OF POSE BY MEASUREMENT OF AN OSCILLATING MAGNETIC FIELD PRODUCED BY NON-ORTHOGONAL GENERATORS

[0003] FIELD OF THE INVENTION

[0004] The present invention relates to the determination of at least one component of the pose, i.e. the position and orientation, of a first object relative to a second object, by measuring at the first object an oscillating magnetic field produced by a transmitter secured to the second object. The present invention relates more particularly to the implementation of this determination when no physical link connects the two objects.

[0005] TECHNOLOGICAL BACKGROUND

[0006] To determine the pose of an object, i.e. its position and orientation, in a frame of reference, it is known to use magnetic technology pose determination systems, commonly called EMTs (from the English "Electromagnetic tracker"). These systems generally comprise a fixed transmitter in the frame of reference, formed of three coils arranged so as to form a substantially orthogonal fixed trihedron, and a receiver secured to the object whose pose is to be determined, this receiver being formed of three magnetic sensors arranged so as to form a substantially orthogonal mobile trihedron. Time-dependent electric currents circulate in the coils of the transmitter and cause three magnetic fields to appear which are picked up by the sensors of the receiver. Each sensor of the receiver measures, for each of the emitted magnetic fields, the projection of this field on the direction which directs the sensor.This gives a total of nine components that allow the transition from the mobile trihedron to the fixed trihedron. Indeed, these nine components depend on the position and orientation of the receiver relative to the transmitter.

[0007] To enable the identification, on the receiver side, of the contribution of each coil to the captured magnetic field, several alternatives exist.

[0008] A first alternative, described in US 5,453,686, uses time division multiplexing: each coil successively produces a continuous magnetic field during a specific time range. Thus, at each instant, the receiver sensors only measure the components of the magnetic field emitted by a single coil. This technique, however, has many drawbacks. First of all, the magnetic field measured on the receiver side is disturbed by constant magnetic fields, such as the Earth's magnetic field, which are themselves disturbed by floors and walls containing metallic elements. Secondly, this technique requires the use of magnetometers as sensors, which are particularly difficult to implement over a wide range.

[0009] Another alternative is to excite the transmitter coils with alternating currents at natural frequencies. The magnetic fields generated are thus alternating magnetic fields that can be distinguished from each other by demodulation using knowledge of the coil excitation frequency. The sensitivity to constant magnetic fields can thus be neglected and the sensors can be formed from simple coils across which the induced voltage is measured.

[0010] This second alternative, however, has a drawback: to determine the sign of each component of each of the magnetic fields generated by the transmitter, it is necessary for the receiver's clock signal to be synchronous with that of the transmitter. Indeed, without this synchronization, the time reference of the signals measured by the receiver's sensors is out of phase by an unknown amount compared to the time reference of the emitted magnetic fields, which creates doubt as to the signs of the components of the measured magnetic fields.

[0011] This need for clock signal synchronization makes it difficult to develop wireless EMT systems, i.e. systems without a physical connection between the transmitter and the receiver. Indeed, although solutions have been proposed for synchronizing the clock signals of the transmitter and receiver without a physical connection between the two, these solutions still have too many drawbacks.

[0012] For example, it has been proposed to synchronize the clock signals using a synchronization signal emitted by the transmitter to the receiver, this synchronization signal being either emitted by a dedicated transmitter or integrated into the excitation currents of the transmitter coils (for example by consisting of a periodic interruption of the emission of the magnetic fields). These solutions are however not entirely satisfactory, because they are cumbersome to implement, require additional components, reduce the availability of the final measurements and / or increase the latency of the system. It was also proposed in FR 3 012 888 to excite each coil of the transmitter not by means of an alternating signal, but by means of a pseudo-random binary sequence, the demodulation then being based on the calculation of a correlation function.Although this method naturally leads to an alignment of the sequences which makes it possible to resolve phase problems, it induces a significant latency which requires the use of other sensors such as an inertial unit to be compensated for, which has the disadvantage of making the system more expensive and complex.

[0013] To solve these problems, attempts have been made to do without the synchronization of clock signals by proposing asynchronous demodulation solutions to remove doubts about the signs of the components of the measured magnetic fields.

[0014] One of these solutions, described in US 10,746,819, consists of combining the EMT system with an inertial unit to remove the ambiguity existing on the signs of the components of the measured magnetic fields. This solution, however, has the disadvantage of increasing the cost and complexity of the system by requiring the integration of external sensors.

[0015] Another solution consists of tracking the movement of the receiver relative to the transmitter or, as described in US 20080120061, tracking the phase shifts between the emitted fields and the reference signals produced by the receiver, after an initialization step consisting of bringing the receiver into a known pose. This solution is however restrictive since it requires an initialization phase before any use of the system. In addition, it is vulnerable to signal losses between the transmitter and the receiver, for example by masking or distance.

[0016] STATEMENT OF THE INVENTION

[0017] An objective of the invention is to enable, in a simple, robust and inexpensive manner, the determination of at least one component of the pose of a first object relative to a second object, by measuring at the first object an oscillating magnetic field produced by a transmitter secured to the second object. Other objectives are to limit the use of additional sensors (other than magnetic sensors), to be able to dispense with physical connection and synchronization of the signals between the transmitter and the receiver, and to dispense with an initialization step consisting of bringing the receiver into a pose known at least approximately. To this end, the invention relates, according to a first aspect, to a method for determining at least one component of the pose of a receiver relative to a transmitter,the transmitter comprising at least two magnetic generators each oriented in a specific direction and capable of generating an alternating magnetic field at a specific frequency, the magnetic generators being arranged relative to each other so that their directions are two by two non-coaxial and non-orthogonal, and the receiver being capable of measuring the components of a resulting magnetic field, formed from the superposition of the alternating magnetic fields generated by the magnetic generators of the transmitter, in three non-coplanar directions, the method comprising the following steps: - measurement of the resulting magnetic field by the receiver so as to obtain a measurement signal representative of the resulting magnetic field,- demodulation of the measurement signal so as to determine a plurality of candidate measurements each formed from a set of candidate contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - application to each candidate measurement of a correction aimed at compensating for the effect induced on the measurement signal by the lack of orthogonality of the directions of the magnetic generators, so as to obtain for each candidate measurement a corresponding corrected measurement, - calculation, for each candidate measurement, by means of the corresponding corrected measurement, of data representative of the likelihood that this candidate measurement gives the real contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - selection of a measurement selected from the candidate measurements,the selected measurement being constituted by that of the candidate measurements whose representative data indicates the highest likelihood, and - deduction, from the corrected measurement corresponding to the selected measurement, of said at least one component of the pose of the receiver relative to the transmitter.,

[0018] According to particular embodiments of the invention, the determination method also has one or more of the following characteristics, taken in isolation or in any technically possible combination(s): - the magnetic generators are at least three in number and are arranged relative to each other so that their directions are non-coplanar; - the corrective is common to all the candidate measurements; - the magnetic generators have substantially coincident centers; - the data representative of the likelihood is calculated by means of a decomposition into singular values ​​of a matrix of the corresponding corrected measurement;- the calculation of the data representative of the likelihood comprises the following sub-step: for each candidate measurement, estimation of a distance of the corresponding corrected measurement to a reference space consisting of the measurements that can be obtained in a model of the system formed by the transmitter and the receiver in which the magnetic generators are orthogonal to each other, the data representative of the likelihood being a function of said distance; - the distance is a function of the diagonal terms of a diagonal matrix resulting from the decomposition into singular values ​​of the matrix of the corresponding corrected measurement; - the distance is determined by the following formula:; where S 11 , S 22 and S 33 are the diagonal terms of a diagonal matrix S of positive real values ​​ordered so that S 11 ≥ S 22 ≥ S 33, this diagonal matrix resulting from a singular value decomposition of the corrected measurement matrix such that the diagonal matrix S verifies the following relation:

[0019] M k = PSQ T where M k is the matrix of the corrected measure, P is a first matrix belonging to the group SO (3) of rotation matrices in dimension 3 and Q Tis the transpose of a second matrix Q also belonging to the group S0(3); - the calculation of the data representative of the likelihood comprises, for each candidate measurement, the following sub-steps: o deduction, from the corresponding corrected measurement, of a candidate pose of the receiver relative to the transmitter, o estimation of a theoretical measurement of the magnetic field resulting in the candidate pose in a model of the system formed by the transmitter and the receiver, and o evaluation of a distance of the candidate measurement or of the corresponding corrected measurement to said theoretical measurement, the data representative of the likelihood being a function of said distance; - the candidate pose of the receiver relative to the transmitter is deduced from the singular value decomposition of the matrix of the corresponding corrected measurement; - the candidate pose is characterized by a pair (r, R) such that: with: o P a first matrix belonging to the group SO(3) and Q a second matrix Q also belonging to the group SO(3) such that M k = PSQ T , where M k is the matrix of the corrected measure and S is a diagonal matrix of ordered positive real values, o Q 11 , Q 21 and Q 31 are the terms of the first column of the matrix Q, and or is given by the following formula: , where μ0the permeability vacuum magnetic field, m the amplitude of the magnetic moments of the magnetic generators and Tr(S) the trace of the matrix S; - the system model takes into account the lack of orthogonality of the magnetic generators and the distance evaluated at the evaluation stage consists of a distance from the candidate measurement to said theoretical measurement; - the system model considers the magnetic generators orthogonal to each other, and the distance evaluated at the evaluation stage consists of a distance from the corrected measurement to said theoretical measurement;- the representative data is a decreasing, respectively increasing, function of the likelihood, the method comprising an additional step of comparing the representative data of each candidate measurement to a predetermined threshold, the selection of the selected measurement being based on the representative data of the candidate measurements only if the representative data of a single candidate measurement is lower, respectively higher, than said predetermined threshold;- when there is not a single candidate measurement whose representative data is lower, respectively higher, than the predetermined threshold, the method comprises the following steps: o deduction, for each candidate measurement, from the corresponding corrected measurement, of a candidate pose of the receiver relative to the transmitter, and o calculation of a distance from the candidate pose to a previous pose, the selected measurement being constituted by that of the candidate measurements for which the corresponding candidate pose has the smallest distance to the previous pose;- when there is not a single candidate measurement whose representative data is lower, respectively higher, than the predetermined threshold, the following step: o determination, for each generated alternating magnetic field, of candidate phase shifts of said generated alternating magnetic field with respect to a demodulation signal used to demodulate the measurement signal, and o selection, for each generated alternating magnetic field, of that of the candidate phase shifts which minimizes a difference with a previous phase shift of said generated alternating magnetic field with respect to this same demodulation signal, the selected measurement being constituted by that of the candidate measurements for which, for each generated alternating magnetic field, the signs of the candidate contributions are consistent with the selected phase shift; - the calculation step is implemented without using measurements from inertial sensors integral with the receiver;and - the receiver has magnetic sensors for measuring the components of the resulting magnetic field and the calculation step is implemented without using measurements from additional sensors other than the magnetic sensors.;

[0020] The invention also relates, according to a second aspect, to a computer program product comprising code instructions for the implementation, by a processor, of a determination method according to the first aspect.

[0021] The invention also relates, according to a third aspect, to a recording medium readable by a computer on which a computer program product according to the second aspect is stored.

[0022] The invention also relates, according to a fourth aspect, to a transmitter for implementing a determination method according to the first aspect, the transmitter comprising at least two magnetic generators each oriented in a specific direction and capable of generating an alternating magnetic field at a specific frequency, the magnetic generators being arranged relative to each other so that: - a first generator is oriented in a first generator direction coinciding with a first direction of an orthogonal reference frame attached to the transmitter, and - a second generator is oriented in a second generator direction forming a first angle with a second direction of the orthogonal reference frame and included in a plane defined by the first and second directions of the orthogonal reference frame, the first angle being greater than or equal to 0.05 radians.

[0023] According to particular embodiments of the invention, the transmitter also has one or more of the following characteristics, taken in isolation or in any technically possible combination(s): - a third magnetic generator capable of generating an alternating magnetic field at a natural frequency, said third generator being oriented along a third generator direction forming a second angle, greater than or equal to 0.05 radians, with a third direction of the orthogonal reference frame; and - the third generator direction is non-coplanar with each of the planes defined by two of the following three directions: the first generator direction, the second generator direction and the third direction of the orthogonal reference frame.

[0024] The invention also relates, according to a fifth aspect, to a method for designing a transmitter for implementing a determination method according to the first aspect, comprising the following steps: - arrangement of a first magnetic generator of the transmitter, capable of generating an alternating magnetic field at a first frequency, such that it is oriented in a first generator direction coinciding with a first direction of an orthogonal reference frame attached to the transmitter, and - arrangement of a second magnetic generator of the transmitter, capable of generating an alternating magnetic field at a second frequency different from the first frequency, such that it is oriented in a second generator direction forming a first angle with a second direction of the orthogonal reference frame and included in a plane defined by the first and second directions of the orthogonal reference frame, the first angle being greater than or equal to 0.05 radians.According to a particular embodiment of the invention, the design method also has the following characteristic: - the method comprises an additional step of arranging a third magnetic generator of the transmitter, capable of generating an alternating magnetic field at a third frequency different from the first and second frequencies, so that it is oriented in a third generator direction forming a second angle, greater than or equal to 0.05 radians, with a third direction of the orthogonal reference frame.

[0025] The invention also relates, according to a sixth aspect, to a method of manufacturing a transmitter for implementing a determination method according to the first aspect, comprising the design of a transmitter by means of a method according to the fifth aspect, followed by the production of this transmitter.

[0026] The invention finally relates, according to a seventh aspect, to a system for determining at least one component of the pose of a first object relative to a second object, said determination system comprising: - a transmitter secured to the second object, said transmitter comprising at least two magnetic generators each oriented in a specific direction and capable of generating an alternating magnetic field at a specific frequency, the magnetic generators being arranged relative to each other so that their directions are two by two non-coaxial and non-orthogonal, - a receiver secured to the first object, said receiver being capable of measuring the components of a resulting magnetic field, formed from the superposition of the alternating magnetic fields generated by the magnetic generators of the transmitter, in three non-coplanar directions,and - a data processing unit configured to implement a determination method according to the first aspect.,

[0027] According to particular embodiments of the invention, the determination system also has one or more of the following characteristics, taken in isolation or in any technically possible combination(s): the magnetic generators are at least three in number and are arranged - relative to each other so that their directions are non-coplanar; and - the transmitter is constituted by a transmitter according to the fourth aspect. BRIEF DESCRIPTION OF THE FIGURES

[0028] Other characteristics and advantages of the invention will appear on reading the description which follows, given solely by way of example and with reference to the appended drawings, in which: - Figure 1 is a schematic view of an assembly formed of a first object and a second object comprising a determination system according to the invention, - Figure 2 is a diagram of a demodulator of a receiver of the determination system of Figure 1, - Figure 3 is a diagram of an example of a determination method capable of being implemented by the determination system of Figure 1, - Figure 4 is a diagram illustrating a first variant of a step of calculating data representative of the method of Figure 3, - Figure 5 is a diagram illustrating a second variant of the step of calculating data representative of the method of Figure 3,- Figure 6 is a diagram illustrating a third variant of the step of calculating data representative of the method of Figure 3, - Figure 7 is a diagram illustrating a first variant of a step of selecting a candidate measurement of the method of Figure 3, - Figure 8 is a diagram illustrating a second variant of the step of selecting a candidate measurement of the method of Figure 3.,

[0029] DETAILED DESCRIPTION OF AN EXAMPLE OF IMPLEMENTATION

[0030] The assembly 10 shown in Figure 1 comprises a first object 12 and a second object 14, the first object 12 being movable relative to the second object 14.

[0031] The first object 12 consists of a moving object in an inertial frame of reference and whose movement relative to this inertial frame of reference is to be followed.

[0032] The second object 14 is constituted by an object whose pose in the inertial frame of reference is known. Here and in the following, the pose is defined as being constituted by all the position and orientation data of an object in space. In a three-dimensional space, the pose therefore comprises six components, consisting of: - three position components, and - three orientation components. The second object 14 is for example constituted by a structure fixed in the inertial frame of reference. Alternatively (not shown), the second object is itself mobile in the inertial frame of reference but is equipped with sensors making it possible to track the movement of the second object in the inertial frame of reference.

[0033] The first object 12 and the second object 14 are typically arranged relative to each other such that there is no permanent line of sight between the two objects 12, 14. In other words, the first object 12 is likely to be hidden from the view of the second object 14 during its movement.

[0034] The speed of movement of the first object 12 relative to the second object 14 is typically less than 30 m / s and 10 rad / s.

[0035] For example, the first object 12 consists of a pen and the second object 14 consists of a housing that is stationary relative to the writing surface: it is thus possible to record the writing. Alternatively, the first object 12 consists of a headset and the second object 14 consists of a structure that is fixed in the environment in which the headset is moving.

[0036] A primary reference frame (R1) is attached to the first object 12. This primary reference frame (R1) is a direct orthogonal reference frame of origin O1 formed from a triplet of axes, represented in Figure 1, comprising: - a first primary axis, - a second primary axis orthogonal to the first axis and - a third primary axis orthogonal to the first and second axes And .

[0037] A secondary reference frame (R2) is attached to the second object 12. This secondary reference frame (R2) is a direct orthogonal reference frame of origin O2 formed from a triplet of axes, represented in Figure 1, comprising: - a first secondary axis , - a second secondary axis orthogonal to the first axis , and - a third secondary axis orthogonal to the first and second axes And .

[0038] The pose of the first object 12 relative to the first object 14 can be characterized by the set formed by the rotation matrix R converting the axes of the reference frame secondary (R1) in the axes of the primary reference frame (R2) and of the vector going from the origin O2 of the secondary reference frame (R2) to the origin O1 of the primary reference frame (R1).

[0039] The assembly 10 also comprises a determination system 20 intended to determine the pose of the first object 12 relative to the second object 14. This determination system 20 is constituted by an electromagnetic tracking system, or EMT. It comprises a transmission device 21 which comprises a transmitter 22 secured to the second object 14 and a reception device 23 which comprises a receiver 24 secured to the first object 12.

[0040] Said transmitter 22 and receiver 24 are typically configured to be functional when separated by a distance of less than 10 m. This makes it possible to limit the size of the transmitter 22 and the receiver 24.

[0041] The transmitter 22 comprises at least two, here three, magnetic generators 30, 32, 34. Each magnetic generator 30, 32, 34 behaves essentially as a magnetic dipole having an alternating magnetic dipole moment of amplitude m and frequency ω. It is oriented in a specific direction, respectively g1, g2, g3, defined here and hereinafter as the direction of said dipole moment.

[0042] The amplitude m of the dipole moment is preferably substantially equal for all the generators 30, 32, 34. The frequency ω of the dipole moment is, on the other hand, specific to each generator 30, 32, 34, so that each generator 30, 32, 34 is thus capable of generating an alternating magnetic field at a specific frequency.

[0043] For this purpose, each magnetic generator 30, 32, 34 comprises a coil, respectively 36, 38, 40, connected to a coil excitation current generator, respectively 42, 44, 46. Each coil 36, 38, 40 is oriented in its own direction, defined by the axis around which the coil extends, this direction constituting the direction of orientation of the magnetic generator 30, 32, 34 to which it belongs.

[0044] Each current generator 42, 44, 46 belongs to the transmission device 21. Each current generator 42, 44, 46 is for example, as shown, integrated into the second object 14. As a variant (not shown), at least a portion of the current generators 42, 44, 46 is offset relative to the second object 14.

[0045] Each current generator 42, 44, 46 is configured to generate the excitation current of the corresponding coil 36, 38, 40 at a natural frequency, this frequency constituting the frequency of the alternating magnetic field generated by the magnetic generator 30, 32, 34 to which the coil 36, 38, 40 connected to this current generator 42, 44, 46 belongs.

[0046] Each current generator 42, 44, 46 is in particular configured to generate the excitation current of the corresponding coil 36, 38, 40 at a frequency between 1 and 100 kHz.

[0047] The magnetic generators 30, 32, 34 are arranged relative to each other so that: - a first generator 30 is oriented along a first generator direction g1 coincident with the first secondary axis , - a second generator 32 is oriented along a second generator direction g2 forming a first non-zero angle θ with the second secondary axis and included in a plane defined by the first and second axes secondary, and - a third generator 34 is oriented along a third generator direction g3 forming a second non-zero angle φ with the third secondary axis , said third generator direction g3 being non-coplanar with each of the following planes: o the plane defined by the first generator direction g1 and the second generator direction g2, o the plane defined by the first generator direction g1 and the third secondary axis , and o the plane defined by the second generator direction g2 and the third secondary axis .

[0048] The third generator direction g3 and the third secondary axis thus define a plane forming a third non-zero angle ψ with the plane defined by the first generator direction g1 and the third secondary axis , this angle ψ being different from the angle between the first and second generator directions g1, g2.

[0049] The first angle θ is in particular greater than or equal to 0.01 radian, preferably greater than or equal to 0.05 radian, for example greater than or equal to 0.1 radian. It is typically strictly less than radian, preferably less than or equal to radian. The first angle 0 is advantageously an indirect angle, that is to say it is measured in the indirect direction of the secondary reference frame (R2) from the second secondary axis

[0050] The second angle φ is in particular greater than or equal to 0.01 radian, preferably greater than or equal to 0.05 radian, for example greater than or equal to 0.1 radian. It is typically strictly less than radian, preferably less than or equal to radian. The second angle φ is advantageously an indirect angle, that is to say it is measured in the indirect direction of the secondary reference frame (R2) from the third secondary axis .

[0051] The third angle ψ is in particular greater than or equal to 0.05 radians, preferably greater than or equal to 0.1 radians. It is typically less than the angle between the first and second generator directions g1, g2 and advantageously strictly less than . For example, it is between 0.75 and 0.80 radians. The third angle ψ is advantageously a direct angle, that is to say it is measured in the direct direction of the secondary reference frame (R2) from the first secondary axis

[0052] This arrangement of the magnetic generators 30, 32, 34 relative to each other results in particular from a design choice of the transmitter 22, unlike the EMTs of the state of the art which are on the contrary designed so that the magnetic generators are as orthogonal as possible relative to each other. The inventors have in fact discovered that this lack of orthogonality of the magnetic generators 30, 32, 34 could be exploited to determine the pose of the receiver 24 relative to the transmitter 22 intrinsically, without physical connection between the receiver 24 and the transmitter 22, without synchronization of the signals between the receiver 24 and the transmitter 22, without additional sensors and without calibration step, as will be detailed below.

[0053] Preferably, the magnetic generators 30, 32, 34 have substantially coincident centers, that is to say they can be modeled as magnetic dipoles with substantially the same center. For this purpose, the coils 36, 38, 40 have substantially coincident centers, that is to say the centers of the coils are two by two distant from each other by a distance less than the average radius of the coils 36, 38, 40. The center of the magnetic generators 30, 32, 34 constitutes the origin O2 of the secondary reference frame (R2).

[0054] The transmission device 21 also comprises a clock 48 providing a reference signal representative of the time. This reference signal is used by the magnetic generators 30, 32, 34 to vary over time the alternating magnetic fields that they generate.

[0055] The receiver 24 is capable of measuring the components of a resulting magnetic field, formed from the superposition of the alternating magnetic fields generated by the generators 30, 32, 34 of the transmitter 22, along the three axes of the primary reference frame. (R1).

[0056] For this purpose, the receiver 24 comprises three magnetic sensors 50, 52, 54 each capable of measuring a component of the resulting magnetic field along a measurement direction C1, C2, C3 specific to the sensor 50, 52, 54, these measurement directions C1, C2, C3 being non-coplanar. These sensors 50, 52, 54 are preferably arranged so that their measurement directions C1, C2, C3 are substantially orthogonal to each other, each measurement direction C1, C2, C3 being typically, as shown, substantially collinear with one of the axes of the primary reference frame (R1). Each magnetic sensor 50, 52, 54 is here formed of a coil, respectively 56, 58, 60, connected to a tensiometer, respectively 62, 64, 66, measuring the voltage at the terminals of the coil. Each coil 56, 58, 60 is oriented in its own direction, defined by the axis around which the coil extends, this direction constituting the measurement direction of the magnetic sensor 50, 52, 54 to which it belongs.

[0057] Each tensiometer 62, 64, 66 belongs to the receiving device 23. Each tensiometer 62, 64, 66 is for example, as shown, integrated into the first object 12. As a variant (not shown), at least part of the tensiometers 62, 64, 66 is offset relative to the first object 12.

[0058] Each tensiometer 62, 64, 66 is capable of producing a voltage signal representative of the voltage at the terminals of the associated coil 56, 58, 60 and therefore representative of the component of the resulting magnetic field along one of the measurement directions C1, C2, C3.

[0059] For this purpose, each tensiometer 62, 64, 66 is typically produced in the form of an amplifier coupled to an analog / digital converter (ADC).

[0060] The voltage signals produced by the tensiometers 62, 64, 66 together form a measurement signal. The measurement directions C1, C2, C3 being non-coplanar, this measurement signal is representative of the resulting magnetic field at the receiver 24.

[0061] The receiving device 23 also comprises a demodulator 70.

[0062] This demodulator 70 is for example, as shown, integrated into the first object 12. As a variant (not shown), the demodulator 70 is offset relative to the first object 12.

[0063] Referring to Figure 2, the demodulator 70 comprises an input 72, 74, 76 for each voltage signal u1, u2, u3 produced by a tensiometer 62, 64, 66. It also comprises a generator 78 of signals for demodulating the voltage signals.

[0064] Each demodulation signal consists of a sinusoidal signal of frequency equal to that of one of the alternating magnetic fields. It is a function of a reference signal, representative of time, provided by a clock 80 (Figure 1) of the receiver 24.

[0065] The demodulation signals comprise three pairs of demodulation signals such that the demodulation signals composing each pair are at the same frequency, this frequency being different from that of each other pair, and phase-shifted with respect to each other by Thus, for each of the alternating magnetic fields, there is a associated pair of demodulation signals composed of demodulation signals of frequency equal to that of said alternating magnetic field. The clock 80 of the receiver 24 is not synchronized with the clock 48 of the transmitter 22. Consequently, for each alternating magnetic field generated by the transmitter 22, the demodulation signals of the pair associated with said alternating magnetic field are at each instant out of phase with respect to the alternating magnetic field by an unknown phase shift Δφ j . This unknown phase shift Δφ j is in fact equal to ω j .Δt+ Δφ j,0 , where ω jis the frequency of the alternating magnetic field (and therefore also of the demodulation signals of the associated pair), Δφ j,0 is an initial phase shift (which can be zero), and At is the time deviation between the signals of clocks 80 and 48, this time deviation At being variable and random.

[0066] The demodulator 70 further comprises a circuit 82 (real or emulated) for multiplying each voltage signal u1, u2, u3 by each of the demodulation signals and an output 84A-84J for the product of each of these multiplications. The demodulator 70 finally comprises a low-pass filter 86 for filtering each of these outputs 84A-84J.

[0067] Preferably, the demodulator 70 is produced in the form of a digital card equipped with an FPGA (“Field-Programmable Gate Array” in English), a DSP (“Digital Signal Processor” in English), an ASIC (“Application-Specific Integrated Circuit” in English) and / or a processor or CPU (“Central Processing Unit” in English).

[0068] Returning to Figure 1, the determination system 20 also comprises a data processing unit 90. This data processing unit 90 is configured to deduce from the measurements carried out by the reception device 23 the pose of the receiver 24 relative to the transmitter 22. It is also configured to deduce from this pose the pose of the first object 12 relative to the second object 14.

[0069] For this purpose, the data processing unit 90 is, in the example shown, constituted by a microcontroller. It comprises a processor or CPU (Central Processing Unit) 92 and a memory 94 of the RAM (Random Access Memory) and / or ROM (Read Only Memory) type. The processor 92 is configured to execute instructions loaded into the memory 94. When the processing unit 90 is powered up, the processor 92 is capable of reading instructions from the memory 94 and executing them. These instructions form a computer program causing the implementation, by the processor 92, of certain steps of a method 100 (Figure 3) which will be detailed below.

[0070] The data processing unit 90 further comprises a buffer memory 96 for the temporary storage of information necessary for the implementation of the method 100.

[0071] In the example shown, the data processing unit 90 is integrated into the first object 12. Alternatively (not shown), at least part of the data processing unit 90 is remote, for example in a mobile terminal (not shown) and / or in a remote server (not shown). In other words, at least part of the steps of the method 100 is performed by a mobile terminal and / or a remote server. The first object 12 then comprises a communication system, typically a wireless communication system, configured to send the data from the receiver 24 to the mobile terminal and / or to the remote server.

[0072] It will be noted that the demodulator 70 can also be moved outside the first object 12.

[0073] A method 100 implemented by the determination system 20 will now be described, with reference to Figure 3.

[0074] This method 100 is typically implemented during a step of initializing or resetting the pose of the receiver 24 relative to the transmitter 22, the pose of the receiver 24 relative to the transmitter 22 otherwise being determined by a tracking method such as that described in the document H. Wu, Y. Zhao and C. Zhang, "Efficient Hemisphere Unambiguous Magnetic Positioning for Helmet Mounted Sights", 2018 IEEE / AIAA 37th Digital Avionics Systems Conference (DASC), London, UK, 2018, pp. 1-6.

[0075] As seen in Figure 3, the method 100 begins with a step 110 of generating magnetic fields. During this step 110, the generators 30, 32, 34 of the transmitter 22 are active and each generates a respective alternating magnetic field. These alternating magnetic fields overlap in space and produce a resulting magnetic field.

[0076] Concomitantly with step 110, the resulting magnetic field is measured by the receiver 24 during a step 120. During this step 120, the coils 56, 58, 60 of the sensors 50, 52, 54 of the receiver 24 are excited by the resulting magnetic field, which induces a potential difference between the terminals of each coil 56, 58, 60. This potential difference is measured by each tensiometer 62, 64, 66, which produces a corresponding voltage signal. A measurement signal, formed from the voltage signals of the tensiometers 62, 64, 66, is thus obtained, this measurement signal being representative of the resulting magnetic field at the receiver 24.

[0077] Then, in a step 130, the measurement signal is demodulated by the demodulator 70. In this step 130, each voltage signal u1, u2, u3 produced by a respective sensor 50, 52, 54 is multiplied by each of the demodulation signals and the product of this multiplication is filtered by a low-pass filter. Eighteen values ​​P i,j,k with i between 1 and 3, j between 1 and 3 and k equal to 1 or 2 are thus obtained, each value P i,j,k being the value resulting from the product of the voltage signal u, with a sinusoidal demodulation signal at the frequency of the magnetic field generated by the generator 30, 32, 34 oriented in the direction g j .

[0078] It will be noted that, to the first order, each value Pi,j, 1, respectively each value Pi,j, 2, is equal to the product of the cosine, respectively the sine, of the phase shift between the magnetic field generated by the generator 30, 32, 34 oriented along the direction g jand the demodulation signals associated with the contribution of this alternating magnetic field to the component of the resulting magnetic field measured along the direction c i . In other words, each P value i,j,1 , respectively each P value i,j,2 , is equal, to the first order, to U i,,j cos(Δφ j ), respectively U i,,j cos(Δφ j ), where: - U i,,j is the contribution of the magnetic field generated by the generator 30, 32, 34 oriented in the direction g j to the component of the resulting magnetic field measured along the direction c i , and - Δφ j is the phase shift between the magnetic field generated by the generator 30, 32, 34 oriented in the direction gj and the associated demodulation signals (i.e. the demodulation signals which have the same frequency as that of said magnetic field).

[0079] These eighteen values ​​are then used to calculate the absolute value of the contribution of each generated alternating magnetic field to each component of the resulting magnetic field. This absolute value is equal to the square root of the sum of the squares of the values ​​resulting from the product of a voltage signal by the demodulation signals of the same pair. In other words, we have:

[0080] The absolute values ​​of the contributions of the generated alternating magnetic fields to the components of the resulting magnetic field are then used to construct a plurality of candidate measures M c each formed from a set of candidate contributions from each generated alternating magnetic field to each component of the magnetic field, that is, a set of values ​​where each value is a value candidate for the contribution of the magnetic field generated by the generator 30, 32, 34 oriented in the direction g j to the component of the resulting magnetic field measured along the direction c i .

[0081] These candidate measures M c can be presented in the form of matrices, in which each column presents the contributions of the same alternating magnetic field and each row presents the contributions to the same component of the resulting magnetic field:

[0082] For this purpose, a first candidate measure is first constructed, such as that: - the absolute value of each candidate contribution is equal to the absolute value of the corresponding (real) contribution - for each alternating magnetic field, the sign of each of the candidate contributions of this alternating magnetic field is equal to the sign of the value P i,j,1, or P i,j,2 resulting from the product of the voltage signal u i with one of the sinusoidal demodulation signals associated with this alternating magnetic field, in other words: - the determinant of the corresponding matrix is ​​positive.

[0083] Then, from this first candidate measure , three other candidate measures are constructed by simply multiplying the matrix of the first candidate measure by each of the following matrices:

[0084] A total of four candidate measures M c is thus obtained, these candidate measures verifying the following condition:

[0085] Note that the number of candidate measures M c is limited to four because the actual measure matrix necessarily has a positive determinant and matrices with negative determinants are therefore not serious candidates.

[0086] The demodulation step 130 is followed by a step 140 of applying a corrective measure to the candidate measurements M. c This correction aims to compensate for the effect induced on the measurement signal, and therefore on the candidate measurements, by the lack of orthogonality of the magnetic generators 30, 32, 34.

[0087] This fix is ​​common to all candidate measures M c . It includes the multiplication, by the right, of the matrix of each candidate measure M c by a matrix B -1 . This matrix B -1 is the inverse of the following matrix B: where b1, b2 and b3 are scale factors, typically determined during a prior calibration step, b1 being a global scale factor making it possible to define the length scale of the measurements provided by the determination system 20 and b2 and b3 are relative scale factors, functions of bi, which cover in particular: - the differences between the frequencies ω jalternating magnetic fields which appear during the induction phenomenon occurring in the coils 56, 58, 60 of the magnetic sensors 50, 52, 54, and - the relative differences between the norms of the dipole moments of the generators 30, 32, 34.

[0088] We thus obtain, for each candidate measure M c , a partial corrected measure M p corresponding, this partial corrected measurement verifying the following relation: , where l3 is the matrix identify.

[0089] The correction also aims to compensate for the effect induced on the measurement signal, and therefore on the candidate measurements, by the other defects of the transmitter 22, the receiver 24 and the environment. To this end, the correction also comprises the application of other usual corrections well known to those skilled in the art to the partial corrected measurement M p so as to obtain, for each candidate measure M c, a final corrected measure M k corresponding. These other defects will be ignored in the following, as those skilled in the art know how to model and compensate for them.

[0090] Step 140 is followed by a calculation step 150, for each candidate measure M c , of a data representative of the likelihood that this candidate measure M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field. This representative data is calculated using the corrected measurement M k corresponding to the candidate measure M c .

[0091] Due to the lack of orthogonality existing between the generators 30, 32, 34 of the transmitter 22, the correction made to the “bad” candidate measurements M c(i.e. those not giving the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field) increases the deviation of these measurements from the theoretical model rather than bringing them closer to it. Thus, the mere fact that the data representative of the likelihood is calculated by means of the corrected measurement M k corresponding is sufficient so that, in most cases, the data representative of the likelihood of the "good" candidate measurement (i.e. the measurement giving the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field) is clearly distinguishable from those of the "bad" candidate measurements. It is therefore not necessary to resort to measurements from additional sensors other than the magnetic sensors 50, 52, 54 to calculate said data representative of the likelihood.

[0092] In a first variant of this step 150, represented in Figure 4, step 150 is constituted by an estimation step 152, for each candidate measurement M c , from a distance of the corrected measurement M k corresponding to a reference space consisting of the measurements that can be obtained in a model of the determination system 20 in which the magnetic generators 30, 32, 34 are orthogonal to each other.

[0093] The distance D of the corrected measurement M k said reference space is for example determined by the following formula: where S 11 , S 22 and S 33 are the diagonal terms of a diagonal matrix S of positive real values ​​ordered so that S 11 ≥ S 22 ≥ S 33 , this diagonal matrix resulting from a singular value decomposition (“Singular Value Decomposition” in English) of the matrix of the corrected measurement M ksuch that the diagonal matrix S verifies the following relation:

[0094] M k = PSQ T where P is a first matrix belonging to the group SO(3) of rotation matrices in dimension 3 and Q T is the transpose of a second matrix Q also belonging to the group SO(3).

[0095] It should be noted that the distance D can also be determined by many other formulas, depending or not on the diagonal terms of the matrix S and possibly giving different values ​​of the distance D, the only important thing is that the formula for calculating the distance D is the same for all the corrected measurements M k . A person skilled in the art will easily be able to determine these other formulas.

[0096] The data representative of the likelihood that the candidate measure M cgives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field is a function of said distance D. For example, this representative data is proportional, in particular equal, to the distance D; it is then a decreasing function of the likelihood (in fact, the lower the distance D, the more likely it is that the candidate measurement M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field). Alternatively, the representative data is an inverse function of the distance D; it is then an increasing function of the likelihood.

[0097] In another variant of step 150, represented in Figure 5, this step 150 comprises a sub-step 154 ​​of deduction, for each candidate measure M c, of a candidate pose of the receiver 24 relative to the transmitter 22, this candidate pose being deduced from the corrected measurement M k corresponding to said candidate measure M c .

[0098] To this end, the data processing unit 90 carries out, in a preferred embodiment of the invention, the decomposition into singular values ​​(“Singular Value Decomposition” in English) of the matrix of the corrected measurement M k such that the corrected matrix M k verifies the following relationship:

[0099] M k = PSQ T where P is a first matrix belonging to the group SO(3) of rotation matrices in dimension 3, Q T is the transpose of a second matrix Q also belonging to the group SO (3), and S is the following matrix: with S 11 , S 22 and S 33 positive real values ​​ordered so that S 11 ≥ S 22 ≥ S 33 .

[0100] From this decomposition into singular values, the data processing unit 90 calculates, by means of the following formula, the vector characterizing the candidate position of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the candidate measurement M c : where Q 11 , Q 21 and Q 31 are the terms of the first column of the matrix Q and r is given by the following formula: with μ0 the magnetic permeability of the vacuum, m the amplitude of the magnetic moments of the generators 30, 32, 34 and Tr(S) the trace of the matrix S (i.e. the sum of the diagonal coefficients S 11 , S 22 and S 33). The data processing unit 90 also uses the singular value decomposition to calculate, by means of the following formula, the rotation matrix R characterizing the candidate orientation of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the candidate measurement M c : where P T is the transpose of the matrix P.

[0101] The data processing unit 90 thus obtains a pair (r, R) characterizing a candidate pose corresponding to the candidate measurement M c .

[0102] In this other variant of step 150, sub-step 154 ​​is followed by a sub-step 155 of estimating a realistic theoretical measurement of the resulting magnetic field in each candidate pose. This estimation is based on a realistic model of the determination system 20 taking into account the lack of orthogonality of the magnetic generators 30, 32, 34. This realistic model models the resulting magnetic field at any point in space in the form of a vector equal to: where t is time, μ0 is the magnetic permeability of the vacuum, m the amplitude of the dipole moments of the generators 30, 32, 34, r is the distance from the origin O2 of the secondary reference frame (R2), x is the coordinate along the first secondary axis , Y est coordinate along the second secondary axis, z is the coordinate along the third secondary axis And are the pulsations, respectively, of the dipole moment of the first magnetic generator 30, of the dipole moment of the second magnetic generator 32 and of the dipole moment of the third magnetic generator 34.

[0103] To estimate the realistic theoretical measurement of the resulting magnetic field in the candidate pose, the data processing unit 90 only needs to calculate the components of the vector above in the position defined by the vector in the frame defined by the rotation matrix R.

[0104] Still in this other variant of step 150, sub-step 155 is itself followed by a sub-step 156 of evaluating the distance of each candidate measurement M c to the realistic theoretical measure associated with said candidate measure M c , i.e. to the realistic theoretical measurement of the resulting magnetic field in the candidate pose corresponding to said candidate measurement M c. During this sub-step 156, the processing unit 90 typically evaluates a distance between the matrix of the candidate measurement M c and the matrix of the associated realistic theoretical measurement, this matrix of the realistic theoretical measurement being constituted by the matrix: such that the realistic theoretical magnetic field in the candidate pose is given by the following vector:

[0105] The distance between matrices M c and M th r is for example given by the norm of

[0106] Frobenius of the difference between matrices.

[0107] The data representative of the likelihood that the candidate measure M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field is then a function of the distance between the matrices M c and M th r. For example, this representative data is proportional, in particular equal, to the said distance; it is then a decreasing function of the likelihood (in fact, the greater the distance between the matrices M c and M th r is weak, the more likely it is that the candidate measure M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field). Alternatively, the representative data is an inverse function of said distance; it is then an increasing function of the likelihood.

[0108] A third variation of step 150 is shown in Figure 6.

[0109] In this third variant, step 150 still includes the deduction sub-step 154, for each candidate measure M c , of a candidate pose of the receiver 24 relative to the transmitter 22, this candidate pose being deduced from the corrected measurement M kcorresponding to said candidate measure M c This third variant nevertheless differs from the previous variant in that step 150 does not include sub-steps 155 and 156.

[0110] Instead, substep 154 ​​is followed by a substep 157 of estimating a simplified theoretical measurement of the resulting magnetic field in each candidate pose. This estimation is based on a simplified model of the determination system 20 which considers the magnetic generators 30, 32, 34 orthogonal to each other. This simplified model models the resulting magnetic field at any point in space in the form of a vector equal to: where t is time, μ0 is the magnetic permeability of the vacuum, m is the amplitude of the dipole moments of the generators 30, 32, 34, r is the distance from the origin O2 of the secondary reference frame (R2), x is the coordinate along the first secondary axis e2, y is the coordinate along the second secondary axis, z is the coordinate along the third secondary axis And are the pulsations, respectively, of the dipole moment of the first magnetic generator 30, of the dipole moment of the second magnetic generator 32 and of the dipole moment of the third magnetic generator 34.

[0111] It is sufficient for the data processing unit 90, to estimate the simplified theoretical measurement of the resulting magnetic field in the candidate pose, to calculate the components of the above vector in the position defined by the vector, in the frame defined by the rotation matrix R.

[0112] Still in this third variant of step 150, sub-step 157 is itself followed by a sub-step 158 of evaluating the distance of each corrected measurement M k corresponding to a candidate measure M c to the simplified theoretical measure associated with said candidate measure M c , that is to say to the simplified theoretical measurement of the resulting magnetic field in the candidate pose corresponding to said candidate measurement M c . During this sub-step 158, the processing unit 90 typically evaluates a distance between the matrix of the corrected measurement M k and the matrix of the associated simplified theoretical measurement, this matrix of the simplified theoretical measurement being constituted by the matrix: such that the simplified theoretical magnetic field in the candidate pose is given by the following vector:

[0113] The distance between matrices M k and M th,sis for example given by the norm of

[0114] Frobenius of the difference between matrices. The data representing the likelihood that the candidate measure M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field is then a function of the distance between the matrices M k and M th,s . For example, this representative data is proportional, in particular equal, to the said distance; it is then a decreasing function of the likelihood (in fact, the greater the distance between the matrices M k and M th,s is weak, the more likely it is that the candidate measure M c gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field). Alternatively, the representative data is an inverse function of said distance; it is then an increasing function of the likelihood.

[0115] Returning to Figure 3, step 150 is followed by a step 160 of selecting a measure selected from the candidate measures M c .

[0116] With reference to Figure 7, step 160 comprises a first sub-step 161 of comparing the data representative of each candidate measurement M c to a threshold. In the case where, as represented here, the representative data is a decreasing function of the likelihood, this sub-step 161 has the function of determining whether one or more candidate measures M c have their representative data lower than said threshold. In the case where the representative data is an increasing function of the likelihood, this sub-step 161 has the function of determining whether one or more candidate measures M c have their representative data above said threshold.

[0117] If a single candidate measure M chas its representative data lower, respectively higher, than the threshold, sub-step 161 is followed by a sub-step 162 of selection of said candidate measurement M c whose representative data is lower, respectively higher, than the threshold. The selected measurement is then made up of that of the candidate measurements M c whose representative data is the lowest, respectively the highest, and therefore indicates the highest likelihood.

[0118] If there is no unique candidate measure M c having its representative data lower, respectively higher, than the threshold, for example because several candidate measurements M c have their representative data lower, respectively higher, than the threshold, or because no candidate measure M chas its representative data lower, respectively higher, than the threshold, the selection can no longer be based on the representative data of the candidate measurements. Indeed, this then reflects the fact that these representative data are not reliable. In a pose tracking (respectively phase shift) method, the processed sample cannot then be used to initialize or reinitialize the tracking. The pose is then determined by applying the tracking method, which takes advantage of the history of previously estimated poses (respectively phases).

[0119] In a first variant of step 160, shown in Figure 7, sub-step 161 is thus followed, when several candidate measurements M c have their representative data lower, respectively higher, than the threshold, of a sub-step 163 of deduction, for each candidate measurement, of a candidate pose of the receiver relatively 24 relative to the transmitter 22.

[0120] This candidate pose is deduced from the corrected measurement M k corresponding to said candidate measure M c by a method similar to that described above in connection with step 154. The data processing unit 90 thus obtains a pair characterizing a candidate pose corresponding to the candidate measure M c .

[0121] The sub-step 163 is then followed by a sub-step 164 of calculating the distance of each candidate pose to a previous pose. This previous pose is typically constituted by a pose previously determined for example by the implementation of the method 100 during a previous iteration of the latter or by the implementation of a tracking method such as that described in the document H. Wu, Y. Zhao and C. Zhang, "Efficient Hemisphere Unambiguous Magnetic Positioning for Helmet Mounted Sights", 2018 IEEE / AIAA 37th Digital Avionics Systems Conference (DASC), London, UK, 2018, pp. 1-6. This previous pose is preferably constituted by the last known pose of the receiver 24 relative to the transmitter 22.

[0122] The distance d between the candidate pose and the previous pose is for example given by the following formula: where is the norm 2 of the logarithm in the SO(3) group of rotation matrices, R cis the rotation matrix defining the orientation in the candidate pose, and R aT is the transpose of the rotation matrix defining the orientation in the prior pose.

[0123] Sub-step 164 is followed by a sub-step 165 of selecting the candidate measure M. c for which the corresponding candidate pose has the smallest distance to the previous pose. The selected measurement is then made up of that of the candidate measurements M c for which the corresponding candidate pose has the smallest distance to the previous pose.

[0124] In another variant of step 160, shown in Figure 8, substep 161 is followed, when there is not a single candidate measure M chaving its representative data lower, respectively higher, than the threshold, of a sub-step 166 of determining, for each alternating magnetic field, two candidate phase shifts of said alternating magnetic field with respect to the associated demodulation signals.

[0125] During this sub-step 166, the data processing unit 90 calculates, for each alternating magnetic field generated by one of the generators 30, 32, 34, the ratio between the values ​​of at least one pair of values ​​resulting from the products of one of the voltage signals with the demodulation signals associated with said alternating magnetic field. The data processing unit 90 then determines an angle a whose tangent is equal to this ratio:

[0126] The data processing unit 90 sets the first candidate phase shift of the alternating magnetic field with respect to the associated demodulation signals as being equal to a, the second candidate phase shift being equal to α+π.

[0127] Sub-step 166 is followed by a sub-step 167 of selecting, for each alternating magnetic field, that of the candidate phase shifts which minimizes a deviation from a known previous phase shift of said alternating magnetic field.

[0128] During this sub-step 167, the data processing unit 90 compares each of the candidate phase shifts of the alternating magnetic field with respect to the associated demodulation signals with a known prior phase shift of said alternating magnetic field with respect to these same demodulation signals. This prior phase shift has typically been determined previously during a previous measurement of the resulting magnetic field by the receiver 24, for example during a previous step of determining a previous pose of the receiver 24 relative to the transmitter. The time interval τ between this previous measurement of the resulting magnetic field by the receiver 24 and the implementation of step 120 must satisfy the following condition: with where each is the absolute value of the time derivative characteristic of the phase shift between a generated alternating magnetic field and the associated demodulation signals.

[0129] In particular, during this sub-step 167, the data processing unit 90 determines the difference between each of the candidate phase shifts of the alternating magnetic field and the previous phase shift of this alternating magnetic field. It then selects the one of the candidate phase shifts having the smallest difference (in absolute value) with the previous phase shift. The sub-step 167 is itself followed by a sub-step 168 of selecting that of the candidate measurements M c for which, for each alternating magnetic field, the signs of the candidate contributions are consistent with the value of the selected phase shift.

[0130] During this sub-step 167, the data processing unit 90 determines, for each alternating magnetic field, the sign of the cosine or sine of the selected phase shift. It then multiplies this sign with that of at least one value (if sign of the cosine) or with that of at least one value P i,j,2(if sign of the sine) resulting from the product of one of the voltage signals with one of the demodulation signals associated with said alternating magnetic field. It finally compares the sign thus obtained with the sign of the corresponding candidate contribution (i.e. whose absolute value is equal to d e each candidate measure M c and selects one of the candidate measures M c for which, for each alternating magnetic field, the sign of said corresponding candidate contribution is equal to said sign thus obtained.

[0131] Furthermore, in this other variant of step 160, sub-step 162 is followed by a sub-step 169 of resetting the phase shift of each alternating magnetic field with respect to the demodulation signals associated with this alternating magnetic field.

[0132] During this sub-step 169, the data processing unit 90 calculates, for each alternating magnetic field generated by one of the generators 30, 32, 34, the ratio between the values ​​of at least one pair of values ​​resulting from the products of one of the voltage signals with the demodulation signals associated with said alternating magnetic field. The data processing unit 90 then determines an angle a whose tangent is equal to this ratio:

[0133] The data processing unit 90 then determines the sign of the cosine or sine of this angle a. Then it multiplies this sign with that of at least one value P i,j,1 (if cosine sign) or with that of at least one P value i,j,2(if sign of the sine) resulting from the product of one of the voltage signals with one of the demodulation signals associated with said alternating magnetic field. It finally compares the sign thus obtained with the sign of the corresponding candidate contribution (i.e. whose absolute value is equal to of the candidate measure M c selected. If the signs are equal, the unit of data processing unit 90 assigns the value a to the phase shift of the alternating magnetic field. If these signs are opposite, the data processing unit 90 assigns the value o+n to the phase shift of the alternating magnetic field.

[0134] Returning to Figure 3, step 160 is followed by a step 170 of deducing the pose of the receiver 24 relative to the transmitter 22, and therefore the pose of the first object 12 relative to the second object 14, from the corrected measurement M k corresponding to the selected measure.

[0135] To this end, the data processing unit 90 carries out, in a preferred embodiment of the invention, the decomposition into singular values ​​(“Singular Value Decomposition” in English) of the matrix of the corrected measurement M k such that the corrected matrix M k verifies the following relationship:

[0136] M k = PSQ T where P is a first matrix belonging to the group SO(3) of rotation matrices in dimension 3, Q T is the transpose of a second matrix Q also belonging to the group SO (3), and S is the following matrix: with S 11 , S 22 and S 33 positive real values ​​ordered so that S 11 ≥ S 22 ≥ S 33 •

[0137] From this decomposition into singular values, the data processing unit 90 calculates, by means of the following formula, the vector characterizing the position of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the selected measurement: where Q 11 , Q 21 and Q 31 are the terms of the first column of the matrix Q and r is given by the following formula: with μ0 the magnetic permeability of the vacuum, m the amplitude of the dipole moments of the generators 30, 32, 34 and Tr(S) the trace of the matrix S (i.e. the sum of the diagonal coefficients S 11 , S 22 and S3)3.

[0138] The data processing unit 90 also uses the singular value decomposition to calculate, by means of the following formula, the rotation matrix R characterizing the orientation of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the selected measurement: where P Tis the transpose of the matrix P. The data processing unit 90 thus obtains a pair (r, R) characterizing the effective pose of the receiver 24 (and therefore of the first object 12 to which it is attached) relative to the transmitter 22 (and therefore relative to the second object 14 to which it is attached).

[0139] Thus, thanks to the invention described above, it is possible to determine the pose of the receiver 24 relative to the transmitter 22 intrinsically, without physical connection between the receiver 24 and the transmitter 22, without synchronization of the signals between the receiver 24 and the transmitter 22, without additional sensors and without calibration step. This pose can thus be determined in a simple, robust and inexpensive manner.

Claims

CLAIMS 1. Method (100) for determining at least one component of the pose of a receiver (24) relative to a transmitter (22), the transmitter (22) comprising at least two magnetic generators (30, 32, 34) each oriented in a specific direction (g1, g2, g3) and capable of generating an alternating magnetic field at a specific frequency, the magnetic generators (30, 32, 34) being arranged relative to each other so that their directions (g1, g2, g3) are two by two non-coaxial and non-orthogonal, and the receiver (24) being capable of measuring the components of a resulting magnetic field, formed from the superposition of the alternating magnetic fields generated by the magnetic generators (30, 32, 34) of the transmitter (22), in three non-coplanar directions (c1, c2, c3), the method (100) comprising the following steps: - measurement (120) of the resulting magnetic field by the receiver (24) so as to obtain a measurement signal representative of the resulting magnetic field,- demodulation (130) of the measurement signal so as to determine a plurality of candidate measurements each formed from a set of candidate contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - application (140) to each candidate measurement of a correction aimed at compensating for the effect induced on the measurement signal by the lack of orthogonality of the directions of the magnetic generators (30, 32, 34), so as to obtain for each candidate measurement a corresponding corrected measurement, - calculation (150), for each candidate measurement, by means of the corresponding corrected measurement, of data representative of the likelihood that this candidate measurement gives the real contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - selection (160) of a measurement selected from the candidate measurements,the selected measure being constituted by that of the candidate measures whose representative data indicates the highest likelihood, and, - deduction (170), from the corrected measurement corresponding to the selected measurement, of said at least one component of the pose of the receiver (24) relative to the transmitter (22).

2. Determination method (100) according to claim 1, in which the corrective is common to all candidate measurements.

3. Determination method (100) according to claim 1 or 2, in which the magnetic generators (30, 32, 34) have substantially coincident centers.

4. Determination method (100) according to any one of the preceding claims, in which the data representative of the likelihood is calculated by means of a decomposition into singular values of a matrix of the corresponding corrected measurement.

5. Determination method (100) according to any one of the preceding claims, in which the calculation (150) of the data representative of the likelihood comprises the following sub-step: - for each candidate measurement, estimation (152) of a distance of the corrected measurement corresponding to a reference space consisting of the measurements which can be obtained in a model of the system (20) formed of the transmitter (22) and the receiver (24) in which the magnetic generators (30, 32, 34) are orthogonal to each other, the data representative of the likelihood being a function of said distance.

6. Determination method (100) according to claims 4 and 5 taken together, in which the distance is a function of the diagonal terms of a diagonal matrix resulting from the decomposition into singular values of the matrix of the corresponding corrected measurement.

7. The determination method (100) according to claim 6, wherein the distance is determined by the following formula: where S 11 , S 22 and S 33 are the diagonal terms of a diagonal matrix S of positive real values ordered so that S 11 ≥ S 22 ≥ SS 33 , this diagonal matrix resulting from a singular value decomposition of the corrected measurement matrix such that the diagonal matrix S verifies the following relation: M k = PSQ T where M k is the matrix of the corrected measure, P is a first matrix belonging to the group SO (3) of rotation matrices in dimension 3 and Q T is the transpose of a second matrix Q also belonging to the group SO(3).

8. Determination method (100) according to any one of claims 1 to 4, wherein the calculation (150) of the data representative of the likelihood comprises, for each candidate measurement, the following sub-steps: - deduction (154), from the corresponding corrected measurement, of a candidate pose of the receiver (24) relative to the transmitter (22), - estimation (155, 157) of a theoretical measurement of the magnetic field resulting in the candidate pose in a model of the system (20) formed of the transmitter (22) and the receiver (24), and - evaluation (156, 158) of a distance of the candidate measurement or of the corrected measurement corresponding to said theoretical measurement, the data representative of the likelihood being a function of said distance.

9. A determination method according to claims 4 and 8 taken together, wherein the candidate pose of the receiver (24) relative to the transmitter (22) is deduced from the singular value decomposition of the matrix of the corresponding corrected measurement.

10. Determination method (100) according to claim 9, in which the candidate pose is characterized by a pair (r, R) such that: with: - P a first matrix belonging to the group SO (3) and Q a second matrix Q also belonging to the group SO (3) such that M k = PSQ T , where M k is the matrix of the corrected measure and S is a diagonal matrix of ordered positive real values, - Q 11 , Q 21 and Q 31 are the terms of the first column of the matrix Q, and - r is given by the following formula where μ0the permeability magnetic field of the vacuum, m the amplitude of the magnetic moments of the magnetic generators (30, 32, 34) and Tr(S) the trace of the matrix S.

11. Determination method (100) according to any one of claims 8 to 10, in which the model of the system takes into account the lack of orthogonality of the magnetic generators (30, 32, 34) and the distance evaluated in the evaluation step (156) consists of a distance from the candidate measurement to said theoretical measurement.

12. Determination method (100) according to any one of claims 8 to 10, wherein the model of the system considers the magnetic generators (30, 32, 34) orthogonal to each other, and the distance evaluated in the evaluation step (158) consists of a distance from the corrected measurement to said theoretical measurement.

13. Determination method (100) according to any one of the preceding claims, in which the representative data is a decreasing, respectively increasing, function of the likelihood, the method (100) comprising an additional step of comparing (161) the representative data of each candidate measurement to a predetermined threshold, the selection (160) of the selected measurement being based on the representative data of the candidate measurements only if the representative data of a single candidate measurement is lower, respectively higher, than said predetermined threshold.

14. Determination method (100) according to claim 13 wherein, when there is not a single candidate measurement whose representative data is lower, respectively higher, than the predetermined threshold, the method (100) comprises the following steps: - deduction (163), for each candidate measurement, from the corresponding corrected measurement, of a candidate pose of the receiver (24) relative to the transmitter (22), and calculation (164) of a distance from the candidate pose to a previous pose, - the selected measurement being constituted by that of the candidate measurements for which the corresponding candidate pose has the smallest distance to the previous pose.

15. Determination method (100) according to claim 13, comprising, when there is not a single candidate measurement whose representative data is lower, respectively higher, than the predetermined threshold, the following step: - determination (166), for each generated alternating magnetic field, of candidate phase shifts of said generated alternating magnetic field with respect to a demodulation signal used to demodulate the measurement signal, and - selection, for each alternating magnetic field, of that of the candidate phase shifts which minimizes a deviation with a previous phase shift of said generated alternating magnetic field with respect to this same demodulation signal, the selected measurement being constituted by that of the candidate measurements for which, for each generated alternating magnetic field, the signs of the candidate contributions are consistent with the selected phase shift.

16. Determination method (100) according to any one of the preceding claims, in which the calculation step (150) is implemented without using measurements from inertial sensors integral with the receiver (24) 17. The determination method of claim 16, wherein the receiver (24) has magnetic sensors (50, 52, 54) for measuring the components of the resulting magnetic field and the calculating step (150) is implemented without using measurements from additional sensors other than the magnetic sensors (50, 52, 54).

18. Computer program product comprising code instructions for the implementation, by a processor, of a determination method (100) according to any one of the preceding claims.

19. A computer-readable recording medium on which a computer program product according to claim 18 is stored.

20. Transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 17, the transmitter (22) comprising at least two magnetic generators (30, 32, 34) each oriented in a specific direction (g1, g2, g3) and capable of generating an alternating magnetic field at a specific frequency, the transmitter (22) being designed so that: - a first generator (30) is oriented along a first generator direction (g1) coincident with a first direction of an orthogonal reference frame attached to the transmitter (22), and - a second generator (32) is oriented along a second generator direction (g2) forming a first angle (θ) with a second direction of the orthogonal reference frame and included in a plane defined by the first and second directions of the orthogonal reference frame, the first angle (θ) being greater than or equal to 0.05 radians.

21. Transmitter (22) according to claim 20, comprising a third magnetic generator (34) capable of generating an alternating magnetic field at a natural frequency, the transmitter (22) being designed so that said third generator (34) is oriented in a third generator direction (g3) forming a second angle (φ), greater than or equal to 0.05 radians, with a third direction of the orthogonal reference point.

22. Method for designing a transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 17, comprising the following steps: - arranging a first magnetic generator (30) of the transmitter (22), capable of generating an alternating magnetic field at a first frequency, so that it is oriented in a first generator direction (g1) coincident with a first direction of an attached orthogonal reference frame to the transmitter (22), and - arrangement of a second magnetic generator (32) of the transmitter (22), capable of generating an alternating magnetic field at a second frequency different from the first frequency, so that it is oriented in a second generator direction (g2) forming a first angle (θ) with a second direction of the orthogonal reference frame and included in a plane defined by the first and second directions of the orthogonal reference frame, the first angle (θ) being greater than or equal to 0.05 radians.

23. Design method according to claim 22, comprising an additional step of arranging a third magnetic generator (34) of the transmitter (22), capable of generating an alternating magnetic field at a third frequency different from the first and second frequencies, so that it is oriented in a third generator direction (g3) forming a second angle (φ), greater than or equal to 0.05 radians, with a third direction of the orthogonal reference frame.

24. Method of manufacturing a transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 16, comprising the design of a transmitter (22) by means of a method according to claim 22 or 23, followed by the production of this transmitter (22).

25. System (20) for determining at least one component of the pose of a first object (12) relative to a second object (14), said determination system (20) comprising: - a transmitter (22) secured to the second object (14), said transmitter (22) comprising at least two magnetic generators (30, 32, 34) each oriented in a specific direction (g1, g2, g3) and capable of generating an alternating magnetic field at a specific frequency, the magnetic generators (30, 32, 34) being arranged relative to each other so that their directions (g1, g2, g3) are two by two non-coaxial and non-orthogonal, - a receiver (24) secured to the first object (12), said receiver (24) being capable of measuring the components of a resulting magnetic field, formed from the superposition of the alternating magnetic fields generated by the magnetic generators (30, 32, 34) of the transmitter (22), in three non-coplanar directions (C1, C2, C3),and - a data processing unit (90) configured for implementing a determination method (100) according to any one of claims 1 to 17.,

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