Determination of pose by measuring an oscillating magnetic field produced by non-orthogonal generators

Abstract

A method 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), 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 intended to compensate for a lack of orthogonality in the directions of the magnetic generators (30, 32, 34), so as to obtain a corresponding corrected measurement, calculating a representative data point for the likelihood that this candidate measurement gives the actual contributions of each alternating magnetic field, selecting a selected measurement corresponding to the highest likelihood, and deducing from said at least one component of the pose of the receiver (24). Figure for the abstract: Fig. 1

Description

Title of the invention: Determination of pose by measuring an oscillating magnetic field produced by non-orthogonal generators. Field of the invention

[0001] The present invention relates to determining at least one component of the pose, that is, the position and orientation, of a first object relative to a second object, by measuring, at the level of the first object, an oscillating magnetic field produced by a transmitter attached to the second object. The present invention relates more particularly to implementing this determination when no physical link connects the two objects. Technological background

[0002] To determine the pose of an object, that is, 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 transmitter fixed in the frame of reference, consisting of three coils arranged to form a fixed, substantially orthogonal trihedron, and a receiver attached to the object whose pose is to be determined. This receiver consists of three magnetic sensors arranged to form a movable, substantially orthogonal trihedron. Time-dependent electric currents flow in the coils of the transmitter and generate three magnetic fields, which are detected by the sensors of the receiver. Each sensor of the receiver measures, for each of the emitted magnetic fields, the projection of that field onto the direction in which the sensor is directed.This gives a total of nine components that allow the transition from a moving trihedron to a fixed trihedron. Indeed, these nine components depend on the position and orientation of the receiver relative to the transmitter.

[0003] To enable the identification, on the receiver side, of the contribution of each coil to the captured magnetic field, several alternatives exist.

[0004] A first alternative, described in US 5,453,686, employs time-division multiplexing: each coil successively produces a continuous magnetic field during a specific time interval. Thus, at any given instant, the receiver sensors measure only the components of the magnetic field emitted by a single coil. However, this technique has many drawbacks. First, the magnetic field measured at the receiver is disturbed by constant magnetic fields, such as the Earth's magnetic field, which are themselves disturbed by floors and walls containing metallic elements. Second, this technique requires the use of magnetometers as sensors, which are particularly difficult to implement over a wide range.

[0005] Another alternative is to excite the transmitter coils with alternating currents at their natural frequencies. The generated magnetic fields are thus alternating magnetic fields that can be distinguished from one another by demodulation using the knowledge of the coil excitation frequency. Sensitivity to constant magnetic fields can therefore be neglected, and the sensors can be simple coils across which the induced voltage is measured.

[0006] This second alternative, however, has a drawback: to determine the sign of each component of each of the magnetic fields generated by the transmitter, the receiver's clock signal must be synchronous with that of the transmitter. Indeed, without this synchronization, the time reference of the signals measured by the receiver's sensors becomes phase-shifted by an unknown amount relative to the time reference of the emitted magnetic fields, which creates uncertainty as to the signs of the measured magnetic field components.

[0007] 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, while solutions for synchronizing the clock signals of the transmitter and receiver without a physical connection between the two have been proposed, these solutions still present too many drawbacks.

[0008] 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 is either emitted by a dedicated transmitter or integrated into the excitation currents of the transmitter coils (for example, by periodically interrupting the emission of the magnetic fields). However, these solutions are not entirely satisfactory, as they are cumbersome to implement and require additional components, or reduce the availability of the final measurements and / or the system latency.

[0009] It has also been 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, with demodulation then based on the calculation of a correlation function. While 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, in order to compensate for it, the use of other sensors such as an inertial measurement unit, which has the disadvantage of increasing the cost and complexity of the system.

[0010] To solve these problems, it has again been attempted to do without the synchronization of the clock signals by proposing asynchronous demodulation solutions that make it possible to remove doubts about the signs of the components of the measured magnetic fields.

[0011] One such solution, described in US 10,746,819, consists of combining the EMT system with an inertial measurement unit to resolve the ambiguity surrounding the signs of the components of the measured magnetic fields. However, this solution has the drawback of increasing the cost and complexity of the system by requiring the integration of external sensors.

[0012] Another solution is to track the movement of the receiver relative to the transmitter or, as described in US 20080120061, to track 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. Furthermore, it is vulnerable to signal loss between the transmitter and the receiver, for example, due to masking or separation. Description of the invention

[0013] One 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 level of the first object, an oscillating magnetic field produced by a transmitter attached to the second object. Other objectives are to limit the use of additional sensors (other than magnetic sensors), to eliminate the need for a physical connection and signal synchronization between the transmitter and the receiver, and to avoid the initialization step 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 along a proper direction and capable of generating an alternating magnetic field at a proper frequency, the magnetic generators being arranged relative to each other so that their directions are in pairs non-coaxial and non-orthogonal, and the receiver being capable of measuring the components of a resulting magnetic field, formed by the superposition of the alternating magnetic fields generated by the magnetic generators of the transmitter, along three non-coplanar directions, the method comprising the following steps: . - measurement of the resulting magnetic field by the receiver in order to obtain a measurement signal representative of the resulting magnetic field, - demodulation of the measurement signal in such a way as to determine a plurality of candidate measurements, each formed from a set of candidate contributions from 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, using the corresponding corrected measurement, of a representative data point indicating the likelihood that this candidate measurement gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - selection of a selected measure from among the candidate measures, the selected measure being the one among the candidate measures 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.

[0014] According to particular embodiments of the invention, the determination method also has one or more of the following characteristics, taken individually or in any technically possible combination(s): - there are at least three magnetic generators and they are arranged relative to each other so that their directions are non-coplanar; - the corrective measure is common to all candidate measures; - the magnetic generators have centers that are essentially coincident; - the calculation of the representative data of the likelihood includes the following sub-step: for each candidate measurement, estimation of a distance of the corrected measurement corresponding to a reference space consisting of the measurements that can be obtained in a model of the system formed by the emitter and the receiver in which the magnetic generators are orthogonal to each other, the representative data of the likelihood being a function of said distance; - The calculation of the representative likelihood data includes, for each candidate measure, the following sub-steps: • deduction, from the corresponding corrected measurement, of a candidate pose of the receiver relative to the transmitter, • estimation of a theoretical measurement of the resulting magnetic field in the candidate pose in a model of the system formed by the emitter and the receiver, and • evaluation of a distance of the candidate measure or the corrected measure corresponding to said theoretical measure, the data representative of the likelihood being a function of said distance; 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 to be 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 process including an additional step of comparing the representative data of each candidate measure to a predetermined threshold, the selection of the selected measure being based on the representative data of the candidate measures only if the representative data of a single candidate measure is less than, respectively greater than, said predetermined threshold; When there is not a single candidate measure whose representative data is below, or above, the predetermined threshold, the process includes the following steps: • deduction, for each candidate measurement, from the corresponding corrected measurement, of a candidate pose of the receiver relative to the transmitter, and • Calculation of the distance from the candidate pose to a previous pose, the selected measurement being that of the candidate measurements for which the corresponding candidate pose has the smallest distance to the previous pose; and when there is not a single candidate measure whose representative data is below, or above, the predetermined threshold, the next step: • 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 • selection, for each alternating magnetic field, of the candidate phase shift that minimizes the difference with a phase shift prior to said alternating magnetic field generated with respect to the same demodulation signal, the selected measurement being that of the candidate measurements for which, for each alternating magnetic field generated, the signs of the candidate contributions are consistent with the selected phase shift.

[0015] 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.

[0016] The invention also relates, according to a third aspect, to a computer-readable recording medium on which a computer program product is stored according to the second aspect.

[0017] 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 along its own direction and capable of generating an alternating magnetic field at its own frequency, the magnetic generators being arranged relative to each other such that: - a first generator is oriented along a first generator direction coinciding with a first direction of an orthogonal frame attached to the emitter, and - a second generator is oriented along a second generator direction forming a first angle with a second direction of the orthogonal frame and included in a plane defined by the first and second directions of the orthogonal frame, the first angle being greater than or equal to 0.05 radians.

[0018] According to particular embodiments of the invention, the transmitter also has one or more of the following characteristics, taken individually 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 coordinate system; and - the third generator direction is not 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 frame.

[0019] The invention also relates, according to a fifth 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 attached to the second object, said transmitter comprising at least two magnetic generators each oriented along a natural direction and capable of generating an alternating magnetic field at a natural frequency, the magnetic generators being arranged relative to each other so that their directions are in pairs non-coaxial and non-orthogonal, - a receiver attached to the first object, said receiver being capable of measuring the components of a resulting magnetic field, formed by the superposition of the alternating magnetic fields generated by the magnetic generators of the emitter, along three non-coplanar directions, and - a data processing unit configured for the implementation of a determination process according to the first aspect.

[0020] According to particular embodiments of the invention, the determination system also has one or more of the following characteristics, taken individually 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 emitter is constituted by an emitter according to the fourth aspect. Brief description of the Figures

[0021] Other features and advantages of the invention will become apparent from the following description, given solely by way of example and with reference to the accompanying drawings, in which: - [Fig. 1] is a schematic view of an assembly consisting of a first object and a second object comprising a determination system according to the invention, - [Fig.2] is a diagram of a demodulator of a receiver of the system for determining [Fig.1], - [Fig.3] is a diagram of an example of a determination process that can be implemented by the determination system of [Fig.1], - [Fig.4] is a diagram illustrating a first variant of a step for calculating representative data from the process of [Fig.3], - [Fig.5] is a diagram illustrating a second variant of the data calculation step representative of the process of [Fig.3], - [Fig.6] is a diagram illustrating a third variant of the data calculation step representative of the process of [Fig.3], - [Fig.7] is a diagram illustrating a first variant of a step for selecting a candidate measure of the process of [Fig.3], - [Fig.8] is a diagram illustrating a second variant of the candidate measure selection step of the process of [Fig.3]. Detailed description of an example of implementation

[0022] The assembly 10 shown in [Fig.1] comprises a first object 12 and a second object 14, the first object 12 being mobile relative to the second object 14.

[0023] The first object 12 consists of a moving object in an inertial reference frame and whose movement relative to this inertial reference frame we wish to follow.

[0024] The second object 14 consists of an object whose pose in the inertial frame of reference is known. Here and subsequently, the pose is defined as consisting of all the position and orientation data of an object in space. In three-dimensional space, the pose therefore comprises six components, consisting of: - three position components, and - three orientation components.

[0025] The second object 14 is, for example, a fixed structure 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 enabling the movement of the second object to be tracked in the inertial frame of reference.

[0026] The first object 12 and the second object 14 are typically arranged relative to each other so 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.

[0027] 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.

[0028] 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 helmet and the second object 14 of a structure fixed in the helmet's movement environment.

[0029] A primary frame (Ri) is attached to the first object 12. This primary frame (Ri) is a direct orthogonal frame with origin Oi formed of a triplet of axes, shown in [Fig. 1], comprising: - a first primary axis ef, - a second primary axis orthogonal to the first axis and - a third primary axis orthogonal to the first and second axes 8| and

[0030] A secondary frame (R2) is attached to the second object 12. This secondary frame (R2) is a direct orthogonal frame with origin O2 formed by a triplet of axes, shown in [Fig. 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 ©2 and sJ •

[0031] The position 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 ef, ef, of the secondary frame (Ri) into the axes 89, rcP^rc primary (R2) and the vector p going from the origin O2 of the secondary frame (R2) to the origin Oi of the primary frame (Ri).

[0032] The assembly 10 also includes a positioning system 20 for determining the position of the first object 12 relative to the second object 14. This positioning system 20 consists of an electromagnetic tracking system, or EMT. It includes a transmitting device 21 comprising a transmitter 22 attached to the second object 14 and a receiving device 23 comprising a receiver 24 attached to the first object 12.

[0033] Said transmitter 22 and receiver 24 are typically configured to be functional when separated by a distance of less than 10 m. This helps to limit the size of the transmitter 22 and the receiver 24.

[0034] The emitter 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 co. It is oriented along a proper direction, respectively gb g2, g3, defined here and thereafter as the direction of said dipole moment.

[0035] The amplitude m of the dipole moment is preferably substantially equal for all the generators 30, 32, 34. The frequency co 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 able to generate an alternating magnetic field at a specific frequency.

[0036] To this end, 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 along a direction proper, defined by the axis around which the coil extends, this direction constituting the orientation direction of the magnetic generator 30, 32, 34 to which it belongs.

[0037] Each current generator 42, 44, 46 belongs to the transmitting device 21. Each current generator 42, 44, 46 is, for example, as shown, integrated into the second object 14. Alternatively (not shown), at least part of the current generators 42, 44, 46 is offset relative to the second object 14.

[0038] 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.

[0039] 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.

[0040] The magnetic generators 30, 32, 34 are arranged relative to each other such that: - a first generator 30 is oriented along a first generator direction gi coinciding with the first secondary axis - a second generator 32 is oriented along a second direction of generator g2 forming a first non-zero angle 0 with the second secondary axis ej and contained in a plane defined by the first and second secondary axes e^, e%, and - a third generator 34 is oriented along a third direction of generator g3 forming a second non-zero angle q> with the third secondary axis, said third direction of generator g3 being non-coplanar with each of the following planes: • the plane defined by the first direction of generator gi and the second direction of generator g2, • the plane defined by the first generator direction gi and the third secondary axis and • the plane defined by the second direction of generator g2 and the third secondary axis

[0041] The third generator direction g3 and the third secondary axis thus define a plane forming a third non-zero angle rp with the plane defined by the first generator direction gi and the third secondary axis, this angle rp being different from the angle between the first and second generator directions gb g2.

[0042] The first angle 0 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 1 radian, preferably less than or equal to 1 radian. The first angle 0 is advantageously an indirect angle, that is to say, it is measured in the indirect direction of the secondary frame (R2) from the second secondary axis 6%.

[0043] The second angle q> 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 a radian, preferably less than or equal to a radian. The second angle q> is advantageously an indirect angle, that is to say, it is measured in the indirect direction of the secondary frame (R2) from the third secondary axis

[0044] The third angle rp is particularly 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 gb g2 and advantageously strictly less than -0. For example, it is between 0.75 and 0.80 radians. The third angle rp is advantageously a direct angle, that is, it is measured in the direct direction of the secondary frame (R2) from the first secondary axis.

[0045] Preferably, the magnetic generators 30, 32, 34 have substantially coincident centers, that is, they can be modeled as magnetic dipoles with substantially the same center. To this end, the coils 36, 38, 40 have substantially coincident centers, that is, the centers of the coils are separated 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 frame (R2).

[0046] The transmitting device 21 further includes a clock 48 providing a reference signal representative of time. This reference signal is used by the magnetic generators 30, 32, 34 to vary over time the alternating magnetic fields that they generate.

[0047] The receiver 24 is capable of measuring the components of a resulting magnetic field, formed by the superposition of the alternating magnetic fields generated by the generators 30, 32, 34 of the transmitter 22, along the three axes ef, e±, 6^ of the primary frame (Ri).

[0048] To this end, 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 cb c2, c3 specific to the sensor 50, 52, 54, these measurement directions cb c2, c3 being non-coplanar. These sensors 50, 52, 54 are preferably arranged so that their measurement directions cb c2, c3 are substantially orthogonal to each other. others, each measurement direction cb c2, c3 being typically, as shown, substantially collinear with one of the axes ef, 6^ of the primary frame (Ri).

[0049] 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 across the coil. Each coil 56, 58, 60 is oriented along a specific 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.

[0050] 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. Alternatively (not shown), at least part of the tensiometers 62, 64, 66 is offset relative to the first object 12.

[0051] Each tensiometer 62, 64, 66 is designed to produce a voltage signal representative of the voltage across the associated coil 56, 58, 60 and therefore representative of the component of the resulting magnetic field along one of the measurement directions cb c2, c3.

[0052] For this purpose, each tensiometer 62, 64, 66 is typically made in the form of an amplifier coupled to an analog-to-digital converter (ADC).

[0053] The voltage signals produced by the tensiometers 62, 64, 66 together form a measurement signal. Since the measurement directions cb c2, c3 are not coplanar, this measurement signal is representative of the resulting magnetic field at the receiver 24.

[0054] The receiving device 23 also includes a demodulator 70.

[0055] This demodulator 70 is, for example, as shown, integrated into the first object 12. In an alternative (not shown), the demodulator 70 is offset relative to the first object 12.

[0056] With reference to [Fig.2], the demodulator 70 includes an input 72, 74, 76 for each voltage signal ub u2, u3 produced by a tensiometer 62, 64, 66. It also includes a generator 78 of voltage signal demodulation.

[0057] Each demodulation signal consists of a sinusoidal signal with a 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 ([Fig.1]) of the receiver 24.

[0058] 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 from each other by 4. Thus, for each of the alternating magnetic fields, there is an associated pair of demodulation signals composed of demodulation signals of frequency equal to that of said alternating magnetic field.

[0059] 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 every instant phase-shifted relative to the alternating magnetic field by an unknown phase shift Aq>j. This unknown phase shift Aq>j is in fact equal to cOj.At+ Aq^o, where cüj is the frequency of the alternating magnetic field (and therefore also of the demodulation signals of the associated pair), A <p, 0 est un déphasage initial (qui peut être nul), et At est la déviation temporelle entre les signaux des horloges 80 et 48, cette déviation temporelle At étant variable et aléatoire.

[0060] The demodulator 70 further includes a circuit 82 (real or emulated) for multiplying each voltage signal ub u2, u3 by each of the demodulation signals and an output 84A-84J for the product of each of these multiplications. The demodulator 70 also includes a low-pass filter 86 for filtering each of these outputs 84A-84J.

[0061] Preferably, the demodulator 70 is made in the form of a digital card with an FPGA (Field-Programmable Gate Array), a DSP (Digital Signal Processor), an ASIC (Application-Specific Integrated Circuit) and / or a processor or CPU (Central Processing Unit).

[0062] Returning to [Fig. 1], the determination system 20 further includes a data processing unit 90. This data processing unit 90 is configured to deduce from the measurements made by the receiving device 23 the position of the receiver 24 relative to the transmitter 22. It is also configured to deduce from this position the position of the first object 12 relative to the second object 14.

[0063] For this purpose, the data processing unit 90 is, in the example shown, a microcontroller. It comprises a processor or CPU (Central Processing Unit) 92 and a RAM (Random Access Memory) and / or ROM (Read Only Memory) type memory 94. The processor 92 is configured to execute instructions loaded into the memory 94. When the processing unit 90 is powered on, the processor 92 is able to read instructions from the memory 94 and execute them. These instructions form a computer program causing the processor 92 to carry out certain steps of a process 100 ([Fig. 3]) which will be detailed below.

[0064] The data processing unit 90 also includes a buffer memory 96 for the temporary storage of information necessary for the implementation of the process 100.

[0065] 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 process 100 is carried out by a mobile terminal and / or a remote server. The first object 12 then includes a communication system, typically a wireless communication system, configured to send the data from the receiver 24 to the mobile terminal and / or the remote server.

[0066] It should be noted that the demodulator 70 can also be located outside the first object 12.

[0067] A process 100 implemented by the determination system 20 will now be described, with reference to [Fig.3].

[0068] This method 100 is typically implemented during an initialization or reset step of 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 1EEE / A1AA 37th Digital Avionics Systems Conference (DASC), London, UK, 2018, pp. 1-6.

[0069] As can be seen in [Fig. 3], the process 100 begins with a step 110 of generating magnetic fields. During this step 110, the generators 30, 32, 34 of the emitter 22 are active and each generates a respective alternating magnetic field. These alternating magnetic fields overlap in space and produce a resultant magnetic field.

[0070] Concurrently with step 110, the resulting magnetic field is measured by the receiver 24 in step 120. In 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 across 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.

[0071] Then, in a step 130, the measurement signal is demodulated by the demodulator 70. In this step 130, each voltage signal ub, 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 ​​Pij,k, with i between 1 and 3, j between 1 and 3, and k equal to 1 or 2, are thus obtained, each value Pij,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 generator 30, 32, 34 oriented along the direction gj.

[0072] It should be noted that, to the first order, each value Ej, b 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 gj and the associated demodulation signals with the contribution of this alternating magnetic field to the component of the resulting magnetic field measured along the direction Ci. In other words, each value Pij,i, respectively each value Pij.2, is equal, to the first order, to A (p^, respectively A (p^, where: - Ujj is the contribution of the magnetic field generated by generator 30, 32, 34 oriented along the direction gj to the component of the magnetic field result measured along the direction cb and A (Pj is the phase shift between the magnetic field generated by the generator 30, 32, 34 oriented along the direction gj and the associated demodulation signals (i.e. the demodulation signals which have the same frequency as that of said magnetic field).

[0073] 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 and the demodulation signals of the same pair. In other words, we have:

[0074] i rr i lp. 2 + p. 2

[0075] 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 Mc each formed of a set of candidate contributions of each alternating magnetic field generated to each component of the magnetic field, that is to say a set of values ​​where each value U^j cst a candidate value for the contribution of the magnetic field generated by the generator 30, 32, 34 oriented along the direction gj to the component of the resulting magnetic field measured along the direction c;.

[0076] These candidate measures Mc 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:

[0077] <2 <31 Mc = ^22 <3 ^3.2 <3;

[0078] To this end, a first candidate measure Af £ is first constructed, such that: - the absolute value of each candidate contribution U^j is equal to the absolute value of the corresponding (real) contribution | , - for each alternating magnetic field, the sign of each of the candidate contributions U?. of this alternating magnetic field is equal to the sign of the value Pij.i, or Pij,2 resulting from the product of the voltage signal u; with one of the sinusoidal demodulation signals associated with this alternating magnetic field, in other words: Vi, sign( Ufj) = sign(Piji) ou Vi, sign( U^j) = sign(Pjj^) the determination of the corresponding matrix is ​​positive.

[0079] Then, starting from this first candidate measure Afp tr°is other measures Candidates are constructed by simply multiplying the matrix of the first measure candidate Af J by each of the following matrices r 1 0 0 0 -1 / / 1 ° 0 0-10 \0 0 -1 /

[0080] A total of four candidate measures Mc is thus obtained, these candidate measures satisfying the following condition:

[0081] / -1 0 0 1 0 0 0 0 -1 / / -1 0 o 0 o -1 /

[0082] It should be noted that the number of candidate measures Mc is limited to four because the matrix of the real measure necessarily has a positive determinant and matrices with a negative determinant therefore do not constitute serious candidates.

[0083] The demodulation step 130 is followed by a step 140 of application of a correction to the candidate measurements Mc. 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.

[0084] This correction is common to all candidate measures Mc. It comprises multiplying, from the right, the matrix of each candidate measure Mc by a matrix B. This matrix B is the inverse of the following matrix B:

[0085] -B2sin(0) B3sin(^)cos(y / ) B = 0 B2cos(0) h3sin(^)sin( y / ) 0 0 b3cos(tp)

[0086] where bb b2 and b3 are scaling factors, typically determined during a step of prior calibration, bi being an overall scaling factor allowing the length scale of the measurements provided by the determination system 20 and b2 and b3 are relative scaling factors, functions of bb which notably cover: the differences between the frequencies cOj of alternating magnetic fields which appear during the induction phenomenon occurring in the coils 56, 58, 60 of magnetic sensors 50, 52, 54, and - the relative differences between the norms of the dipole moments of generators 30, 32, 34.

[0087] Thus, for each candidate measure Mc, we obtain a corresponding partial corrected measure Mp, this partial corrected measure satisfying the following relation:

[0088] = M C B' 1 ' avec pi -b2sin(e) B' 1 0 B2cos(0) 0 0 b3sin(ç))cos( y / ) b3sin(tp)sin( i / / ) = I3 b3co^(p) / , where I3 is the identity matrix.

[0089] The correction also aims to compensate for the effect induced on the measurement signal, and therefore on the candidate measurements, by other defects in the transmitter 22, the receiver 24, and the environment. To this end, the correction also includes the application of other common and well-known corrections to the measurement. The partial correction Mp is performed so as to obtain, for each candidate measure Mc, a corresponding final corrected measure Mk. These other defects will be disregarded in the following discussion, 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 Mc, of a representative data point indicating the likelihood that this candidate measure Mc gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field. This representative data point is calculated using the corrected measure Mk corresponding to the candidate measure Mc.

[0091]

[0092]

[0093]

[0094]

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[0098]

[0099] In a first variant of this step 150, represented in [Fig.4], step 150 consists of a step 152 of estimation, for each candidate measurement Mc, of a distance from the corrected measurement Mk 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. The distance D of the corrected measurement Mk in the reference space is, for example, determined by the following formula: D= [(Su-2S2f^Sir2S^\V'2 \ S^+45^+45^ ] where Su, S22 and S33 are the diagonal terms of a diagonal matrix S of ordered positive real values ​​such that S^ — S33, this diagonal matrix resulting from a singular value decomposition of the corrected measure matrix Mk such that the diagonal matrix S satisfies the following relation: M k = PSQ T where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3 and QT is the transpose of a second matrix Q also belonging to the SO(3) group. It should be noted that the distance D can also be determined by numerous other formulas, depending or not on the diagonal terms of the matrix S, and possibly yielding different values ​​for the distance D. The only important point is that the formula for calculating the distance D is the same for all corrected measurements Mk. A person skilled in the art will easily be able to determine these other formulas. The representative datum of the likelihood that the candidate measurement Mc gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field is a function of the distance D. For example, this representative datum is proportional to, or in particular equal to, the distance D; it is then a decreasing function of the likelihood (indeed, the smaller the distance D, the more likely it is that the candidate measurement Mc gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field). Alternatively, the representative datum is an inverse function of the distance D; it is then an increasing function of the likelihood. In another variant of step 150, shown in [Fig. 5], this step 150 includes a substep 154 ​​of deduction, for each candidate measure Mc, of a

[0100]

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[0110] [YES] candidate pose of receiver 24 relative to transmitter 22, this candidate pose being deduced from the corrected measurement Mk corresponding to said candidate measurement Mc. To this end, the data processing unit 90 performs, in a preferred embodiment of the invention, the singular value decomposition of the corrected measure matrix Mk such that the corrected matrix Mk satisfies the following relationship: M k =PSQ T where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3, QT is the transpose of a second matrix Q also belonging to the SO(3) group, and S is the following matrix: If he $22 0 s. with Su Sn> S S22 and S33 are positive real values ​​ordered such that 22- °33' From this decomposition into singular values, the data processing unit 90 calculates, using the following formula, the vector r 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 Mc: 11 21 ^31 / where Qu, Q21 and Q31 are the terms of the first column of the matrix Q and r is given by the following formula: / 4u m )1 / / 3 1 = \ 4nTdS) / with po the magnetic permeability of free space, m the amplitude of the magnetic moments of generators 30, 32, 34 and Tr(S) the trace of the matrix S (i.e. the sum of the diagonal coefficients Su, S22 and S33). The data processing unit 90 also uses singular value decomposition to calculate, using 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 Mc: \0 0 -1 /

[0112] where PT is the transpose of the matrix P.

[0113] The data processing unit 90 thus obtains a pair (r, R) characterizing a

[0114]

[0115] candidate pose corresponding to candidate measure Mc. In this alternative variant of step 150, substep 154 ​​is followed by substep 155, which estimates 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 orthogonality error of the magnetic generators 30, 32, 34. This realistic model models the resulting magnetic field at any point in space as a vector ith^\ equal to: II '1 IU 3xy 1 cos(uqt) -siru0cos(w2é) +sin( <p)cos( v / )cos(w3t) 3xy + cos( ^Icosfw-jt) +sin( sin( iy)cos(w3t) 3y2-r2 +cos(0)cos(w3t) \ UM 3xz / l\ 3yz !

[0116] where t is time, q0 is the magnetic permeability of free space, m is the amplitude of the dipole moments of generators 30, 32, 34, r is the distance from the origin O2 of the secondary frame (R2), x is the coordinate along the first secondary axis, y is the coordinate along the second secondary axis, z is the coordinate along the third secondary axis, and co1, co2 and co3 are the angular frequencies, respectively, of the dipole moment of the first magnetic generator 30, of the dipole moment of the second magnetic generator 32 and the dipole moment of the third generator magnetic 34.

[0117] The data processing unit 90 is sufficient to estimate the theoretical measure realistic of the resulting magnetic field in the candidate pose, to calculate the components of the vector above in the position defined by the vector r. in the frame of reference defined by the rotation matrix R.

[0118] Still in this other variant of step 150, substep 155 is itself followed by a substep 156 for evaluating the distance of each candidate measure Mc to the realistic theoretical measurement associated with said candidate measurement Mc, that is to say, to the realistic theoretical measurement of the resulting magnetic field in the candidate pose corresponding to said candidate measure Mc. During this substep 156, the processing unit 90 typically evaluates a distance between the candidate measure Mc matrix and the associated realistic theoretical measure matrix, this realistic theoretical measure matrix being constituted by the matrix:

[0119] TTth,r ul,l Tjth,r ul,2 t Tth,r1 01.3 Mth^ = rrth^ U2,l TTth,r ^2.2 r Tthjr u3.2 TTth^ u 3.3

[0120] such that the realistic theoretical magnetic field in the candidate pose is given by the following vector:

[0121] TTth,r\ • t rthfT! ^1,2 1 TTth^\ ul,3 bth,r(t)= 008(^^) TTth,r + COS(Cd2t) tt thx ^2,2 + COS(td3Ù) T rtll,!' ^3.1 tt^ U3.2

[0122] The distance between the matrices Mc and Mth 'r is, for example, given by the norm of Frobenius of the difference between matrices.

[0123] The representative data for the likelihood that the candidate measure Mc gives the real 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 Mc and Mth'r. For example, this representative data is proportional, in particular equal, to said distance; it is then a decreasing function of the likelihood (indeed, the smaller the distance between the matrices Mc and Mth'r, the more It is likely that the candidate measurement Mc 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.

[0124] A third variant of step 150 is shown in [Fig.6].

[0125] In this third variant, step 150 still includes substep 154 ​​of For each candidate measurement Mc, a candidate pose of the receiver 24 relative to the transmitter 22 is deducted, this candidate pose being deduced from the corrected measurement Mk corresponding to said candidate measurement Mc. This third variant is distinguished however, from the previous variant in that step 150 does not include the sub- steps 155 and 156.

[0126] Instead, substep 154 ​​is followed by a substep 157 for estimating a simplified theoretical measurement of the resulting magnetic field in each pose candidate. This estimate is based on a simplified model of the system of determination 20 which considers the orthogonal magnetic generators 30, 32, 34 to each other. This simplified model models the resulting magnetic field in all point in space in the form of a vector

[0127] cos( '3x2-r2' 3xy + cos(w2t) ' 3xy 1 3y2-r2 + cos(cu3t) ' 3xz ■ 3yz 1 i 3xz । 3yz \3z2-r2 1

[0128] where t is time, q0 is the magnetic permeability of free space, m is the amplitude of the dipole moments of generators 30, 32, 34, r is the distance from the origin O2 of the frame secondary (R2), x is the coordinate along the first secondary axis, Y is the constant coordinate along the second secondary axis, z is the coordinate along the third secondary axis, and a > i, (¾ and co3 are the angular frequencies, respectively, of the dipole moment of the first magnetic generator 30, of the dipole moment of the second magnetic generator 32 and the dipole moment of the third generator magnetic 34.

[0129] The data processing unit 90 is sufficient to estimate the theoretical measure simplified calculation of the resulting magnetic field in the candidate pose, to calculate the components of the vector above in the position defined by the vector "r, in the frame of reference defined by the rotation matrix R.

[0130] Still in this third variant of step 150, substep 157 is itself followed by a substep 158 of evaluation of the distance of each corrected measure Mk corresponding to a candidate measure Mc to the simplified theoretical measure associated with said candidate measurement Mc, that is to say, the simplified theoretical measurement of the resulting magnetic field in the candidate pose corresponding to said candidate measure Mc. During this substep 158, the processing unit 90 typically evaluates a distance between the corrected measure matrix Mk and the associated simplified theoretical measure matrix, this simplified theoretical measure matrix being constituted by the matrix:

[0131] TTth,s ^1.1 t Tth,s ul,2 yt thfS ■ ^1.3 Mth's = T ^01,S u2,lt u2.2 T ^3.1 T rth,STT th,s u3,3

[0132] such that the simplified theoretical magnetic field in the candidate pose is given by the following vector:

[0133] cos(w1t + <p1) TTth,s\ U 1.1 T rthrS u2,l Trth,S U3,l + cos(to2t+{p2) th,.s\ 1,2 T -rtll / S u2,2 TT thjS u 3,2 + cos("3t+ <p3) t rtii.s ^1,3 T rthrS u2,3 r rthjS u 3,3

[0134] The distance between the matrices Mk and Mth is for example given by the Frobenius norm of the difference between the matrices.

[0135] The representative data for the likelihood that the candidate measure Mc 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 Mk and Mth's. For example, this representative data is proportional, in particular equal, to said distance; it is then a decreasing function of the likelihood (indeed, the smaller the distance between the matrices Mk and Mth's, the more likely it is that the candidate measure Mc gives the real 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.

[0136] Returning to [Fig.3], step 150 is followed by a step 160 of selecting a measure selected from among the candidate measures Mc.

[0137] With reference to [Fig. 7], step 160 includes a first substep 161 of comparing the representative data of each candidate measure Mc to a threshold. In the case where, as shown here, the representative data is a decreasing function of the likelihood, this substep 161a has the function of determining whether one or more candidate measures Mc have their representative data below said threshold. In the case where the representative data is an increasing function of the likelihood, this substep 161a has the function of determining whether one or more candidate measures Mc have their representative data above said threshold.

[0138] If a single candidate measure Mc has its representative data below, or above, the threshold, substep 161 is followed by a substep 162 for selecting said candidate measure Mc whose representative data is below, or above, the threshold. The selected measure is then the one of the candidate measures Mc whose representative data is the lowest, or the highest, and therefore indicates the highest likelihood.

[0139] If there is no single candidate measure Mc with its representative data below, or above, the threshold, for example, because several candidate measures Mc have their representative data below, or above, the threshold, or because no candidate measure Mc has its representative data below, or above, the threshold, then the selection can no longer be based on the representative data of the candidate measures. Indeed, this reflects the fact that this representative data is unreliable. In a pose (or phase shift) tracking method, the processed sample cannot then be used to initialize or reset the tracking. The pose is then determined by applying the tracking method, which takes advantage of the history of poses (or phases) estimated previously.

[0140] In a first variant of step 160, represented in [Fig.7], substep 161 is thus followed, when several candidate measurements Mc have their representative data lower, respectively higher, than the threshold, by a substep 163 of deduction, for each candidate measurement, of a candidate pose of the receiver relative 24 relative to the emitter 22.

[0141] This candidate pose is deduced from the corrected measurement Mk corresponding to said candidate measurement Mc by a process similar to that described above in connection with step 154. The data processing unit 90 thus obtains a pair (r, R) characterizing a candidate pose corresponding to the candidate measurement Mc.

[0142] Substep 163 is then followed by substep 164, which calculates the distance of each candidate pose to a previous pose. This previous pose is typically a pose determined previously, for example, by implementing method 100 in a previous iteration of the latter or by implementing 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", 20181EEE / A1AA 37th Digital Avionics Systems Conference (DASC), London, UK, 2018, pp. 1-6. This previous pose is preferably the last known pose of the receiver 24 relative to the transmitter 22.

[0143] The distance d between the candidate pose and the previous pose is given, for example, by the following formula: [°144] [014-5] where || • || ? is the 2-norm of the logarithm in the SO(3) group of rotation matrices, Rc is the rotation matrix defining the orientation in the candidate pose, and is the transpose of the rotation matrix defining the orientation in the previous pose. [014-6] Substep 164 is followed by substep 165 of selecting the candidate measurement Mc for which the corresponding candidate pose has the shortest distance to the previous pose. The selected measurement is then the one of the candidate measurements Mc for which the corresponding candidate pose has the shortest distance to the previous pose. [014-7] In another variant of step 160, shown in [Fig.8], substep 161 is followed, when there is not a single candidate measurement Mc having its representative data lower, respectively higher, than the threshold, by a substep 166 of determination, for each alternating magnetic field, of two candidate phase shifts of said alternating magnetic field with respect to the associated demodulation signals. [014-8] During this substep 166, the data processing unit 90 calculates, for each alternating magnetic field generated by one of the generators 30, 32, 34, the ratio PU2 between the values ​​of at least one pair of values ​​{Fij i, Pijj2} resulting Pw products of one of the voltage signals with the associated demodulation signals audit alternating magnetic field. The data processing unit 90 then determines an angle α whose tangent is equal to this ratio:

[0149] . (PuA a = arctanlp—

[0150] 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 a+ir.

[0151] Substep 166 is followed by a substep 167 of selection, for each alternating magnetic field, of that of the candidate phase shifts which minimizes a deviation with a known prior phase shift of said alternating magnetic field.

[0152] During this substep 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

[0153] 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 prior pose of the receiver 24 relative to the transmitter. The time interval r between this previous measurement of the resulting magnetic field by the receiver 24 and the implementation of step 120 must satisfy the following condition:

[0154] T <p<#

[0155] with ¢)-maX^|0.|j where each |ç).| is the absolute value of the time derivative characteristic of the phase shift between a generated alternating magnetic field and the associated demodulation signals.

[0156] In particular, during this substep 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 candidate phase shift with the smallest difference (in absolute value) with the previous phase shift.

[0157] Substep 167 is itself followed by a substep 168 of selection of that candidate measures Mc for which, for each alternating magnetic field, the The signs of the Ufj candidate contributions are consistent with the phase shift value selected.

[0158] During this substep 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 by that of at least one value Pij i (if sign of the cosine) or with that of at least one value P;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 the absolute value is 2) of each candidate measure M and selects the candidate measure Mc for which, for each alternating magnetic field, the sign of said corresponding candidate contribution is equal to said sign thus obtained.

[0159] Furthermore, in this other variant of step 160, substep 162 is followed by a substep 169 of resetting the phase shift of each alternating magnetic field with respect to the demodulation signals associated with this alternating magnetic field.

[0160] During this substep 169, the data processing unit 90 calculates, for each alternating magnetic field generated by one of the generators 30, 32, 34, the ratio Ew between the values ​​of at least one pair of values ​​{P;j>b Pîj.2} resulting P i,j,l 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 α whose tangent is equal to this ratio:

[0161] . (PijA a = arctanl p—J

[0162] The data processing unit 90 then determines the sign of the cosine or sine of this angle α. It then multiplies this sign by that of at least one value Pij i (if the cosine is known) or by that of at least one value Pj 2 (if the sine is known) resulting from the product of one of the voltage signals with one of the demodulation signals associated with said alternating magnetic field. Finally, it compares the sign thus obtained with the sign of the corresponding candidate contribution (i.e., whose absolute value is equal to / p 2 p 2") of the candidate measurement Mc selected. If the signs are equal, the data processing unit 90 assigns the phase shift of the alternating magnetic field the value a. If these signs are opposite, the data processing unit 90 assigns the phase shift of the alternating magnetic field the value a+ir.

[0163] Returning to [Fig.3], step 160 is followed by a step 170 of deduction of the pose of the receiver 24 relative to the transmitter 22, and therefore of the pose of the first object 12 relative to the second object 14, from the corrected measurement Mk corresponding to the selected measurement.

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[0176] To this end, the data processing unit 90 performs, in a preferred embodiment of the invention, the singular value decomposition of the corrected measure matrix Mk such that the corrected matrix Mk satisfies the following relationship: M k = PSQ T where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3, QT is the transpose of a second matrix Q also belonging to the SO(3) group, and S is the following matrix: 11 0 ^22 0 $33 / with Su, S22 and S33 being positive real values ​​ordered such that 11 22 From this decomposition into singular values, the data processing unit 90 calculates, using the following formula, the vector p characterizing the position of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the selected measurement: 11 21 ^31 / where Qu, Q2i and Q3i are the terms of the first column of the matrix Q and r is given by the following formula: / \ ^3 r= l 4nTriS) / with po the magnetic permeability of free space, m the amplitude of the dipole moments of generators 30, 32, 34 and Tr(S) the trace of the matrix S (i.e. the sum of the diagonal coefficients Su, S22 and S33). The data processing unit 90 also uses singular value decomposition to calculate, using 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 PT is the transpose of the matrix P.

[0177] The data processing unit 90 thus obtains a pair (p, 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).

[0178] Thus, thanks to the invention described above, it is possible to determine the position of the receiver 24 relative to the transmitter 22 intrinsically, without a 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 a calibration step. This position can therefore be determined in a simple, robust, and inexpensive manner.

Claims

1. Demands 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 along a natural direction (gb g2, g3) and capable of generating an alternating magnetic field at a natural frequency, the magnetic generators (30, 32, 34) being arranged relative to each other such that their directions (gb g2, g3) are pairwise non-coaxial and non-orthogonal, and the receiver (24) being capable of measuring the components of a resulting magnetic field, formed by the superposition of the alternating magnetic fields generated by the magnetic generators (30, 32, 34) of the transmitter (22), along three non-coplanar directions (cb 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 from 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, using the corresponding corrected measurement, of a data representative of the likelihood that this candidate measurement gives the actual contributions of each generated alternating magnetic field to each component of the resulting magnetic field, - selection (160) of a selected measure from among the candidate measures, the selected measure being 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), in which the receiver (24) has magnetic sensors (50, 52, 54) to measure the components of the resulting magnetic field and the determination method (100) is implemented without any other sensor than said magnetic sensors (50, 52, 54).

2. A determination method (100) according to claim 1, wherein the correction is common to all candidate measures.

3. Method of determination (100) according to claim 1 or 2, wherein the magnetic generators (30, 32, 34) have substantially coincident centers.

4. Method of determination (100) according to any one of the preceding claims, wherein the representative data of the likelihood is calculated by means of a singular value decomposition of a matrix of the corresponding corrected measure.

5. A method for determining (100) according to any one of the preceding claims, wherein the calculation (150) of the representative data of the likelihood comprises the following substep: - for each candidate measurement, estimation (152) of a distance of the corrected measurement corresponding to a reference space consisting of the measurements that 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 representative data of the likelihood being a function of said distance.

6. Method of determination (100) according to claims 4 and 5 taken together, wherein the distance is a function of the diagonal terms of a diagonal matrix resulting from the singular value decomposition of the matrix of the corresponding corrected measure.

7. Method of determination (100) according to claim 6, wherein the distance is determined by the following formula: = / \ 1 / 2 ( 8^+48^448^ /

8. where Su, S22 and S33 are the diagonal elements of a diagonal matrix S of positive real values ​​ordered such that > ^22- <$33, this diagonal matrix resulting from a singular value decomposition of the corrected measure matrix such that the diagonal matrix S satisfies the following relation: Mk=PSQT where Mk is the corrected measure matrix, P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3 and QT is the transpose of a second matrix Q also belonging to the SO(3) group. A method for determining (100) according to any one of claims 1 to 4, wherein the calculation (150) of the representative data for the likelihood comprises, for each candidate measure, the following sub-steps: deduction (154), from the corresponding corrected measurement, of a candidate pose of the receiver (24) relative to the emitter (22), estimation (155, 157) of a theoretical measurement of the resulting magnetic field in the candidate pose in a model of the system (20) formed by the emitter (22) and the receiver (24), and evaluation (156, 158) of a distance from the candidate measure or the corrected measure corresponding to said theoretical measure, the representative data of the likelihood being a function of said distance.

9. Method of determination according to claims 4 and 8 taken together, in which the candidate pose of the receiver (24) relative to the issuer (22) is deduced from the singular value decomposition of the measure matrix corrected version.

10. Method of determination (100) according to claim 9, in which The candidate pose is characterized by a pair (y, R) such that: with : and 1 R=Q 0 \0 0 0 -1 0 P T 0 -1 / - P a first matrix belonging to the SO(3) group and Q a second matrix Q also belonging to the SO(3) group such that _ pgQ^, where Mk is the matrix of the corrected measure and S is a diagonal matrix of ordered positive real values, - Qi i, Q21 and Q3i are the terms of the first column of the matrix Q, and - r is given by the following formula: / 4^ m ) , r \ 4nTr(S) / where po the magnetic permeability of free space, m the amplitude of the magnetic moments of the magnetic generators (30, 32, 34) and Tr(S) the trace of the matrix S.

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

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

13. A method for determining (100) according to any one of the preceding claims, wherein 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 measure to a predetermined threshold, the selection (160) of the selected measure being based on the representative data of the candidate measures only if the representative data of a single candidate measure is lower, respectively higher, than said predetermined threshold.

14. A determination method (100) according to claim 13, wherein, when there is not a single candidate measurement whose representative data is below, respectively above, 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 of the candidate pose to a previous pose, the selected measurement being that of the candidate measurements for which the corresponding candidate pose has the smallest distance to the previous pose.

15. Method of determination (100) according to claim 13, comprising, where there is not a single candidate measurement whose representative data is less than, respectively greater 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 that same demodulation signal, the selected measurement being 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. Product computer program comprising code instructions for implementation, by a processor, of a determination method (100) according to any one of the preceding claims.

17. Computer-readable recording medium on which is stored a computer program product according to claim 16.

18. Transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 15, the transmitter (22) comprising at least two magnetic generators (30, 32, 34), each oriented along a specific direction (gb g2, g3) and suitable to generate an alternating magnetic field at a natural frequency, the emitter (22) being designed so that: - a first generator (30) is oriented along a first generator direction (gi) coinciding with a first direction (6^) of an orthogonal frame attached to the emitter (22), and - a second generator (32) is oriented along a second generator direction (g2) forming a first angle (0) with a second direction (e^) of the orthogonal frame and included in a plane defined by the first and second directions (S^, e^) of the orthogonal frame, the first angle (0) being greater than or equal to 0.05 radians.

19. Transmitter (22) according to claim 18, 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 along a third generator direction (g3) forming a second angle (q>), greater than or equal to 0.05 radians, with a third direction (62) of the orthogonal frame.

20. A method for designing a transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 15, comprising the following steps:

21.

22.

23. - arrangement of a first magnetic generator (30) of the emitter (22), capable of generating an alternating magnetic field at a first frequency, such that it is oriented along a first generator direction (gi) coinciding with a first direction (6^) of an orthogonal frame attached to the emitter (22), and - arrangement of a second magnetic generator (32) of the emitter (22), capable of generating an alternating magnetic field at a second frequency different from the first frequency, so that it is oriented along a second generator direction (g2) forming a first angle (0) with a second direction (&p) of the orthogonal frame and included in a plane defined by the first and second directions (e^, 6^) of the orthogonal frame, the first angle (0) being greater than or equal to 0.05 radians. A design method according to claim 20, comprising an additional step of arranging a third magnetic generator (34) of the emitter (22), capable of generating an alternating magnetic field at a third frequency different from the first and second frequencies, so that it is oriented along a third generator direction (g3) forming a second angle (q>), greater than or equal to 0.05 radians, with a third direction (e|) of the orthogonal frame. Method of manufacturing a transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 15, comprising designing a transmitter (22) by means of a method according to claim 20 or 21, followed by the realization of this transmitter (22). System (20) for determining at least one component of the pose of a first object (12) relative to a second object (14), said system of determination (20) comprising: an emitter (22) attached to the second object (14), said emitter (22) comprising at least two magnetic generators (30, 32, 34) each oriented along a proper direction (gb g2, g3) and capable of generating an alternating magnetic field at a proper frequency, the magnetic generators (30, 32, 34) being arranged relative to each other so that their directions (gb g2, g3) are in pairs non-coaxial and non-orthogonal, a receiver (24) attached to the first object (12), said receiver (24) being capable of measuring the components of a resulting magnetic field, formed by the superposition of the alternating magnetic fields generated by the magnetic generators (30, 32, 34) of the transmitter (22), along three non-coplanar directions (cb c2, c3), and a data processing unit (90) configured for the implementation of a determination method (100) according to any one of claims 1 to 15.

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