FR3151915A1 - Determination of pose by measurement of an oscillating magnetic field produced by non-orthogonal generators - Google Patents

Abstract

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: measurement of a resulting magnetic field, demodulation of the measurement signal so as to determine a plurality of candidate measurements, application to each candidate measurement of a correction aimed at compensating for a lack of orthogonality of directions of the magnetic generators (30, 32, 34), so as to obtain a corresponding corrected measurement, calculation of data representative of the likelihood that this candidate measurement gives the real contributions of each alternating magnetic field, selection of a selected measurement corresponding to the highest likelihood, and deduction of said at least one component of the pose of the receiver (24). Figure for abstract: Fig. 1

Description

Determination of pose by measurement of an oscillating magnetic field produced by non-orthogonal generators Field of invention

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.

Technological background

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 include a fixed transmitter in the frame of reference, formed by 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 by three magnetic sensors arranged so as to form a substantially orthogonal mobile trihedron. Time-dependent electric currents flow in the coils of the transmitter and cause three magnetic fields to appear which are captured by the sensors of the receiver. Each sensor of the receiver measures, for each of the magnetic fields emitted, the projection of this field on the direction which directs the sensor. This gives a total of nine components which make it possible to move from the mobile trihedron to the fixed trihedron. In fact, these nine components depend on the position and orientation of the receiver relative to the transmitter.

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

A first alternative, described in US 5,453,686, uses time 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. However, this technique 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 metal elements. Then, this technique requires the use of magnetometers as sensors, which are particularly difficult to implement over a wide range.

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

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 phase shift compared to the time reference of the emitted magnetic fields, which gives rise to doubt as to the signs of the components of the measured magnetic fields.

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.

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 and require additional components or reduce the availability of the final measurements and/or 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. 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 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.

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.

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 making the system more expensive and complex by requiring the integration of external sensors.

Another solution consists in tracking the movement of the receiver relative to the transmitter or, as described in US 20080120061, in tracking the phase shifts between the emitted fields and the reference signals produced by the receiver, after an initialization step consisting in 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.

• mesure du champ magnétique résultant par le récepteur de manière à obtenir un signal de mesure représentatif du champ magnétique résultant,
• démodulation du signal de mesure de manière à déterminer une pluralité de mesures candidates formées chacune d’un ensemble de contributions candidates de chaque champ magnétique alternatif généré à chaque composante du champ magnétique résultant,
• application à chaque mesure candidate d’un correctif visant à compenser l’effet induit sur le signal de mesure par le défaut d’orthogonalité des directions des générateurs magnétiques, de manière à obtenir pour chaque mesure candidate une mesure corrigée correspondante,
• calcul, pour chaque mesure candidate, au moyen de la mesure corrigée correspondante, d’une donnée représentative de la vraisemblance que cette mesure candidate donne les contributions réelles de chaque champ magnétique alternatif généré à chaque composante du champ magnétique résultant,
• sélection d’une mesure sélectionnée parmi les mesures candidates, la mesure sélectionnée étant constitué par celle des mesures candidates dont la donnée représentative indique la vraisemblance la plus élevée, et
• déduction, à partir de la mesure corrigée correspondant à la mesure sélectionné, de ladite au moins une composante de la pose du récepteur relativement à l’émetteur.

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 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. For this purpose, 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,
• demodulating 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 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 representing the likelihood that this candidate measurement gives the real contributions of each generated alternating magnetic field to each component of the resulting magnetic field,
• selecting a selected measure from among the candidate measures, the selected measure being constituted by that of 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.

• les générateurs magnétiques sont au moins au nombre de trois et sont agencés relativement les uns aux autres de sorte que leurs directions soient non coplanaires ;
• le correctif est commun à toutes les mesures candidates ;
• les générateurs magnétiques ont des centres sensiblement confondus ;
• le calcul de la donnée représentative de la vraisemblance comprend la sous-étape suivante : pour chaque mesure candidate, estimation d’une distance de la mesure corrigée correspondante à un espace de référence constitué des mesures pouvant être obtenues dans un modèle du système formé de l’émetteur et du récepteur dans lequel les générateurs magnétiques sont orthogonaux les uns aux autres, la donnée représentative de la vraisemblance étant fonction de ladite distance ;
• le calcul de la donnée représentative de la vraisemblance comprend, pour chaque mesure candidate, les sous-étapes suivantes :
  • déduction, à partir de la mesure corrigée correspondante, d’une pose candidate du récepteur relativement à l’émetteur,
  • estimation d’une mesure théorique du champ magnétique résultant dans la pose candidate dans un modèle du système formé de l’émetteur et du récepteur, et
  • évaluation d’une distance de la mesure candidate ou de la mesure corrigée correspondante à ladite mesure théorique, la donnée représentative de la vraisemblance étant fonction de ladite distance ;
• le modèle du système tient compte du défaut d’orthogonalité des générateurs magnétiques et la distance évaluée à l’étape d’évaluation consiste en une distance de la mesure candidate à ladite mesure théorique;
• le modèle du système considère les générateurs magnétiques orthogonaux les uns et aux autres, et la distance évaluée à l’étape d’évaluation consiste en une distance de la mesure corrigée à ladite mesure théorique;
• la donnée représentative est une fonction décroissante, respectivement croissante, de la vraisemblance, le procédé comprenant une étape supplémentaire de comparaison de la donnée représentative de chaque mesure candidate à un seuil prédéterminé, la sélection de la mesure sélectionnée n’étant basée sur les données représentatives des mesures candidates que si la donnée représentative d’une unique mesure candidate est inférieure, respectivement supérieure, audit seuil prédéterminé;
• lorsqu’il n’y a pas une unique mesure candidate dont la donnée représentative est inférieure, respectivement supérieure, au seuil prédéterminé, le procédé comprend les étapes suivantes :
  • déduction, pour chaque mesure candidate, à partir de la mesure corrigée correspondante, d’une pose candidate du récepteur relativement à l’émetteur, et
  • calcul d’une distance de la pose candidate à une pose antérieure, la mesure sélectionnée étant constituée par celle des mesures candidates pour laquelle la pose candidate correspondante présente la plus faible distance à la pose antérieure ; et
• lorsqu’il n’y a pas une unique mesure candidate dont la donnée représentative est inférieure, respectivement supérieure, au seuil prédéterminé, l’étape suivante :
  • détermination, pour chaque champ magnétique alternatif généré, de déphasages candidats dudit champ magnétique alternatif généré par rapport à un signal de démodulation utilisé pour démoduler le signal de mesure, et
  • sélection, pour chaque champ magnétique alternatif, de celui des déphasages candidats qui minimise un écart avec un déphasage antérieur dudit champ magnétique alternatif généré par rapport à ce même signal de démodulation, la mesure sélectionnée étant constituée par celle des mesures candidates pour laquelle, pour chaque champ magnétique alternatif généré, les signes des contributions candidates sont cohérents avec le déphasage sélectionné.

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 fix is common to all candidate measures;
• magnetic generators have centers that are substantially coincident;
• the calculation of the data representative of the likelihood comprises 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 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 calculation of the data representing the likelihood 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 transmitter and the receiver, and
  • evaluation of a distance from the candidate measurement or from the corrected measurement corresponding to said theoretical measurement, the data representing 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 step 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 step 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:
  • deduction, for each candidate measurement, from the corresponding corrected measurement, of a candidate pose of the receiver relative to the transmitter, and
  • calculating a distance from the candidate pose to a prior pose, the selected measurement being that of the candidate measurements for which the corresponding candidate pose has the smallest distance to the prior pose; and
• when there is not a single candidate measure whose representative data is lower, respectively higher, than the predetermined threshold, the following step:
  • determining, for each generated alternating magnetic field, candidate phase shifts of said generated alternating magnetic field relative to a demodulation signal used to demodulate the measurement signal, and
  • selecting, for each alternating magnetic field, that of the candidate phase shifts which minimizes a deviation from a previous phase shift of said alternating magnetic field generated with respect to this same demodulation signal, the selected measurement being constituted by 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.

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.

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.

• un premier générateur soit orienté suivant une première direction de générateur confondue avec une première direction d’un repère orthogonal attaché à l’émetteur, et
• un deuxième générateur soit orienté suivant une deuxième direction de générateur formant un premier angle avec une deuxième direction du repère orthogonal et comprise dans un plan défini par les première et deuxième directions du repère orthogonal, le premier angle étant supérieur ou égal à 0,05 radians.

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 according to a first generator direction coincident with a first direction of an orthogonal reference attached to the transmitter, and
• a second generator is oriented along 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.

• un troisième générateur magnétique apte à générer un champ magnétique alternatif à une fréquence propre, ledit troisième générateur étant orienté suivant une troisième direction de générateur formant un deuxième angle, supérieur ou égal à 0,05 radians, avec une troisième direction du repère orthogonal ; et
• la troisième direction de générateur est non coplanaire avec chacun des plans définis par deux des trois directions suivantes : la première direction de générateur, la deuxième direction de générateur et la troisième direction du repère orthogonal.

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 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; 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 coordinate system.

• un émetteur solidaire du deuxième objet, ledit émetteur comprenant au moins deux générateurs magnétiques chacun orienté suivant une direction propre et apte à générer un champ magnétique alternatif à une fréquence propre, les générateurs magnétiques étant agencés relativement les uns aux autres de sorte que leurs directions soient deux à deux non coaxiales et non orthogonales,
• un récepteur solidaire du premier objet, ledit récepteur étant apte à mesurer les composantes d’un champ magnétique résultant, formé de la superposition des champs magnétiques alternatifs générés par les générateurs magnétiques de l’émetteur, suivant trois directions non coplanaires, et
• une unité de traitement de données configurée pour la mise en œuvre d’un procédé de détermination selon le premier aspect.

The invention finally 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 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.

• les générateurs magnétiques sont au moins au nombre de trois et sont agencés relativement les uns aux autres de sorte que leurs directions soient non coplanaires ; et
• l’émetteur est constitué par un émetteur selon le quatrième aspect.

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

• la est une vue schématique d’un ensemble formé d’un premier objet et d’un second objet comprenant un système de détermination selon l’invention,
• la est un diagramme d’un démodulateur d’un récepteur du système de détermination de la ,
• la est un diagramme d’un exemple de procédé de détermination susceptible d’être mis en œuvre par le système de détermination de la ,
• la est un diagramme illustrant une première variante d’une étape de calcul de données représentatives du procédé de la ,
• la est un diagramme illustrant une deuxième variante de l’étape de calcul de données représentatives du procédé de la ,
• la est un diagramme illustrant une troisième variante de l’étape de calcul de données représentatives du procédé de la ,
• la est un diagramme illustrant une première variante d’une étape de sélection d’une mesure candidate du procédé de la ,
• la est un diagramme illustrant une deuxième variante de l’étape de sélection d’une mesure candidate du procédé de la .

Other characteristics and advantages of the invention will appear on reading the description which follows, given solely by way of example and made with reference to the appended drawings, in which:

• there is a schematic view of an assembly formed of a first object and a second object comprising a determination system according to the invention,
• there is a diagram of a demodulator of a receiver of the system for determining the ,
• there is a diagram of an example of a determination method that may be implemented by the determination system. ,
• there is a diagram illustrating a first variant of a step of calculating data representative of the method of the ,
• there is a diagram illustrating a second variant of the step of calculating representative data of the method of the ,
• there is a diagram illustrating a third variant of the step of calculating representative data of the method of the ,
• there is a diagram illustrating a first variant of a step of selecting a candidate measure of the method of the ,
• there is a diagram illustrating a second variant of the candidate measure selection step of the method of the .

Detailed description of an example of realization

The set 10 shown on the comprises a first object 12 and a second object 14, the first object 12 being movable relative to the second object 14.

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

• trois composantes de position, et
• trois composantes d’orientation.

The second object 14 is constituted by an object whose pose in the inertial frame 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, constituted by:

• 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. As a variant (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.

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 obscured from view by the second object 14 as it moves.

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.

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 stationary in the environment in which the headset moves.

• un premier axe primaire ,
• un deuxième primaire axe orthogonal au premier axe , et
• un troisième axe primaire orthogonal aux premier et deuxième axes et .

A primary frame (R ₁ ) is attached to the first object 12. This primary frame (R ₁ ) is a direct orthogonal frame of origin O ₁ formed by a triplet of axes, represented on the , including:

• 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 .

• un premier axe secondaire ,
• un deuxième axe secondaire orthogonal au premier axe , et
• un troisième axe secondaire orthogonal aux premier et deuxième axes et .

A secondary frame (R ₂ ) is attached to the second object 12. This secondary frame (R ₂ ) is a direct orthogonal frame of origin O ₂ formed by a triplet of axes, represented on the , including:

• 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 .

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 secondary reference (R ₁ ) in the axes , , of the primary reference (R ₂ ) and of the vector going from the origin O ₂ of the secondary reference frame (R ₂ ) to the origin O ₁ of the primary reference frame (R ₁ ).

The assembly 10 also comprises a determination system 20 intended for determining 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.

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.

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 g ₁ , g ₂ , g ₃ , defined here and hereinafter as the direction of said dipole moment.

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, such that each generator 30, 32, 34 is thus capable of generating an alternating magnetic field at a specific frequency.

For this purpose, each magnetic generator 30, 32, 34 comprises a coil, respectively 36, 38, 40, connected to a generator of excitation current of the coil, 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.

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 part of the current generators 42, 44, 46 is offset relative to the second object 14.

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.

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.

• un premier générateur 30 soit orienté suivant une première direction de générateur g₁confondue avec le premier axe secondaire ,
• un deuxième générateur 32 soit orienté suivant une deuxième direction de générateur g₂formant un premier angle θ non nul avec le deuxième axe secondaire et comprise dans un plan défini par le premier et deuxième axes secondaires , , et
• un troisième générateur 34 soit orienté suivant une troisième direction de générateur g₃formant un deuxième angle φ non nul avec le troisième axe secondaire , ladite troisième direction de générateur g₃étant non coplanaire avec chacun des plans suivants :
  • le plan défini par la première direction de générateur g₁et la deuxième direction de générateur g₂,
  • le plan défini par la première direction de générateur g₁et le troisième axe secondaire , et
  • le plan défini par la deuxième direction de générateur g₂et le troisième axe secondaire .

The magnetic generators 30, 32, 34 are arranged relative to each other so that:

• a first generator 30 is oriented according to a first generator direction g ₁ coincident with the first secondary axis ,
• a second generator 32 is oriented along a second generator direction g ₂ forming a first non-zero angle θ with the second secondary axis and included in a plane defined by the first and second secondary axes , , And
• a third generator 34 is oriented along a third generator direction g ₃ forming a second non-zero angle φ with the third secondary axis , said third generator direction g ₃ being non-coplanar with each of the following planes:
  • the plane defined by the first generator direction g ₁ and the second generator direction g ₂ ,
  • the plane defined by the first generator direction g ₁ and the third secondary axis , And
  • the plane defined by the second generator direction g ₂ and the third secondary axis .

The third generator direction g ₃ 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 g ₁ and the third secondary axis , this angle ψ being different from the angle between the first and second generator directions g ₁ , g ₂ .

The first angle θ is in particular greater than or equal to 0.01 radians, preferably greater than or equal to 0.05 radians, for example greater than or equal to 0.1 radians. It is typically strictly less than radian, preferably less than or equal to radian. The first angle θ is advantageously an indirect angle, that is to say it is measured in the indirect direction of the secondary reference frame (R ₂ ) from the second secondary axis .

The second angle φ is in particular greater than or equal to 0.01 radians, preferably greater than or equal to 0.05 radians, for example greater than or equal to 0.1 radians. 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 (R ₂ ) from the third secondary axis .

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 g ₁ , g ₂ 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 that it is measured in the direct direction of the secondary reference (R ₂ ) from the first secondary axis .

Preferably, the magnetic generators 30, 32, 34 have substantially coincident centers, that is to say that they can be modeled as magnetic dipoles substantially of the same center. For this purpose, the coils 36, 38, 40 have substantially coincident centers, that is to say that 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 O ₂ of the secondary reference frame (R ₂ ).

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.

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 point (R ₁ ).

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 c ₁ , c ₂ , c ₃ specific to the sensor 50, 52, 54, these measurement directions c ₁ , c ₂ , c ₃ being non-coplanar. These sensors 50, 52, 54 are preferably arranged so that their measurement directions c ₁ , c ₂ , c ₃ are substantially orthogonal to each other, each measurement direction c ₁ , c ₂ , c ₃ typically being, as shown, substantially colinear to one of the axes , , of the primary reference point (R ₁ ).

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.

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.

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 c ₁ , c ₂ , c ₃ .

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

The voltage signals produced by the tensiometers 62, 64, 66 together form a measurement signal. The measurement directions c ₁ , c ₂ , c ₃ being non-coplanar, this measurement signal is representative of the resulting magnetic field at the receiver 24.

The receiving device 23 also comprises a demodulator 70.

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.

In reference to the , the demodulator 70 comprises an input 72, 74, 76 for each voltage signal u ₁ , u ₂ , u ₃ produced by a tensiometer 62, 64, 66. It also comprises a generator 78 of signals for demodulating the voltage signals.

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 ( ) of receiver 24.

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 exists an associated demodulation signal pair 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 phase-shifted relative 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 _j is 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 may be zero), and Δt is the time deviation between the signals of the clocks 80 and 48, this time deviation Δt being variable and random.

The demodulator 70 further comprises a circuit 82 (real or emulated) for multiplying each voltage signal u ₁ , u ₂ , u ₃ 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.

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).

Back to the , the determination system 20 further 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.

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 processor 92 to implement certain steps of a method 100 ( ) which will be detailed below.

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.

In the example shown, the data processing unit 90 is integrated into the first object 12. As a variant (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.

It should be noted that the demodulator 70 can also be moved outside the first object 12.

A method 100 implemented by the determination system 20 will now be described, with reference to the .

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.

As visible on the , 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 generate a respective alternating magnetic field. These alternating magnetic fields are superimposed in space and produce a resulting magnetic field.

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.

Then, in a step 130, the measurement signal is demodulated by the demodulator 70. In this step 130, each voltage signal u ₁ , u ₂ , u ₃ 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 _i 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 .

• est la contribution du champ magnétique généré par le générateur 30, 32, 34 orienté suivant la direction g_jà la composante du champ magnétique résultant mesurée suivant la direction c_i, et
• est le déphasage entre le champ magnétique généré par le générateur 30, 32, 34 orienté suivant la direction g_jet les signaux de démodulation associés (c’est-à-dire les signaux de démodulation qui ont la même fréquence que celle dudit champ magnétique).

It will be noted that, to the first order, each value P _{i,j, 1} , respectively each value P _{i,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 in the direction g _j and the demodulation signals associated with the contribution of this alternating magnetic field to the component of the resulting magnetic field measured in the direction c _i . In other words, each value P _{i,j, 1} , respectively each value P _{i,j, 2} , is equal, to the first order, to , respectively , Or :

• 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 in the direction c _i , and
• is the phase shift between the magnetic field generated by the generator 30, 32, 34 oriented in the direction g _j and the associated demodulation signals (i.e. the demodulation signals which have the same frequency as that of said magnetic field).

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:

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 of each generated alternating magnetic field to each component of the magnetic field, i.e. a set of values where each value is a candidate value 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 in the direction c _i .

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:

• la valeur absolue de chaque contribution candidate soit égale à la valeur absolue de la contribution (réelle) correspondante ,
• pour chaque champ magnétique alternatif, le signe de chacune des contributions candidates de ce champ magnétique alternatif soit égal au signe de la valeur P_i,j,1, ou P_i,j,2résultant du produit du signal de tension u_iavec l’un des signaux sinusoïdaux de démodulation associés à ce champ magnétique alternatif, en d’autres termes : ou
• le détermination de la matrice correspondante soit positif.

To this end, a first candidate measure is first constructed, such 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: Or
• the determination of the corresponding matrix is positive.

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

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

, with

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

The demodulation step 130 is followed by a step 140 of applying a correction 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.

This correction is common to all candidate measures M ^c . It involves multiplying, on the right, 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 :

• les différences entre les fréquences ω_jdes champs magnétiques alternatifs qui apparaissent lors du phénomène d’induction se produisant dans les bobines 56, 58, 60 des capteurs magnétiques 50, 52, 54, et
• les différences relatives entre les normes des moments dipolaires des générateurs 30, 32, 34.

where b ₁ , b ₂ and b ₃ are scale factors, typically determined during a prior calibration step, b ₁ being a global scale factor making it possible to define the length scale of the measurements provided by the determination system 20 and b ₂ and b ₃ are relative scale factors, functions of b ₁ , which cover in particular:

• the differences between the frequencies ω _j of the alternating 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.

We thus obtain, for each candidate measure M ^c , a corresponding partial corrected measure M ^p , this partial corrected measure verifying the following relation:

, with , where I ₃ is the identity matrix.

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. For this purpose, 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 measurement M ^c , a corresponding final corrected measurement M ^k . These other defects will be ignored in the following, since those skilled in the art know how to model and compensate for them.

Step 140 is followed by a step 150 of calculating, for each candidate measurement M ^c , a data item representing the likelihood that this candidate measurement M ^c gives the real contributions of each generated alternating magnetic field to each component of the resulting magnetic field. This representative data item is calculated using the corrected measurement M ^k corresponding to the candidate measurement M ^c .

In a first variant of this step 150, shown in , step 150 consists of a step 152 of estimating, for each candidate measurement M ^c , a distance from 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.

The distance D of the corrected measurement M ^k to 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 , this diagonal matrix resulting from a singular value decomposition (“Singular Value Decomposition” in English) of the corrected measurement matrix M ^k such that the diagonal matrix S verifies the following relation:

where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3 and Q ^T 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 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 being that the formula for calculating the distance D is the same for all the corrected measurements M ^k . The person skilled in the art will easily be able to determine these other formulas.

The data representative of the likelihood that the candidate measurement M ^c gives the real 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 (indeed, the lower the distance D, the more likely it is that the candidate measurement M ^c 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 the distance D; it is then an increasing function of the likelihood.

In another variation of step 150, shown in , this step 150 comprises a substep 154 of deduction, for each candidate measurement 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 measurement M ^c .

For this purpose, 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 satisfies the following relation:

where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3, Q ^T is the transpose of a second matrix Q also belonging to the SO(3) group, and S is the following matrix:

with S ₁₁ , S ₂₂ and S ₃₃ positive real values ordered so that .

From this singular value decomposition, 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 µ ₀ 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.

The data processing unit 90 thus obtains a pair ( , R) characterizing a candidate pose corresponding to the candidate measure M ^c .

In this other variant of step 150, substep 154 is followed by a substep 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, μ ₀ 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 O ₂ of the secondary reference frame (R ₂ ), 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 ω ₁ , ω ₂ and ω ₃ 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.

The data processing unit 90, in order to estimate the realistic theoretical measurement of the resulting magnetic field in the candidate pose, 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.

Still in this other variant of step 150, substep 155 is itself followed by a substep 156 of evaluating the distance of each candidate measurement M ^c to the realistic theoretical measurement associated with said candidate measurement M ^c , that is to say to the realistic theoretical measurement of the magnetic field resulting in the candidate pose corresponding to said candidate measurement M ^c . During this substep 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:

The distance between matrices M ^c and M ^{th ,r} is for example given by the Frobenius norm of the difference between the matrices.

The data representative of the likelihood that the candidate measurement M ^c 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 M ^c and M ^{th ,} 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 M ^c and M ^{th ,r} , the more likely it is that the candidate measurement M ^c 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.

A third variation of step 150 is presented in .

In this third variant, step 150 still includes sub-step 154 of deducing, for each candidate measurement M ^c , 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 measurement M ^c . This third variant is nevertheless distinguished from the previous variant in that step 150 does not include sub-steps 155 and 156.

Instead, substep 154 is followed by a substep 157 of estimating a simplified theoretical measure 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, μ ₀ 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 O ₂ of the secondary reference frame (R ₂ ), 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 ω ₁ , ω ₂ and ω ₃ 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.

The data processing unit 90, in order to estimate the simplified theoretical measurement of the resulting magnetic field in the candidate pose, 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.

Still in this third variant of step 150, substep 157 is itself followed by a substep 158 of evaluating the distance of each corrected measurement M ^k corresponding to a candidate measurement M ^c to the simplified theoretical measurement associated with said candidate measurement 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 substep 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:

The distance between matrices M ^k and M ^{th, s} is for example given by the Frobenius norm of the difference between the matrices.

The data representative of the likelihood that the candidate measurement M ^c 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 M ^k and M th ^{, 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 M ^k and M ^{th, s} , the more likely it is that the candidate measurement M ^c 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.

Back to the , step 150 is followed by a step 160 of selecting a measure selected from the candidate measures M ^c .

In reference to the , step 160 comprises a first substep 161 of comparing the representative data of each candidate measurement M ^c to a threshold. In the case where, as shown here, the representative data is a decreasing function of the likelihood, this substep 161 has the function of determining whether one or more candidate measurements 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 substep 161 has the function of determining whether one or more candidate measurements M ^c have their representative data higher than said threshold.

If a single candidate measure M ^c has its representative data lower, respectively higher, than the threshold, substep 161 is followed by a substep 162 of selecting said candidate measure M ^c whose representative data is lower, respectively higher, than the threshold. The selected measure is then constituted by that of the candidate measures M ^c whose representative data is the lowest, respectively the highest, and therefore indicates the highest likelihood.

If there is no single candidate measurement 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 measurement M ^c has its representative data lower, respectively higher, than the threshold, the selection can then 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 (respectively phase shift) tracking 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).

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

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

The substep 163 is then followed by a substep 164 of calculating the distance of each candidate pose to a previous pose. This previous pose is typically constituted by a pose determined previously 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.

The distance d between the candidate pose and the previous pose is for example given by the following formula:

Or is the 2-norm of the logarithm in the SO(3) group of rotation matrices, 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.

Substep 164 is followed by a substep 165 of selecting the candidate measurement M ^c for which the corresponding candidate pose has the smallest distance to the previous pose. The selected measurement is then constituted by that of the candidate measurements M ^c for which the corresponding candidate pose has the smallest distance to the previous pose.

In another variation of step 160, shown in , sub-step 161 is followed, when there is not a single candidate measurement M ^c having its representative data lower, respectively higher, than the threshold, by a sub-step 166 of determining, for each alternating magnetic field, two candidate phase shifts of said alternating magnetic field relative to the associated demodulation signals.

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 {P _i,j,1 , P _i,j,2 } 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 α whose tangent is equal to this ratio:

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

Substep 166 is followed by a substep 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.

In 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 verify the following condition:

with where each is the absolute value of the characteristic time derivative of the phase shift between a generated alternating magnetic field and the associated demodulation signals.

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.

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 selected phase shift value.

In 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 with that of at least one value P _i,j,1 (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 candidate contribution. corresponding (i.e. whose absolute value is equal to ) of each candidate measurement M ^c and selects that of the candidate measurements M ^c for which, for each alternating magnetic field, the sign of said candidate contribution corresponding is equal to said sign thus obtained.

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 relative to the demodulation signals associated with this alternating magnetic field.

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 {P _i,j,1 , P _i,j,2 } 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 α whose tangent is equal to this ratio:

The data processing unit 90 then determines the sign of the cosine or sine of this angle α. Then it multiplies this sign with that of at least one value P _i,j,1 (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. Finally, it compares the sign thus obtained with the sign of the candidate contribution. corresponding (i.e. whose absolute value is equal to ) of the selected candidate measurement M ^c . If the signs are equal, the data processing unit 90 assigns the value α to the phase shift of the alternating magnetic field. If these signs are opposite, the data processing unit 90 assigns the value α+π to the phase shift of the alternating magnetic field.

Back to the , 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 measurement.

For this purpose, 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 satisfies the following relation:

where P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3, Q ^T is the transpose of a second matrix Q also belonging to the SO(3) group, and S is the following matrix:

with S ₁₁ , S ₂₂ and S ₃₃ positive real values ordered so that .

From this singular value decomposition, 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 µ ₀ 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 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 orientation of the receiver 24 (and therefore of the first object 12 to which it is attached) corresponding to the selected measurement:

where P ^T is the transpose of the matrix P.

The data processing unit 90 thus obtains a pair ( , R) characterizing the effective position of the receiver 24 (and therefore of the first object 12 with which it is attached) relative to the transmitter 22 (and therefore relative to the second object 14 with which it is attached).

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 (24)

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 natural 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 directions (c₁, c₂, c₃) non-coplanar, 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,
• demodulating (130) 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 and without using measurements from inertial sensors integral with the receiver (24), of data representing 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 selected measure from among the candidate measures, 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).

The determination method (100) of claim 1, wherein the corrective is common to all candidate measurements. Determination method (100) according to claim 1 or 2, in which the magnetic generators (30, 32, 34) have substantially coincident centers. 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. 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 from the corrected measurement corresponding to a reference space consisting of the measurements obtainable in a model of the system (20) formed by the transmitter (22) and the receiver (24) in which the magnetic generators (30, 32, 34) are orthogonal to each other, the data representing the likelihood being a function of said distance.

A determination method (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 decomposition into singular values of the matrix of the corresponding corrected measurement. The determination method (100) of 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 , this diagonal matrix resulting from a singular value decomposition of the corrected measurement matrix such that the diagonal matrix S verifies the following relation:

where M ^k is the matrix of the corrected measure, P is a first matrix belonging to the SO(3) group of rotation matrices in dimension 3 and Q ^T is the transpose of a second matrix Q also belonging to the SO(3) group. Determination method (100) according to any one of claims 1 to 4, in which 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),
• estimating (155, 157) a theoretical measurement of the resulting magnetic field in the candidate pose in a model of the system (20) formed by the transmitter (22) and the receiver (24), and
• evaluation (156, 158) of a distance from the candidate measurement or from the corrected measurement corresponding to said theoretical measurement, the data representing the likelihood being a function of said distance.

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. The determination method (100) of claim 9, wherein the candidate pose is characterized by a pair ( , R) such that:
And
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 , where M ^k is the corrected measurement matrix 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 µ ₀ is the magnetic permeability of the vacuum, m is the amplitude of the magnetic moments of the magnetic generators (30, 32, 34) and Tr(S) is the trace of the matrix S.

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. A determination method (100) according to any one of claims 8 to 10, wherein the system model 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. 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. Determination method (100) according to claim 13 in which, 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 measure being constituted by that of the candidate measures for which the corresponding candidate pose presents the smallest distance to the previous pose. 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:

• determining (166), for each generated alternating magnetic field, candidate phase shifts of said generated alternating magnetic field relative 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 from a previous phase shift of said alternating magnetic field generated with respect to this same demodulation signal,

the selected measure being constituted by that of the candidate measures for which, for each generated alternating magnetic field, the signs of the candidate contributions are consistent with the selected phase shift. A determination method (100) according to any preceding claim, wherein the receiver (24) has magnetic sensors (50, 52, 54) for measuring components of the resulting magnetic field and the calculating step (150) is carried out without using measurements from additional sensors other than the magnetic sensors (50, 52, 54). 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. A computer-readable recording medium on which a computer program product according to claim 17 is stored. Transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 16, 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 natural frequency, the transmitter (22) being designed so that:

• a first generator (30) is oriented according to a first generator direction (g ₁ ) coincident with a first direction ( ) of an orthogonal reference attached to the transmitter (22), and
• a second generator (32) is oriented along a second generator direction (g ₂ ) 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,

the first angle (θ) being greater than or equal to 0.05 radians. Transmitter (22) according to claim 19, 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 (g ₃ ) forming a second angle (φ), greater than or equal to 0.05 radians, with a third direction ( ) of the orthogonal reference frame. Method for designing a transmitter (22) for implementing a determination method (100) according to any one of claims 1 to 16, comprising the following steps:

• arrangement of a first magnetic generator (30) of the transmitter (22), capable of generating an alternating magnetic field at a first frequency, such that it is oriented in a first generator direction (g ₁ ) coincident with a first direction ( ) of an orthogonal reference attached 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, such that it is oriented in a second generator direction (g ₂ ) 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.

Design method according to claim 21, 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 (g ₃ ) forming a second angle (φ), greater than or equal to 0.05 radians, with a third direction ( ) of the orthogonal reference frame. 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 21 or 22, followed by the production 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 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 (g ₁ , g ₂ , g ₃ ) 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 (g ₁ , g ₂ , g ₃ ) 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 (c ₁ , c ₂ , c ₃ ), and
• a data processing unit (90) configured for implementing a determination method (100) according to any one of claims 1 to 16.