法国专利FR3069649A1 METHOD OF CALIBRATING A MAGNETOMETER

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专利摘要:
The invention relates to a method for calibrating a magnetometer comprising the following steps: the magnetometer traverses (S1) a set of travel positions; acquisition (S2) by the magnetometer of a plurality of measurements of the magnetic field; - Providing trajectory information (S3) representative of the location and orientation of an integral point of the magnetometer, - Matching (S4) measurements of the magnetic field with the trajectory information, - Determination (S5) ) calibration parameters of the magnetometer by minimizing a cost function involving, for a plurality of instants of determination, at least said calibration parameters, a measurement of the magnetic field, and a relationship linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer derived from the trajectory information.
公开号:FR3069649A1
申请号:FR1757082
申请日:2017-07-26
公开日:2019-02-01
发明作者:David VISSIERE；Charles-Ivan Chesneau；Mathieu Hillion；Hendrik Meier；David Caruso
申请人:Sysnav SAS；
IPC主号:

专利说明:

CALIBRATION METHOD OF A MAGNETOMETER
GENERAL TECHNICAL AREA
The present invention relates to the field of magnetometers. More specifically, it relates to a method for calibrating at least one magnetometer.
BACKGROUND AND TECHNOLOGICAL BACKGROUND
The magnetic field is a vector field in the three-dimensional case, that is to say associating a magnetic field vector denoted B and of dimension three at each location in space. The magnetic field at a point is thus characterized by its norm and its direction.
A magnetometer measures the magnetic field at a point. A magnetometer can be a mono-axial magnetometer, capable of measuring a component of the magnetic field in a position, i.e. the projection of the vector magnetic field B at the level of said magnetometer along its axis. A magnetometer can also be a tri-axis magnetometer, capable of measuring the magnetic field along its three axes, which can consist of three single-axis magnetometers rigidly linked together and oriented along different axes, generally substantially orthogonal.
However, the measurement of the magnetic field by a magnetometer is not perfect, so that the measurement of the magnetic field deviates from the actual magnetic field. For example, the effects of hard irons can be created by the remanence of certain components at strong magnetic fields and cause measurement bias. Scale factors can also distort the measurement. In addition, effects due to the physical configuration of the magnetometer and the mounting of the magnetometer can also affect the measurement.
We can for example write the measurement of a triaxial magnetometer in the following linear form:
B _m - DB + b where B _m is the measurement of the magnetic field by the magnetometer, B is the real magnetic field, D is a matrix called scale factor, and b is a measurement bias. The scale factor and the measurement bias are therefore measurement parameters which pollute the measurement of the magnetic field compared to the real magnetic field. These parameters should be estimated in order to be able to correct the measurement of the magnetic field before using it elsewhere. Calibrating a magnetometer is equivalent to determining these parameters and deducing from them corrections (by inverting the shape of the measurement model for example) to be made to the outputs of the magnetometer so that the corrected measurement more faithfully reflects the real magnetic field.
In particular, precise calibration of the magnetometer is required for applications that require high precision. In particular, a magneto-inertial unit can comprise, in addition to accelerometers, a network of several magnetometers arranged at different locations which allow the simultaneous estimation of the magnetic field and the gradient, in order to make it possible in particular to determine an estimate of the speed vector and of the position vector during navigation. The documents FR2914739B1 and EP2541199 thus present two so-called magneto-inertial navigation approaches. The accuracy of these measurements is essential to the good performance of reconstruction of the movement of the magneto-inertial power plant.
Furthermore, the respective position and orientation of each of the magnetometers of such a magneto-inertial unit can also constitute parameters influencing the measurement. The calibration can also include the determination of these parameters.
Several methods for calibrating a magnetometer have been proposed. One of these methods is to rotate the magnetometer in a space where the magnetic field is constant and undisturbed, for example the earth's magnetic field in a place free from disturbances, such as an agricultural field. A triaxial affine response magnetometer placed in the constant magnetic field in an arbitrary orientation sees the space of its raw measurements identifiable with an ellipse. A reciprocal transformation makes it possible to return this raw measurement space to a spherical calibrated measurement space by identifying the parameters of the ellipse, which gives the calibration parameters almost directly.
This method is however complicated since it requires having a place with a homogeneous and constant field over time (constant standard). The magnetometers to be calibrated and their individual handling must also be transported outside. In addition, this method, if it effectively identifies the intrinsic parameters of a magnetic sensor (bias, scale factor), does not identify the geometric calibration parameters (relative position of the magnetometers) of a network of magnetometers.
Another method consists in placing the magnetometers to be calibrated in an imposed magnetic field, for example generated by means of Helmholtz coils controlled in current so that the magnetic field generated is homogeneous and of constant standard. As the magnetic field is known, in amplitude and in orientation, it then suffices to parameterize an error model of the magnetometers by comparing the outputs of the magnetometers with the imposed magnetic field. However, this method requires, in order to have an imposed undisturbed magnetic field, the establishment of a complex infrastructure which can be expensive, heavy and cumbersome. In addition, there is also the question of the accuracy of the knowledge of the magnetic field generated, also requiring a calibration thereof.
PRESENTATION OF THE INVENTION
The invention aims to remedy these drawbacks at least in part and preferably to all, and aims in particular to propose a method for calibrating a magnetometer or a network of magnetometers which is simple to implement and precise. This method is made possible by the exploitation of a relation linking the evolution of the magnetic field and the movement of the magnetometer.
To this end, a method for calibrating a magnetometer is proposed, comprising the following steps:
the magnetometer traverses a set of travel positions, said positions being distinguished from one another by a location of the magnetometer and / or by an orientation of the magnetometer;
- Acquisition by the magnetometer at times of acquisition of a plurality of measurements of the magnetic field when the magnetometer traverses said set of path positions;
- providing trajectory information representative of the location and orientation of a point secured to the magnetometer during the course of the set of course positions at times of the course,
- for each of a plurality of instants of determination determined from the instants of acquisition and instants of journey, matching of the measurements of the magnetic field with the trajectory information,
determination of magnetometer calibration parameters by minimizing a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field, and a relation linking the evolution of '' a magnetic field with the evolution of the location and the orientation of the magnetometer derived from the trajectory information.
The method thus proposes, from information on the movement of the magnetometer, to deduce the calibration parameters of the magnetometer which then make it possible to precisely measure the magnetic field, and possibly the magnetic field gradient.
The process is advantageously supplemented by the following characteristics, taken alone or in any of their technically possible combinations:
- the cost function involves error terms concerning the evolution of the location and the orientation of the magnetometer derived from trajectory information the cost function involves error terms concerning sensor measurements, said measurements sensors taken alone making it possible to obtain the trajectory information, the trajectory information then being determined at the same time as the calibration parameters.
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- the cost function is minimized with a state observer;
the cost function is based on comparisons between a theoretical estimate of the measurement of the magnetic field at a determination time and a measurement of the magnetic field at said determination time, the theoretical estimate of the magnetic field taking into account the calibration parameters ;
- The theoretical estimate of the measurement of the magnetic field is determined from the relationship linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer derived from the trajectory information;
- the theoretical estimate of the measurement of the magnetic field is determined at least from:
- a measurement of the magnetic field at a previous determination instant,
the evolution of the location and the orientation of a point secured to the magnetometer between the instant of determination and the instant of previous determination, determined from the trajectory information,
- calibration parameters;
the method also comprises an acquisition at instants of acquisition of a plurality of measurements of a gradient of the magnetic field when the magnetometer traverses said set of path positions, and the theoretical estimate of the magnetic field is also determined from a measurement of the magnetic field gradient at the previous determination time;
- the relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer locally translates an equation of the particle derivative of the magnetic field:
B = VB.v + Ωχ B with B a magnetic field vector, VB a gradient vector of the magnetic field, B a vector of the time derivative of the magnetic field, vun velocity vector representative of the modification of the location and Ω a matrix of rotation representative of the change in orientation;
- the theoretical estimate of the measurement of the magnetic field at a time of determination is determined from:
- of a magnitude of the magnetic field at a reference point,
- a gradient of the magnetic field at said reference point, and
- the difference between the location of the point secured to the magnetometer and a location of the reference point,
- the rotation between the orientation of the point secured to the magnetometer and an orientation at the reference point, the magnitude of the magnetic field at a reference point and the gradient of the magnetic field at said reference point being determined by minimizing the function of cost.
- the calibration parameters include:
- a first magnetometric bias affecting the measurement of the magnetic field, and / or
- a second magnetometric bias affecting a measurement of a gradient of the magnetic field, and / or
a scale parameter affecting an amplitude of the measurement of the magnetic field and / or
- spatial configuration parameters of the magnetometer;
- the mapping consists in interpolating at least one set from:
- a set of magnetic field and magnetic field gradient measurements,
- a set of trajectory information, so that at each instant of determination corresponds to at least one measurement of the magnetic field and of trajectory information;
the trajectory information is provided by the use of an imager locating the location and the orientation of the magnetometer at each instant of travel when the magnetometer traverses the first set of positions;
the imager is integral with the magnetometer, and a fixed target is placed in a field of vision of said imager, the trajectory information being derived from the location of the target in images acquired by the imager when the magnetometer traverses all of course positions;
a mechanical displacement device moves the magnetometer from one position to another position in the first position set when the magnetometer traverses said set of travel positions, the trajectory information being derived from position measurements of said mechanical displacement device or position setpoints of said mechanical displacement device;
- The magnetometer is integral with inertial sensors configured to determine accelerations and angular velocities at each instants of travel, and the trajectory information is derived from said accelerations and angular velocities;
- the magnetometer is placed in a magneto-inertial unit.
The invention also relates to an automated data processing unit comprising a processor, a memory and input and output interfaces, configured to implement the method according to the invention, and in particular for:
receiving a plurality of measurements of the magnetic field acquired at instants of acquisition by a magnetometer traversing a set of travel positions, said being distinguished from each other by the spatial location of the magnetometer and / or by the orientation of the magnetometer;
- receive trajectory information representative of the location and orientation of a point secured to the magnetometer during the course of the positions of the set of course positions at times of course,
- for each of a plurality of instants of determination determined on the basis of the acquisition instants and the instants of travel, to match measurements of the magnetic field and of the magnetic field gradient with the trajectory information,
determining the magnetometer calibration parameters by minimizing a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field, and a relation linking the evolution of '' a magnetic field with the evolution of the location and the orientation of the magnetometer derived from the trajectory information.
The invention also relates to a computer program product comprising program code instructions recorded on a non-volatile medium readable by a computer for the execution of the steps of the method according to the invention when said program code instructions are executed on a computer.
PRESENTATION OF THE FIGURES
The invention will be better understood from the following description, which relates to embodiments and variants according to the present invention, given by way of nonlimiting examples and explained with reference to the appended schematic drawings, in which :
FIG. 1 is a diagram illustrating an example of equipment comprising magnetometers to be calibrated,
FIG. 2 is a diagram illustrating a possible configuration for the implementation of the calibration method according to a possible embodiment of the invention,
- Figure 3 is a schematic diagram showing steps of the calibration method according to a possible embodiment of the invention.
DETAILED DESCRIPTION
By position is meant the combination of a location and an orientation, which makes it possible to completely describe the spatial configuration of an object. In a vector writing of a three-dimensional space, the location is defined by a vector with three components (the spatial coordinates in a coordinate system), and the orientation is also defined by a vector with three components (the angles of rotation relative to the benchmark).
The term trajectory information is understood to mean data representative of the position of a point secured to the magnetometer over time when the magnetometer traverses all of the travel positions. The position of a point secured to the magnetometer can in particular be that of a solid rigidly linked to the magnetometer. These data can be chronologically ordered according to travel instants corresponding to each travel position. These data can for example be locations and orientations or derivatives with respect to time, such as in particular speeds or accelerations, angular speeds or angular accelerations.
An automated data processing unit, such as a computer, comprising at least one processor and a memory, is configured to implement the method. The automated data processing unit is also configured to receive at least magnetic field measurements from the magnetometer. Preferably, the automated data processing unit is configured to also receive measurements of a gradient of the magnetic field.
In the present description, the magnetometer to be calibrated is a triaxial magnetometer capable of measuring the magnetic field along its three axes. The magnetometer can be part of a network of magnetometers solidly linked to the same sensor, as for example in the case of a magnetoinertial power station, in which case the network of magnetometers also makes it possible to measure a gradient of the magnetic field in the reference frame of the sensor .
By way of illustration, FIG. 1 shows an example of a magnetometer network 2 equipping a magneto-inertial unit 1. The magnetometers 2 are here tri-axis magnetometers, each consisting of three single-axis magnetometers oriented along substantially perpendicular axes between them. The magneto-inertial unit 1 comprises at least eight single-axis magnetometers, and typically nine single-axis magnetometers organized into three magnetometers 2 tri-axes, as shown in FIG. 1. The magnetometers 2 are integral with the magneto-inertial unit 1 , ie they present a substantially identical movement in the terrestrial frame of reference. The magneto-inertial unit 1 also includes inertial sensors such as accelerometers and gyrometers 24, generally three accelerometers and three gyrometers arranged in tri-axis. The magneto-inertial unit 1 also comprises processing means 21 (typically a processor), data storage means 22, and communication means 25 to an external device.
As part of the calibration method, the magnetometer 2 traverses (step S1) a set of path positions, said path positions being distinguished from each other by a location of the magnetometer 2 and / or by an orientation of the magnetometer 2. Unlike the methods from the state of the art, there are no constraints of homogeneity or constancy of the magnetic field in which the course of the magnetometer 2 takes place. It is therefore not necessary to have an imposed magnetic field or undisturbed. Preferably, all of the travel positions are not defined a priori, it results from the displacement of the magnetometer 2 during its travel. The travel positions are simply the positions taken by the magnetometer 2 during its travel.
To carry out this journey, the magnetometer 2 can simply be manipulated manually by an operator. One can also provide a mechanical displacement device which moves the magnetometer 2 from one travel position to another travel position. For example, this mechanical displacement device can be a robotic arm, a treadmill, or any other device making it possible to vary the location and the orientation of the magnetometer 2.
During its journey, the magnetometer 2 acquires at acquisition times a plurality of measurements of the magnetic field (step S2). Thus, for each acquisition instant, the magnetometer 2 acquires a measurement B _m of the magnetic field, which depends on the location of the magnetometer 2 and on its orientation. It is possible to filter the magnetometer measurements to compensate for certain non-stationarity of the magnetic field. For example, electric currents from electrical installations can disturb the magnetic field. Filtering (for example notch) at 50 Hz or 60 Hz makes it possible to limit these disturbances. Likewise, the magnetic field generated by the positioning or position measurement system can, if known, be removed from the measurement of the magnetometer.
Trajectory information representative of the location and the orientation of a point secured to the magnetometer 2 during the journey at times of travel is provided (step S3). This trajectory information need not reflect the absolute location or the absolute orientation of the magnetometer 2, for example with respect to a reference frame of the magnetic field which would typically be the Earth reference frame. Indeed, the proposed method exploits the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer 2, and not the knowledge of the magnetic field at any point in the trajectory of the magnetometer 2. It is therefore sufficient to know the location and the orientation of a point secured to the magnetometer 2 during the course.
Using a point secured to the magnetometer rather than magnetometer 2 itself has many advantages. First of all, it is often easier to identify the location and orientation of a point secured to the magnetometer 2 than to the magnetometer itself. For example, when a target and an imager are used, it is the target or the imager which will be integral with the magnetometer 2 and whose location and orientation will be determined. Then, when several magnetometers 2 are organized in a network integral with each other, as is typically the case with a magneto-inertial unit 1, this makes it possible to be able to calibrate all the magnetometers 2 of the network with the same trajectory information. In addition to simplicity and significant time savings, this also makes it possible to harmonize the calibration of magnetometers 2 with one another.
This trajectory information can be obtained in different ways. The trajectory information can be provided by the use of an imager locating the location and the orientation of the magnetometer at each instant of travel when the magnetometer 2 traverses the travel positions.
It is possible for example to rigidly fix an imager with the magnetometer 2 and to determine the trajectory information from the processing of the images acquired by the imager during the displacement of the assembly formed by the magnetometer 2 and the imager. One can for example implement a method of simultaneous localization and mapping (better known by the acronym SLAM for the English simultaneous localization and mapping), exploiting a stereovision of the imager, an additional depth camera or inertial sensors. In particular, in the case of an imager attached to a magneto-inertial unit 1 incorporating the magnetometer 2, it is possible to use the imager / accelerometer / gyrometer triplet to determine the trajectory information, using the technique SLAM or a vision / inertial odometry technique.
You can also use a test pattern or benchmarks whose positions are known. For example, the imager can be integral with the magnetometer 2 and a fixed target arranged in a field of vision of said imager. The trajectory information is then derived from the location of the target in images acquired by the imager when the magnetometer 2 traverses the set of course positions. Finally, the imager can be fixed in the environment and optical sights fixed to the system (for example motion capture room).
FIG. 2 thus shows an example of configuration using a test pattern when the magnetometer 2 moves from one course position to another. The imager 10 is here a camera secured to the inertial unit 1 incorporating the magnetometer 2. A test pattern 11 is fixed in an external reference frame (typically the terrestrial reference frame) and placed in the field of vision 12 of the imager 11. In this example, the test pattern 11 comprises several regularly distributed blocks 13 each having a distinct pattern, so that each block is identifiable. If necessary, the imager 10 can be calibrated beforehand by placing the target in front of the imager at different locations and in different orientations in order to obtain a series of images showing the target 11 in different spatial configurations. Image processing detects in each of them the position of the projection of the particular points of the test pattern 11. This detected position is then used (for example by non-linear optimization methods) to determine the intrinsic parameters of the imager 10, such as the focal length and distortion parameters as well as the position of the optical center required for the expression of a projection / projection function for the imager optical system. Target 11 in this example is a flat target, which has the particularity of being easy to produce since it can be simply printed on a sheet of paper. It is also possible to use test patterns 11 in three dimensions, more difficult to produce but making calibration easier and more precise.
Since the test pattern 11 is fixed, an operator moves the assembly formed by the imager 10 and by the magnetometer 1, taking care to keep the test pattern 11 in the field of vision 12 of the imager 10. The movement movements can be made at random or according to a pre-established course. The imager 10 acquires images during this displacement. The position of the pattern 11 is then detected in each image. The relative position of the imager 10 relative to the fixed target 11 is then calculated by a computer vision algorithm for each image, making it possible to determine the position of the imager 10 in the frame of reference attached to the target 11 at the instants of the course corresponding to the instants of shooting of the imager 10. The imager 10 being integral with the magnetometer 2, one thus obtains trajectory information representative of the location and the orientation of a point integral with the magnetometer 2 at during the course.
It is understood that it is also possible to use a fixed imager 10 and a test pattern 11 integral with the magnetometer 2. Several test patterns 11 can also be used in order to allow greater freedom of movement. It is also possible to dispense with the test pattern 11 if the location and orientation of the magnetometer in the images can be identified directly from the images of the assembly incorporating the magnetometer 2. It is also possible to provide a motion capture configuration (motion capture in English) where several optical targets are arranged integrally with the magnetometer 2.
Other methods make it possible to obtain this trajectory information. For example, in the case already mentioned where a mechanical displacement device moves the magnetometer 2 from one course position to another course position, the trajectory information can be derived from position measurements or position instructions of said device. mechanical displacement. The use of a robotic arm makes it possible in particular to have direct data on the location in space and on the orientation of the end of the robotic arm, which is a point secured to the magnetometer 2 which it carries.
It is also possible to use a possible radio navigation system, for example with a receiver secured to the magnetometer 2 which receives waves emitted by several stations. The position of the receiver is then determined by a triangulation process, merging the relative positions with respect to each transmitting station. Thus, any method making it possible to provide trajectory information representative of the location and the orientation of a point secured to the magnetometer 2 during the course can be used. Several methods can also be combined.
In the case of a magnetometer 2 integrated into a magneto-inertial unit 1, it is also possible to compare the measurements of the accelerometers and gyrometers with the trajectory information in order to be able to calibrate the accelerometers and gyrometers 24, and in particular to eliminate bias . It is also possible to obtain the trajectory information from these measurements of the accelerometers and gyrometers 24. It is even then possible to simultaneously calibrate the magnetometers 2, the accelerometers and the gyrometers 24, by integrating the different biases in the cost function. which will be described later.
The calibration process is based on the exploitation of measurements of the magnetic field, acquired at times of acquisition, synchronous with information of trajectories at times of travel. However, these two types of data come from different origins, and the acquisition times do not generally correspond to the travel times. A match (step
S4) is therefore required between the magnetic field measurements and the trajectory information. This matching aims to associate and synchronize measurements of the magnetic field and trajectory information, so as to be able to have, for each of a plurality of determination times, a measurement of the magnetic field and trajectory information representative of the 'location and orientation of a point secured to the magnetometer 2 at this instant of determination.
To this end, the mapping can include the interpolation of at least one set or subset from:
- a set of magnetic field and magnetic field gradient measurements,
- a set of trajectory information.
For example, it may only be necessary to interpolate the trajectory information, since it generally has a lower frequency than the magnetic field measurements. Indeed, a magnetometer 2 can easily acquire measurements of the magnetic field at a frequency of 200 Hz, while the trajectory information can be more fragmented, in particular when an imager 10 is used. However, it is also possible that it is the reverse. It should be noted that in the case where the acquisition instants correspond to the travel instants, the mapping is limited to associating the measurements of the magnetic field with the trajectory information at the same instants, which would then become determination instants.
To interpolate an assembly, time splines are preferably used, but other approaches can be adopted, such as for example a discrete representation of the trajectory traveled by the magnetometer 2. The spline representation makes it possible in particular to force the continuity of the trajectory . Preferably, the splines used for the interpolation are differentiable at least twice. For example, one can interpolate the locations and orientations of the point secured to the magnetometer. The spline representation also makes it possible to optimize the various intervening parameters, in particular the time synchronization parameters, using a method based on the gradient of a criterion to be minimized.
For example, when inertial sensors are integral with the magnetometer 2, as in the case of a magneto-inertial unit 1, it is then possible, by deriving the splines, to calibrate the acceleration or rotation measurements of these sensors. Indeed, the derivative of the orientation spline at each time step must be consistent with the cleared and harmonized measurement of the gyrometer. Similarly, the second derivative of the location spline at each time step must be consistent with the cleared and harmonized measurement of the accelerometers as well as with the estimated value of gravity.
Different parameters such as spline coefficients, inertial bias, desynchronization of the inertial sensors, and the direction of gravity in the target frame, the difference in position between the imager 10 and the percussion point of the accelerometer , can be optimized to minimize a multi-criteria cost function comprising terms of gyrometric error, terms of accelerometric error. These error terms are for example expressed in least squares. When an imager 10 and a test pattern 11 are used, it is also possible to take into account in the cost function a reprojection criterion based on the comparison between the theoretical projection of particular points of the test pattern and their positions in the acquired images by imager 10.
Thanks to the mapping, we can define a plurality of determination times for each of which we have a measurement of the magnetic field and trajectory information representative of the location and orientation of a point of solidarity of the magnetometer at this moment of trajectory. The instants of determination are therefore determined from the instants of acquisition and the instants of travel, since it is they which determine the availability of the measurements of the magnetic field and trajectory information, or possibly their interpolation. Similarly, it is also possible for each instant to determine a measurement of the magnetic gradient if this measurement is available.
Preferably, the instants of determination are chosen close enough to prevent the magnetic field from varying too much between the positions occupied by the magnetometer 2 between two consecutive instants of determination. In particular, when the gradient of the magnetic field is used, the instants of determination are preferably sufficiently close to be able to consider the gradient of the magnetic field as locally uniform between the positions occupied by the magnetometer between two consecutive instants of determination. For example, the instants of determination are spaced apart by a duration less than or equal to 1 s, preferably less than or equal to 10 ms, and more preferably less than or equal to 5 ms. Likewise, the magnetometer 2 preferably acquires the measurements at a frequency sufficient to be able to correctly account for the movement of the magnetometer. Preferably, the magnetometer 2 acquires the measurements at a frequency greater than 100 Hz, such as for example 200 Hz. However, these two preferences are not always useful. In particular, when the method uses an integral formulation, that is to say that only a field model is used as a relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer as described below, the instants of travel, acquisition or determination can be of any distance.
To determine the calibration parameters of the magnetometer 2 (step S5), the method involves minimizing a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field , and a relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer 2 derived from the trajectory information.
Preferably, the cost function is based on comparisons between a theoretical estimate of the magnetic field at a time of determination and a measurement of the magnetic field at said time of determination, the theoretical estimate of the magnetic field taking into account the calibration parameters. Typically, the theoretical estimate of the magnetic field is determined from the relationship linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer 2 derived from the trajectory information.
The theoretical estimate of the magnetic field can be determined at least from:
- a measurement of the magnetic field at a previous determination instant,
the evolution of the location and the orientation of a point secured to the magnetometer 2 between the instant of determination and the instant of previous determination, determined from the trajectory information,
- calibration parameters.
Preferably, the theoretical estimate of the magnetic field is also determined from a measurement of the gradient of the magnetic field at the previous determination time.
For example, the relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer 2 derived from the trajectory information can be a local translation of the equation of the derivative particle of the magnetic field:
B = VB.v + Q..B (1) with B a magnetic field vector, VB a gradient vector of the magnetic field, B a vector of the time derivative of the magnetic field, v a velocity vector representative of the modification of the location and Ω a rotation matrix representative of the speed of rotation, and therefore of the modification of the orientation. Thereafter, the notation of the arrow surmounting the vectors will be omitted, but it is understood that the fields, measures, locations, orientations and bias are vectors. We can of course use other relationships linking the evolution of a magnetic field with the evolution of the location and orientation of the magnetometer, such as using derived from equation (1), the form V _n B = / _η (Ω) .ν _η Β + ^ _n (V _{n + 1} B). V, where V _n B is an n-th derivative of the magnetic field, and / _n and g _n of the predetermined functions, as described in application FR1756675.
Concretely, this equation of the particle derivative of the magnetic field is integrated between two instants of determination t _k and t _{k +} i by:
5 (t / c + i) = R ^T (t / c + i) + R (tk) VB (tk) R ^T (tk) (p (t _{k +} i) - p (t _fc ))) (2) with B (t _{k + 1} ) the magnetic field at the instant of determination t _{k +} i which we subsequently denote by B _{k +} i, B (t _k ) the magnetic field at the previous determination instant t _k that we denote by B _k , 75 (t _k ) the gradient of the magnetic field at the previous determination time t _k denoted by VB _k , R (t _{k + 1} ) represents the orientation of the magnetometer 2 to l the instant of determination t _{k +} i which is subsequently noted R _{k + 1} , R (t _k ) represents the orientation of the magnetometer 2 at the previous instant of determination t _k which is subsequently noted R _k , p (t _{k + 1} ) represents the location of the magnetometer 2 at the instant of determination t _{k +} i denoted thereafter p _{k + 1} , p (t _k ) represents the location of the magnetometer 2 at the instant of determination previous t _k noted subsequently p _k . By simplifying the notations, equation (2) becomes:
Bk + 1 = R _k + i Î ^ Rk ^ k + Rk VBkRk (.Pk + l ~ Pki) (3)
The location p (r) and the orientation R (t) are derived from the trajectory information provided previously. They can directly correspond to this trajectory information, or else be obtained by calculation from it, for example by integrating or deriving it. It is also possible that the location or location is calculated at the same time as the calibration parameters. It is thus possible to combine in the same cost function the error terms relating to magnetic calibration with the error terms relating to other measurements, called sensor measurements, which, taken alone, make it possible to determine the trajectory information. (for example the projection of test patterns or visual landmarks in the imager (s) or other reference). In this case, the estimation in position is not an intermediate output but an internal variable of the optimization algorithm, and there is no distinction between "calculation of the location" and "magnetic calibration", the algorithm solving the two problems by minimizing a single cost function. This is particularly the case when the trajectory information can come from a minimized cost function, for example in the case of a reprojection error of a physical point on an imager (s) (in front of a target, during SLAM, or in a motion capture room). This possibility applies to all the embodiments, and to all the trajectory information, and in particular, in addition to the location and the orientation, the derivatives thereof.
We can also rewrite equation (3) according to the modifications of the location and the orientation. By noting R _k ⁺¹ the orientation relative to the instant of determination t _k + i with respect to the orientation at the previous instant of determination t _k , that is to say the evolution of the orientation between the previous determination time t _k and the determination time t _k + i, and noting _k Bp _{k + i} the location of the magnetometer at the determination time t _k + i in the frame defined by the location of the magnetometer at the previous determination time t _k , we obtain:
B _{k + i} = (R% ⁺¹ Bk + R% ⁺¹ VBk Â ₊ i) (4)
This fundamental relationship should be verified locally by the measurements of magnetometer 2 if it was properly calibrated. The existence of the different parameters to be calibrated therefore has the consequence of giving rise to discrepancies between the measurement of the magnetic field and a theoretical estimate of the magnetic field based on this relationship. It is by seeking to minimize the differences appearing during the application of this relationship that the values of the calibration parameters can be determined. For this, we build a cost function to minimize. For a plurality of instants of determination, the relationship formulated by equation (3) or equation (4) is expressed by incorporating therein the parameters to be calibrated tainting the measurement of the magnetic field by the magnetometer 2.
For example, if, for simplicity, we are only interested in the compensation of magnetic biases caused by the effects of hard irons, the measurement of the magnetic field at an instant of determination t _k and the gradient of the magnetic field can be written : B _k = Bm _k -B _b (5)
VB _k = VBm _k - v2g (H _b ) (6)
With Bm _k the measurement of the magnetic field for the instant of determination t _k , B _b the magnetometric bias affecting the measurement of the magnetic field, VBm _k the measured gradient of the magnetic field for the instant of determination t _k , and 5 v2g ( H _b ) the magnetometric bias affecting the measurement of the gradient of the magnetic field. The magnetometric biases are therefore parameterized by the vector B _b of dimension 3 and the vector H _b of dimension 5, with v2g a function of transformation from vector to gradient such that:
at b vs b d e -VS e —Ci - d-
(7)
By replacing in equation (3) the expressions of the magnetic field B _k and the gradient of the magnetic field VB _k expressed in (5) and (6), one can obtain a criterion to be minimized based on a comparison between a theoretical estimate of the magnetic field, resulting from the exploitation of the relationship mentioned, and at least one measurement of the magnetic field:
Bm _{fe + 1} -B _b = R% ₊₁ [R _k (Bm _k - B _b ) + R _k (VBm _k - v2g (H _b )) Rl (p _{k + 1} - p _k ) j (8)
The cost function can be constructed by adding a norm p of this criterion for a plurality of instants of determination t _k :
Zfc = oP (Sfc + 1 -B _b - Æfc + i (Χ (Λ “B _b ) + R _k (VB _k - v2g (H _b )) Rl (p _{k + 1} - p _k ) ty (9)
The standard p used can for example be the standard L2 (square root of the modules of the components), or the standard L1 (the sum of the modules of the components) more robust, or any other robust standard used in the M-estimators (for example Huber, Cauchy or Tukey). The sum may not contain all the measurement samples of the magnetic field, a step of selecting the samples may take place upstream.
The cost function can then be minimized with respect to the biases B _b and H _b (or v2g (H _b )) by any algorithmic method, for example an iterative algorithm of Newton, Gauss-Newton, Levenberg-Marquard, ... etc. in order to obtain the calibration parameters. As criterion (8) to which the standard is applied is linear in bias parameters, the resolution of the minimization is very efficient. The use of a robust standard however requires several iterations before convergence. A Gauss-Newton type algorithm can therefore advantageously be used. In addition to the methods based on an optimization of the cost function of the gradient descent type, other approaches can be used to minimize the cost function, as for example with tools of the state observer type (Kalman filter, filter of extended Kalman, observer of Luenberger or other). It is thus possible, for example, to construct an extended Kalman filter from prediction (8) where the covariance matrix of the error represents the cost function to be minimized.
The example above has been simplified to a case where the only parameters to be calibrated are constant magnetometric biases. The same approach can also be used to determine other calibration parameters, such as scale factors of the measurements, or parameters of the spatial configuration of the magnetometer, such as for example the orientation positions of the magnetometer relative to the point secured to the magnetometer. for which trajectory information is provided. This method therefore makes it possible to estimate the geometry of a network of magnetometers. It is also possible to use the minimization of the cost function to determine the parameters of a parametric model of the magnetic field in which the magnetometer 2 operates when it traverses the course positions.
As indicated above, the method can advantageously be used to calibrate several magnetometers 2 at the same time, in particular when these are integrated into a magneto-inertial unit 1. In the example below, several magnetometers 2 form a network, and the parameters to be calibrated aim to compensate not only for a magnetometric bias affecting the measurement of the magnetic field, but also for scaling factors. It is assumed that a measurement of a magnetometer 2 i of a network is described in a linear fashion according to the equation.
B ^ DJJ + bj (10)
Where B is the real magnetic field and B _mi the measurement of the magnetic field of the magnetometer i (polluted by a scale factor Dj which can be diagonal or a solid matrix and a bias b,). It should be noted, however, that other magnetometric parameters could be used in a similar manner.
By taking again the relation expressed by the equation (1), with a local modeling with the first order of the magnetic field around a magnetometer 2 of reference (indexed 0) of the network, the magnetometer 2i at the position dx, of a set of magnetometers positioned in a close volume gives the measurement of the magnetic field B _mi by the magnetometer 2 /:
Bmî = θί · (Bo + PBo-dXj) + bj (11)
With Bo the magnetic field at the position of the reference magnetometer 2, and VB ₀ the gradient of the magnetic field at the position of the reference magnetometer 2.
We can rewrite equation (11) by vectorizing column by column Vec (VB):
intervene the gradient matrix (12)
Bmi = ([l <dXj] 0Dj) y _{ec (} - _7Bo y + ^b i where 0 here represents the product of Kronecker on the matrices.
For a set of n three-axis magnetometers, we can concatenate the measurements and the magnetometric biases:
^B m -
[l, dx ₁ ^T ] 0D ₁ Bo [1, dx _n ^T ] 0 D _n Vec (7B ₀ ).
+ b [1, dx _x ] 0 I _3x3 (13)
B _m = diag (D ₁ , ..., D _n ) [1, dx _n ] 0 I3X3
Bo
Vec (7B ₀ ).
(14)
We can then note [1, dx _x ] 0 I _3x3 c = ^v, mag [1, dx _n ] 0 I _3x3 (15) consequence, the relation between
The size of C _mag is (n, 12). Depending on the rank of the matrix C _mag , there may or may not be ambiguity on the magnetic field and the gradient of the magnetic field. In
Bo
Vec (7B ₀ ).
and the measurements B _m can be invertible or not. If the rank of the matrix is smaller than its number of lines, it is possible to reduce the number of parameters of the first order field model by taking into account the constraints related to Maxwell's equations (the gradient is symmetric to trace nothing).
In these two cases we denote C _mag ⁺ the linear relation which verifies:
B
Vec (7B).
(16) with D _inv = diag (^ -, ..., - ^ -).
^υ ι ^υ η
Assuming the stationary magnetic field globally, one can write throughout the trajectory of a magnetometer 2 the relation linking the evolution of the magnetic field with the evolution of the location and the orientation of said magnetometer 2:
B = - <oxB ₀ + VB ₀ .v (17) with ω the speed of rotation of the magnetometer, and v its speed of movement (change of location). It is therefore a reformulation of the relation formulated by equation (1).
The evolution of the measurement of the magnetic field of the reference magnetometer 2 is linked between two instants of determination with the difference in position derived from the trajectory information. Thanks to the trajectory information, the evolution of the location and the orientation of the magnetometers 2 is available. In fact, the magnetometers of the network are interdependent, and the trajectory information is representative of the location and of the orientation of a point secured to these magnetometers 2. Preferably, the location and the orientation of the reference magnetometer 2 are determined from the trajectory information.
By noting 6R _pred the rotation matrix (known) passing from the orientation of the reference magnetometer 2 to the previous instant of determination t _k and the orientation of the same reference magnetometer 2 at the instant of determination tk + i and dx _pred the (known) location of this same magnetometer 2 of reference at the instant of determination t _{k +} i in the reference frame formed by the same magnetometer 2 of reference at the instant of determination previous t _k , a theoretical estimate of the field at the determination time t _{k +} i is written, from the magnetic field and the magnetic field gradient at the previous determination time t _k :
Bfc + l ^- δ Rp _r ed (B _k + 7B _k dx _pred ) (18)
The theoretical estimate can be reduced to the measurement space (polluted by the parameters to be calibrated) of the reference magnetometer 2. The predicted measure Λ Λ ——- ~ ~
Bopred (b <Dj; dx _pred , δR _pred , B _{m; k} ) can then be expressed as a function of
Λ Λ estimates of the bias b and the scale factor Dj, as well as the inputs dx _pred , δ R _pred , B _{m; k} , with B _{m; k} the measurement of the magnetic field by the reference magnetometer 2 at the moment of previous determination t _k .
Indeed, the measurements of the magnetic field at the previous determination instant t _k makes it possible to generate a local model of the magnetic field around the position of the reference magnetometer 2 at the previous determination instant t _k :
.With (7B _k ).
(19)
This local modeling makes it possible to formulate a theoretical estimate of the measurement of the magnetic field by the reference magnetometer 2. The transition from the theoretical estimate of the magnetic field to the theoretical estimate of the measurement of the magnetic field is done by applying parameter estimates
Λ of calibration, in this case the estimate of the magnetometric bias b and the estimate of the scale factor Dj:
- Dq δ R _pre d (β / c H ^- FB / c dx _pred ) + b ₀
(20)
By injecting (19) into (20), we obtain the relation linking the estimate of the measurement to the instant of determination t _{k +} ials measurements to the previous determination instant t _k and to the parameters of the model of each magnetometer 2:
(21)
This relation makes it possible to construct the following prediction:
Λ Λ ~ ~
Bopred (B, Dj; dXp _{re (} j, δ Rp _re d> ^ m; k) ^-
(22)
We can then construct the cost function from the residuals in the measurement space as follows:
Σ / c P (Bk + l; Opred; k + l; (b> θϊ I dXp _{re (} j, δ Rp _re d> ^ m; k) ^- ^ m; k + l) (23) where as before, p is a norm which can be the L2 norm, the L1 norm or another norm, and B _{m; k + 1} represents the measurement of the magnetic field by a magnetometer, polluted by a scale factor and a bias. do not contain all the magnetic field measurement samples, a step of selection of the samples can occur upstream. The cost function can then be minimized compared to the estimates (noted with a circumflex accent here) by any algorithmic method, by example an iterative algorithm of Newton, Gauss-Newton, Levenberg-Marquard, ... etc. in order to obtain the calibration parameters. As before, in addition to the methods based on an optimization of the cost function of the gradient descent type, other approaches can be used to minimize the cost function, such as with tools ls of the state observers type (Kalman filter, extended Kalman filter, Luenberger observer or other). We can thus for example build an extended Kalman filter from prediction (22) where the covariance matrix of the error represents the cost function to be minimized.
Note that the minimum of the cost function formulated by equation (23) may not be unique. The minimums then correspond to degenerate situations. For example, it can be shown that in certain cases certain linear combinations of the magnetometric biases are not observable, even if one seeks to estimate only these (for example by assuming the scale factors with the unit). In this case, we can easily reparametrize the influence of magnetometric biases in the cost function formulated by equation (23) on an observable subspace by making the following variable change:
fb [boi [Cmag] 4: 8Dinv b] (24) where the notation [Χ] _{ί :;} · Corresponds to the sub-matrix formed by the lines deX whose index is between i and j inclusive. This amounts to reducing the cost function (24) to the cost function formulated in (9). It may also be necessary to fix at least one of the scale factors, or else an overall average scale factor to reject the degenerate situation in which all the scale factors are identically harmful. Other solutions to non-uniqueness problems, such as regularization, make it possible to prevent the non-uniqueness of the minimum from affecting the convergence of the algorithm. These regularization methods act on the minimization process by limiting the modification of the estimate along a direction that does not vary the cost function. These remarks apply to the different formulations of the cost functions.
The example above is given by way of nonlimiting example for the case of a network of 2 tri-axis magnetometers. One could also consider considering a network of 2-axis magnetometers 2. The measurement model expressed by (10) then becomes, for each of the axes:
B _mi = f /. B + bi (25) where B is the real magnetic field and B _mi the measurement of the magnetic field, ή a vector of dimension 3, associated with the sensitivity of the sensor and b, the bias of this sensor. In this case, with the same reasoning as that presented in the case of the network of 2 tri-axis magnetometers, it is possible to deduce a similar cost function which also depends on the new parameters:
Z _fe p (B _{k +} l; 0pred; k + l (b, fj J ÙXpred <Ô Rp _re d, B _{m; k} ) Bm; k + 1) (26)
The examples above exploit the relation established by the equation of the particle derivative of the magnetic field (1), possibly with a local approximation of the first order as in (11). It is however possible to adopt a simpler approach when the magnetic field in which the path of the magnetometer 2 is carried out is stationary, that is to say independent of time but dependent on space.
Suppose that there are n 2-axis magnetometers with an affine response rigidly placed on a sensor card, as in the case of a magneto-inertial unit 1. The measurements of these magnetometers 2 can be modeled by:
mfB) = (afB) + b _L (27) where ai represents the three calibration parameters of the single-axis magnetometer 2 i associated with its linear response with respect to the magnetic field B expressed in sensor reference, and f is a scalar representing the bias of the magnetometer 2 monoax i. Each magnetometer 2 being placed at a different position on the sensor card, if we denote x, the vector representing the position in a fixed reference with respect to the sensor card, then we can write as a first approximation that at any time of determination t _k :
= (ajBCxptfc)) + ¼ (28) where B represents the magnetic field in sensor reference as a function of position and time. When the sensor card is set in motion in a magnetic field assumed to be stationary (independent of time, but dependent on space) to traverse a set of travel positions, the magnetic field B seen in the reference frame of magnetometer 2 only depends on the location and orientation of the sensor card in space. Since these locations and orientations are known by the trajectory information provided, simultaneously with the magnetic field measurements from the magnetometers 2 for each instant of determination, then the parameters a _h x _{h and} bi, are observable, to within a global scale factor for the parameters ai corresponding to the magnetic field unit, as soon as the system is placed in an inhomogeneous stationary field, that is to say that it depends on space. It should be noted, however, that the overall scale factor for the parameters a ,, which corresponds to a calibration of the measurement system on a unit of magnetic field, may be superfluous for certain applications, such as a magnetic tachometer of a magneto-inertial unit 1 or heading calculation.
A possible cost function to be minimized can then be of general formula
E = ZjPÎmiiti) - ({a ^ BÎxptf)) + h,)) (29) where miitj ') represents the measurement at the time of determination tj from the magnetometer 2i, for the parameters a _h x _b etbi and a description of the field magnetic B stable in the position reference, and p a standard as previously explained.
By way of example, if the gradient of the magnetic field is considered to be spatially constant, the magnetic field can be described by an affine model. By noting u the spatial variable describing the location in the external coordinate system, we can describe the magnetic field as being:
B ₀ (u) = B _o (O) + VB (0). U (30) where B _o (O) is a constant vector representing the magnetic field at a reference position, and VB (0) is a symmetric matrix with zero trace representing the magnetic field gradient at the reference position.
By noting • o (t ₇ ) the position of the origin of the sensor reference in the external reference frame at time tj, • / (T ₇ ) the rotation matrix representing the orientation of the sensor card relative to the reference frame external at time t ₇ , • B ₀ (u) the magnetic field in external reference function of u, one can write:
+ «(TyX) (31)
By combining equation (30) with equation (31), it comes:
Β (χ ^ ₇ ·) = R ^T (tj) (b ₀ (0) + VB (0). (O (t ₇ ) + (32)
This expression (32) can be injected into the cost function E given as an example in expression (29). For example, with p the norm L2 squared, we obtain:
By minimizing the cost function, we can thus not only determine the scale and orientation factors a, and the biases b ,, but also identify by way of description of the field the three independent parameters 5 _o (O) and the five independent parameters of VB (0). We can therefore proceed without any information on the magnetic field other than its stationarity, since the parameters of the magnetic field model are determined via the cost function.
The method can also be applied similarly using other magnetic field models as a relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer. Thus, we can use magnetic field models with development at higher orders, for example by estimating the hessian of this magnetic field or derivatives of higher orders.
Once the calibration parameters of a magnetometer 2 have been determined, it suffices to apply corrections resulting from the calibration parameters to the measurements of the magnetometer 2 to calibrate the magnetometer (step S6). For example, to compensate for a magnetometric bias b, it suffices to subtract from the measurement the bias value b determined during calibration.
It should be noted that the present calibration method can be implemented not only during a calibration of the magnetometer prior to its use, but also during the use of the magnetometer, in order to recalibrate it during use. . It suffices to have the trajectory information. This is particularly the case for a magneto-inertial power plant.
The invention also relates to a computer program product comprising program code instructions recorded on a non-volatile medium readable by a computer for the execution of the steps of the method according to the invention when said program code instructions are executed on a computer.
The invention is not limited to the embodiment described and shown in the appended figures. Modifications remain possible, in particular from the point of view of the constitution of the various technical characteristics or by substitution of technical equivalents, without thereby departing from the scope of protection of the invention.

权利要求:
Claims (18)
[1" id="c-fr-0001]
claims
1. Method for calibrating a magnetometer (2) comprising the following steps:
- The magnetometer (2) traverses (S1) a set of travel positions, said positions being distinguished from each other by a location of the magnetometer (2) and / or by an orientation of the magnetometer (2);
- acquisition (S2) by the magnetometer (2) at times of acquisition of a plurality of measurements of the magnetic field when the magnetometer (2) traverses said set of path positions;
- providing trajectory information (S3) representative of the location and the orientation of a point secured to the magnetometer (2) during the course of the set of course positions at times of course,
- for each of a plurality of instants of determination determined from the instants of acquisition and instants of travel, correspondence (S4) of the measurements of the magnetic field with the trajectory information,
determination (S5) of calibration parameters of the magnetometer (2) by minimizing a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field, and a relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer (2) derived from the trajectory information.
[2" id="c-fr-0002]
2. Method according to claim 1, in which the cost function involves error terms relating to sensor measurements, said sensor measurements taken alone making it possible to obtain the trajectory information, the trajectory information then being determined at the same time as the calibration parameters.
[3" id="c-fr-0003]
3. Method according to one of the preceding claims, in which the minimization of the cost function is carried out with a state observer.
[4" id="c-fr-0004]
4. Method according to one of the preceding claims, in which the cost function is based on comparisons between a theoretical estimate of the measurement of the magnetic field at a determination instant and a measurement of the magnetic field at said determination instant, the theoretical estimate of the magnetic field taking into account the calibration parameters.
[5" id="c-fr-0005]
5. Method according to claim 4, in which the theoretical estimate of the measurement of the magnetic field is determined from the relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer derived from trajectory information.
[6" id="c-fr-0006]
6. Method according to one of claims 4 to 5, in which the theoretical estimate of the measurement of the magnetic field is determined at least from:
- a measurement of the magnetic field at a previous determination instant,
- the evolution of the location and the orientation of a point secured to the magnetometer (2) between the instant of determination and the previous instant of determination, determined from the trajectory information,
- calibration parameters.
[7" id="c-fr-0007]
7. Method according to the preceding claim, also comprising an acquisition at times of acquisition of a plurality of measurements of a gradient of the magnetic field when the magnetometer (2) traverses said set of path positions, and the theoretical estimate of the magnetic field is also determined from a measurement of the gradient of the magnetic field at the previous determination time.
[8" id="c-fr-0008]
8. Method according to one of the preceding claims, in which the relation linking the evolution of a magnetic field with the evolution of the location and the orientation of the magnetometer locally translates an equation of the particle derivative of the magnetic field :
B = VB. v + Ω x B with B a magnetic field vector, VB a gradient vector of the magnetic field, B a vector of the time derivative of the magnetic field, vun velocity vector representative of the modification of the location and Ω a rotation matrix representative of changing the orientation.
[9" id="c-fr-0009]
9. Method according to claim 4 or 5, in which the theoretical estimate of the measurement of the magnetic field at a time of determination is determined from:
- of a magnitude of the magnetic field at a reference point,
- a gradient of the magnetic field at said reference point, and
- the difference between the location of the point secured to the magnetometer and a location of the reference point,
- the rotation between the orientation of the point secured to the magnetometer and an orientation at the reference point, the magnitude of the magnetic field at a reference point and the gradient of the magnetic field at said reference point being determined by minimizing the function of cost.
[10" id="c-fr-0010]
10. Method according to any one of the preceding claims, in which the calibration parameters comprise:
- a first magnetometric bias affecting the measurement of the magnetic field, and / or
- a second magnetometric bias affecting a measurement of a gradient of the magnetic field, and / or
a scale parameter affecting an amplitude of the measurement of the magnetic field and / or
- spatial configuration parameters of the magnetometer.
[11" id="c-fr-0011]
11. Method according to any one of the preceding claims, in which the mapping consists in interpolating at least one set from:
- a set of magnetic field and magnetic field gradient measurements,
- A set of trajectory information, so that at each instant of determination corresponds to at least one measurement of the magnetic field and of trajectory information.
[12" id="c-fr-0012]
12. Method according to any one of the preceding claims, in which the trajectory information is provided by the use of an imager (10) identifying the location and the orientation of the magnetometer (2) at each instant of travel when the magnetometer traverses the first set of positions.
[13" id="c-fr-0013]
13. Method according to the preceding claim, wherein the imager (10) is integral with the magnetometer (2), and a fixed target (11) is arranged in a field of vision of said imager, the trajectory information being derived from the location of the target in images acquired by the imager when the magnetometer traverses the set of course positions.
[14" id="c-fr-0014]
14. Method according to any one of claims 1 to 11, in which a mechanical displacement device moves the magnetometer (2) from one position to another position in the first set of positions when the magnetometer traverses said set of positions of course, the trajectory information being derived from position measurements of said mechanical displacement device or from position setpoints of said mechanical displacement device.
[15" id="c-fr-0015]
15. Method according to any one of claims 1 to 11, in which the magnetometer (2) is integral with inertial sensors (24) configured to determine at each instants of travel accelerations and angular velocities, and the trajectory information. are derived from said accelerations and angular velocities.
[16" id="c-fr-0016]
16. Method according to any one of the preceding claims, in which the magnetometer (2) is arranged in a magneto-inertial unit (1).
[17" id="c-fr-0017]
17. Automated data processing unit comprising a processor, a memory and input and output interfaces, configured for:
- receiving a plurality of measurements of the magnetic field acquired at instants of acquisition by a magnetometer (2) traversing a set of path positions, said ones being distinguished from each other by the spatial location of the magnetometer and / or by the orientation of the magnetometer;
- receive trajectory information representative of the location and orientation of a point secured to the magnetometer (2) during the course of the positions of the set of course positions at times of course,
- for each of a plurality of instants of determination determined on the basis of the acquisition instants and the instants of travel, to match measurements of the magnetic field and of the magnetic field gradient with the trajectory information,
determining the magnetometer calibration parameters by minimizing a cost function involving, for a plurality of determination times, at least said calibration parameters, a measurement of the magnetic field, and a relation linking the evolution of '' a magnetic field with the evolution of the location and the orientation of the magnetometer derived from the trajectory information.
[18" id="c-fr-0018]
18. computer program product comprising program code instructions recorded on a non-volatile medium readable by a computer for the execution of the steps of the method according to claims 1 to 15 when said program code instructions are executed on a computer .

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法律状态:
2019-02-01| PLSC| Publication of the preliminary search report|Effective date: 20190201 |

2019-07-09| PLFP| Fee payment|Year of fee payment: 3 |

2020-07-16| PLFP| Fee payment|Year of fee payment: 4 |

2021-07-27| PLFP| Fee payment|Year of fee payment: 5 |

优先权:

申请号 | 申请日 | 专利标题

FR1757082|2017-07-26|

FR1757082A|FR3069649B1|2017-07-26|2017-07-26|CALIBRATION PROCESS OF A MAGNETOMETER|FR1757082A| FR3069649B1|2017-07-26|2017-07-26|CALIBRATION PROCESS OF A MAGNETOMETER|

KR1020207005676A| KR20200041889A|2017-07-26|2018-07-26|How to calibrate the magnetometer|

JP2020503900A| JP2020528553A|2017-07-26|2018-07-26|How to calibrate the magnetometer|

US16/634,045| US20200233053A1|2017-07-26|2018-07-26|Method for calibrating a magnetometer|

CN201880062290.9A| CN111149002A|2017-07-26|2018-07-26|Method for calibrating a magnetometer|

EP18758934.6A| EP3658921B1|2017-07-26|2018-07-26|Method for calibrating a magnetometer|

PCT/FR2018/051914| WO2019020945A1|2017-07-26|2018-07-26|Method for calibrating a magnetometer|

ES18758934T| ES2882377T3|2017-07-26|2018-07-26|Calibration procedure for a magnetometer|

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