DE102015203686B4 - Method and arrangement for determining the position of a magnetic body using magnetic field sensors - Google Patents

Abstract

Method for determining the position of a magnetic body (3) by means of one or more magnetic field sensors (2), which moves relative to the one or more magnetic field sensors (2), in which one or more locally repeats one or more magnetic field sensors (2). of three directional components of a magnetic flux density of a magnetic field generated by the magnetic body (3) are detected and evaluated in order to determine the respective position of the magnetic body (3), the one or more magnetic field sensors (2) in the near field of the magnetic body ( 3) are arranged and - the evaluation is carried out at least partially with an optimal estimator based on a magnetic field model, characterized in that during the evaluation the position is either first roughly determined using a neural network and then further refined with the optimal estimator or initially with is roughly determined using the optimal estimator and then refined using a neural network.

Description

Technical application area

The present invention relates to a method for determining the position of a magnetic body by means of one or more magnetic field sensors, which moves relative to the one or more magnetic field sensors, in which one or more of three directional components of the magnetic flux density of the magnetic field are locally determined with the one or more magnetic field sensors Magnetic field generated by the magnetic body is recorded and evaluated in order to determine the respective position of the magnetic body. The invention also relates to an arrangement for determining the position of a magnetic body, which works according to the proposed method.

In many technical applications, the change in the relative position (location and/or location or orientation) of objects must be recorded. Non-contact processes have many advantages such as wear resistance and freedom from maintenance. Magnet-based processes are particularly suitable for use in harsh environments as they are not affected by dirt, oil and water.

The established magnetic position measurement has so far been limited to a few degrees of freedom, a maximum of two translational movements or two angles, or requires a complicated mechanical structure with a large number of magnetic sensors. In fact, the movements to be recorded are always spatial due to assembly and manufacturing tolerances as well as wear. A series of movable mechanical connections, e.g. joints or couplings, also allow displacements and/or rotations in several axes, even on larger scales. Until now, such movements have often not been able to be measured magnetically with precise precision using a simple structure, but only by using several discrete sensors, which inevitably determine the desired variables individually at different locations. This is time-consuming, error-prone and therefore not very reliable.

State of the art

There are a number of sensors that are based on very different physical principles to determine the location and position of objects. In addition to optical, inertial, inductive and capacitive measuring systems, magnet-based sensors are also used, as is the case with the method and the associated arrangement proposed here. The most important physical measurement principles in this area are the Hall effect and magnetoresistive effects (AMR, GMR, TMR).

Typical magnet-based position sensor systems consist of a moving magnetic source and a stationary magnetic field sensor. The magnetic source, referred to as a magnetic body in the present patent application, is typically a permanent magnet. However, electromagnets are sometimes also used. With the magnetic field sensor, one or more of the three directional components of the magnetic flux density of the magnetic body are measured and converted into target variables such as distance (e.g. with linear distance measurement) or angle (e.g. with rotary encoders) via downstream signal processing.

For movements with a single mechanical degree of freedom, it is known to create a so-called linearization table from experimentally determined measured values, which discretely describes the unique mapping between the measured value of a flux density component and a position component (path or angle) of the magnetic body. In this way, the associated position can be determined directly using the measured value. In principle, position determination with more than one degree of freedom is also possible using this approach. However, with each degree of freedom, the need for storage space and computing power increases significantly. Therefore, no practically relevant resolutions can be achieved with it.

For the long-range location of magnetic bodies, it is known to carry out vector measurements of the magnetic flux density. Distributed measurements in the far field of the magnetic body are used. The distance between the magnetic body and the magnetic field sensors is much larger than a characteristic length of the magnetic body. Depending on the application, the magnitude is between > 10 cm and up to kilometers. These far-field location methods are based either on the measurement of disturbances in the earth's magnetic field by the magnetizable secondary source to be located, for example when locating ships, aircraft or mines, or they involve the location of a very small magnetic field source with highly sensitive sensors in an area around the source distributed, discrete sensor arrays, as is known, for example, from the localization of catheters or magnetic markers in medical technology. The methods of vector magnetic position determination use a dipole approximation for the magnetic source or the magnetic body, which enables a simple description of the magnetic field. An example of such a position determination in the far field is shown in: EP 1 040 369 B1 , in which the position of a vehicle is determined using this dipole approximation.

From the EP 2 606 411 B1 a method and an arrangement for a magnetic sensor user interface are known, in which a table (LUT: Look-up Table) is created based on a magnetic model, from which the position of the magnetic body is determined by comparison with the vectorially measured values of the magnetic flux density or the actuator to which the magnetic body is attached. The publication also mentions the possibility of specifying an analytical model to which the measured data are then adapted, without, however, going into further detail about this procedure.

The WO 2014/ 182 246 A1 describes a method for determining the position of a magnetic body using one or more magnetic field sensors, in which the magnetic field sensors are arranged in the near field of the magnetic body. The publication uses a neural network for evaluation.

The DE 10 2006 042 725 A1 describes a method for determining the tilt angle of a moving body to which a magnet is attached using several magnetic field sensors. For the evaluation, table values are used that are stored in a memory for the various tilt positions. The use of a neural network to evaluate the sensor signals is also mentioned as an alternative.

The US 5,524,086 A deals with the estimation of dipole parameters using a neural network.

From the WO 2005/ 047 823 A1 a method for determining the position of a magnetic body using one or more magnetic field sensors according to the preamble of claim 1 is known.

The object of the present invention is to provide a method and an arrangement for determining the magnetic position of a magnetic body, with which the position of the magnetic body can be reliably determined in a small space in several mechanical degrees of freedom. The position means the location and the position or orientation of the magnetic body.

Presentation of the invention

The task is solved with the method and arrangement according to claims 1 and 8. Advantageous embodiments of the method and the arrangement are the subject of the dependent patent claims or can be found in the following description and the exemplary embodiments.

In the proposed method, one or more of the three directional components of the magnetic flux density of the magnetic field generated by the magnetic body are repeatedly locally detected and evaluated using one or more magnetic field sensors in order to determine the respective position of the magnetic body. The one or more magnetic field sensors is or are arranged in the near field of the magnetic body. The near field is understood to mean a distance to the magnetic body that is smaller in magnitude than twice the characteristic length of the magnetic body. The diameter of the smallest sphere enclosing the body is defined as the characteristic length. The distance of the magnetic field sensor or sensors from the center of this sphere is at least at one point in the movement trajectory of the magnetic body below this twice the characteristic length. When using several magnetic field sensors, they are arranged at a small distance from one another, preferably at a distance from one another that is also smaller than twice the characteristic length. In the proposed method, the evaluation of the measured values for position determination is then carried out at least in part with the help of an optimal estimator based on a preferably analytical magnetic field model.

By arranging the magnetic field sensor or the magnetic field sensors in the near field, the measurement and evaluation enable the determination of several mechanical degrees of freedom of the position of the magnetic body. To determine three degrees of freedom, just one magnet is sufficient field sensor that detects all three directional or spatial components, ie the x, y and z components in the Cartesian coordinate system, of the magnetic flux density. When using two of these 3D magnetic field sensors, six mechanical degrees of freedom in the position can be determined with a suitable magnet shape. These are the three translational and three rotational degrees of freedom of the magnetic body. Position determination is also possible with magnetic field sensors, which only detect one directional component of the magnetic flux. For example, three so-called z-sensors can be used to determine three degrees of freedom of the position of the magnetic body.

Preferably, all three directional components of the magnetic flux are detected with the one or more magnetic field sensors, i.e. a vectorial measurement is carried out in order to be able to determine at least three mechanical degrees of freedom in the position of the magnetic body.

The desired position values are then calculated in a processor from the measured values of the magnetic flux density. In the proposed method, this is done at least in part with the help of an optimal estimator.

A Kalman filter, for example, can be used as an optimal estimator. The optimal estimator requires a magnetic field model that represents a mathematical parameterization of the measurement system through its possible degrees of freedom. An analytical model is preferably provided for this. In principle, the model can also be provided in the form of a table (LUT). Techniques for creating a magnetic field model, for example using the Maxwell equations or the Biot-Savart law, are familiar to those skilled in the art.

Hall sensors or sensors based on the magnetoresistive effect, for example, can be used as magnetic field sensors in the proposed method and the associated arrangement. For the implementation of the method and the associated arrangement, it is irrelevant which physical process is used to record the component(s) of the magnetic flux density by the sensors. It is essential that the directional components of the magnetic flux are detected by the sensors in the near field of the magnetic body (according to the definition above), preferably vectorially, i.e. in all three spatial directions of the Cartesian coordinate system. By means of a suitable number and type (with regard to the detection of the directional components) of the magnetic field sensors, the position of the magnetic body can then be determined in up to six mechanical degrees of freedom using the proposed method and the associated arrangement. The magnetic field sensors can be integrated monolithically, whereby their position relative to one another is very precisely defined. However, this is not absolutely necessary.

The proposed arrangement includes the magnetic body, one or more magnetic field sensors in the near field of the magnetic body and an evaluation and measuring device which repeatedly locally detects one or more of three directional components of the magnetic flux density of the magnetic field generated by the magnetic body via the one or more magnetic field sensors and evaluated to determine the respective position of the magnetic body. When using several magnetic field sensors, these are arranged at a small distance from one another, preferably at a distance from one another that is less than twice the characteristic length of the magnetic body. The evaluation and measuring device is designed in such a way that it carries out the evaluation at least partially using an optimal estimator based on a magnetic field model.

In the proposed method, the one or more magnetic field sensors are arranged in the vicinity of the magnetic body. This means that solutions cannot be used, such as those used in far-field positioning methods that are based on the dipole approximation. Depending on the size of the magnetic body, the arrangement in the near field typically requires a distance of between 10 cm and less than 1 mm. At this distance, the multipole components required for the process dominate the shape of the flux density field, which disappear in the far field compared to the dipole component. Due to these multipole components or higher order multipole terms, a strong change in the magnetic field takes place in a very small space. The multipole terms of the flux density are required in this range in order to be able to obtain a unique relationship between the magnetic field vector and position. If several magnetic field sensors are used, they should therefore preferably also be arranged in a very small space together, for example on an IC chip (IC: integrated circuit). In this case, the sensor array is not distributed over a wide area in the field of the magnetic body, but is located in a small section of the highly nonlinear near field of the magnetic body.

Methods or configurations for determining the position of the magnetic body from the magnetic field measurement values that are insensitive to homogeneous interference fields and/or temperature effects are preferably used in the evaluation.

In a further advantageous embodiment of the method, other variables influencing the measurement are determined - in addition to the mechanical degrees of freedom. For this purpose, in the case of an optimal estimator, a preferably analytical description of the influence of the size on the sensor measured values is included in the model and the state vector to be determined is expanded to include the additional sizes. Additional properties can be estimated from the magnetic field measurement values, such as a homogeneous interference field and/or sensor parameters (e.g. sensitivity or orthogonality error) and/or parameters of the magnetic source such as temperature-dependent remanence or mismagnetization.

The use of interference field and temperature-insensitive methods or the explicit determination of the interference field and/or temperature parameters results in an expanded permissible range of application of the position sensor systems even in the presence of such influences, which is often the case and then previously results in lower levels of accuracy or requires complex shielding measures. The advantage is the gain in accuracy and/or no effort for protective measures in environments with strong interference fields (electric motors, power lines, arcs, ...) or temperature fluctuations.

The proposed method and the associated arrangement use combinations of different methods or algorithms for position determination. A rough approximation of the position is initially made using the optimal estimator or a neural network, which is then improved using a further process (hybridization). Another method used is an optimal estimator or a neural network.

Finally, after determining the degrees of freedom, a method from the group of optimal estimators, neural networks or optimization methods can also be used to check the plausibility of the results of the method used to determine the position. The procedure used for plausibility checks should of course differ from the procedure used for position determination.

The arithmetic operations required for the evaluation are preferably carried out by a processor associated with the measuring system, i.e. the proposed arrangement, which can be integrated, embedded or also arranged externally. With the proposed method and the associated arrangement, several degrees of freedom of a magnetic body can be determined with just one sensor or sensor array. This enables, for example, the simultaneous measurement of displacement and rotation. Additional degrees of freedom can be recorded that are not primarily sought in the measurement task. The use of these degrees of freedom for monitoring second-order variables, for correction or similar causes the measuring system to be more robust against mechanical tolerances. This has the advantage, for example, that installation position errors of the magnetic body do not have to be compensated for by expensive end-off-line calibration. This means that cheaper manufacturing processes can be used if necessary, as their generally larger tolerances do not have a negative impact on the measurement result. In addition, assembly tolerances can be measured directly in this way, e.g. for production monitoring or quality control. The method and arrangement enable the implementation of simpler measuring systems, which are therefore less error-prone, more compact and cheaper. If necessary, sensors can be saved and installation space is gained.

Monolithic integration of the magnetic field sensors on an IC chip enables a particularly significant reduction in installation space. This also leads to a drastic reduction in the development and manufacturing effort for the measuring system compared to a discrete structure. The susceptibility to errors and production costs are reduced significantly.

The use of hybrid methods for position determination allows computing power to be optimally tailored to the required accuracy. This has the advantage that a cheaper microcontroller can be used without compromising the accuracy requirements or a higher level of accuracy can be achieved without increasing costs.

The proposed method and the associated arrangement can basically be used in all applications in which mechanical parts move in several degrees of freedom or axes. The magnetic body is attached to the respective object to be monitored. In the fol Examples of different applications are listed in which the magnetic position measurement of the proposed method offers significant advantages.

With the help of the method, it is possible, for example, to construct a control element (multi-DoF control element) that, in addition to three tilt angles (rotation around the x, y and z axes), detects further degrees of freedom, namely translational movements in all spatial directions. The structure then consists of a lever that can be tilted and moved in all directions. The deflections here can be in the range of ± 10° or ± 5mm. There is a cuboid magnetic encoder (magnetic body) on the control element, which moves with the control element over a stationary sensor IC.

Another example concerns pneumatic cylinders. Using a ring cylinder magnet on the piston rod of a hydraulic or pneumatic cylinder, the translational position of the piston rod and thus the stroke of the cylinder can be determined using a classic, magnet-based position sensor. However, precision movements of the magnet on the piston rod cause measurement errors. With a vectorial measuring sensor structure and method according to the present invention, the tilting and twisting of the magnet is detected in addition to the displacement, which enables a significantly more precise stroke measurement.

Further examples are the detection of the rotation of an object with displacement (2 DoF, e.g. rotation angle sensor, steering angle sensor, steering column switch, gear selector switch, etc.), the double tilting of an object with displacement (3 DoF, e.g. joystick with pressure function, air spring), the three-way displacement of an object (3 DoF, e.g. unbalance, drift, valve travel sensor), the double tilting of an object with displacement and rotation (4 DoF, e.g. push-turn joystick), the triple tilting of an object (3 DoF, e.g. ball joints, trackball), the double tilting of an object with triple displacement (5 DoF, e.g. metal bellows coupling), or the triple displacement and tilting of an object (6 DoF, e.g. 6D mouse, bearing play sensor). The method and the arrangement enable the determination of several degrees of freedom in order to compensate for tolerances, for example in the case of a triple displacement with a main axis and additional marginal displacements due to play (monitored linear encoder) or with rotation around a main axis and additional marginal rotations due to play (monitored rotary encoder). . This is of course not an exhaustive list of the possibilities for using the proposed method and the associated arrangement.

Brief description of the drawings

• 1 eine schematische Darstellung einer Anordnung der Magnetfeldsensoren sowie des magnetischen Körpers gemäß dem vorgeschlagenen Verfahren und der zugehörigen Anordnung;
• 2 ein Beispiel für eine Signalverarbeitung innerhalb eines Neurons eines neuronalen Netzes, wie es bei dem vorgeschlagenen Verfahren und der zugehörigen Anordnung zum Einsatz kommen kann; und
• 3 eine Darstellung eines Beispiels für die Positionsbestimmung mit einem neuronalen Netz.

The proposed method and the associated arrangement are explained in more detail below using exemplary embodiments in conjunction with the drawings. Show here:

• 1 a schematic representation of an arrangement of the magnetic field sensors and the magnetic body according to the proposed method and the associated arrangement;
• 2 an example of signal processing within a neuron of a neural network, as can be used in the proposed method and the associated arrangement; and
• 3 a representation of an example of position determination with a neural network.

Ways of carrying out the invention

Two exemplary embodiments are given below in which the position of a moving magnetic body is determined using the proposed method. The magnetic body has no rotational symmetry.

The first example shows a procedure for position determination with optimal estimators, which is used in the proposed method in combination with a neural network. In 1 A position measuring system or an arrangement according to the present invention is shown here. The figure shows an IC chip 1, also referred to below as a sensor chip, on which five magnetic field sensors 2 are located. Each of these magnetic field sensors 2 can measure the magnetic field vectorially, that is, detect all three directional components. The sensor chip therefore delivers 15 scalar sensor readings. A processor, not shown, which determines the position, ie location and/or position, of the magnetic body from the measured values and thus serves as a measuring and evaluation device can be integrated into the IC chip 1 or as an embedded system or as a computer, for example. as a PC.

A cuboid permanent magnet 3 magnetized in the z direction is used as the magnetic body or magnetic source. This is firmly connected to the object to be monitored, which can move translationally and rotationally in space and whose location and position can be determined relative to the sensor. The sensor (IC chip 1) is located in the near field of the magnet 3.

beschrieben. Gemeinsam mit affinen Transformationen bildet diese die Messfunktion des Positionsmesssystems, also den Übergang des Positionsvektors $\left(\overrightarrow{r}\right)$

auf die Messwerte $$

${\overrightarrow{ƒ}}_{\text{B}}\left(\overrightarrow{\text{r}}\right)={\left({\text{B}}_{\text{x}}{}^1,{\text{B}}_{\text{y}}{}^1,{\text{B}}_{\text{z}}{}^1\mathrm{...,}{\text{B}}_{\text{z}}{}^{\text{m}}\right)}^{\text{T}}$

für die m = 5 vektoriellen Magnetfeldsensoren 2. Um die sechs Positionswerte (drei translatorische und sechs rotatorische Freiheitsgrade) zu berechnen, muss die Mess- oder Modellfunktion f_B:R⁶→R^3m im Rahmen des Algorithmus invertiert werden. Dies kann meist nicht direkt erfolgen, da eine explizite Inverse der Messfunktion nur in sehr speziellen Fällen bekannt ist. Die Positionswerte werden daher beim vorliegenden Verfahren geschätzt. Eine Möglichkeit hierfür ist die Technik mit optimalen Schätzern. Diese beruht auf statistischen Methoden. Beispielsweise wird im Falle eines Kalman-Filter-basierten Ansatzes in einem zweistufigen Berechnungsablauf eine zu bestimmende Position zunächst anhand eines Bewegungsmodelles vorhergesagt und dann durch die Messwerte $\overrightarrow{y}$

korrigiert. Um der nichtlinearen Messfunktion Rechnung zu tragen, wird bei diesem Ansatz eine Linearisierung (extended Kalman-Filter) oder die sog. Unscented Transformation verwendet.The location-dependent flux density field of the magnet 3 is determined by a nonlinear function $\overrightarrow{b}\left(\overrightarrow{r}\right)$

described. Together with affine transformations, this forms the measuring function of the position measuring system, i.e. the transition of the position vector $\left(\overrightarrow{r}\right)$

on the measured values $$

${\overrightarrow{ƒ}}_{\text{b}}\left(\overrightarrow{\text{r}}\right)={\left({\text{b}}_{\text{x}}{}^1,{\text{<figure-callout id="1" label="b y" filenames="DE102015203686B4\_0025.png,DE102015203686B4\_0026.png" state="{{state}}">b</figure-callout>}}_{\text{y}}{}^1,{\text{b}}_{\text{e.g}}{}^1\mathrm{...,}{\text{b}}_{\text{e.g}}{}^{\text{m}}\right)}^{\text{T}}$

for the m = 5 vector magnetic field sensors 2. In order to calculate the six position values (three translational and six rotational degrees of freedom), the measurement or model function f _B :R ⁶ →R ^3m must be inverted as part of the algorithm. This usually cannot be done directly because an explicit inverse of the measurement function is only known in very special cases. The position values are therefore estimated in the present method. One possibility for this is the technique with optimal estimators. This is based on statistical methods. For example, in the case of a Kalman filter-based approach, a position to be determined is first predicted using a motion model and then using the measured values in a two-stage calculation process $\overrightarrow{y}$

corrected. In order to take the non-linear measurement function into account, this approach uses linearization (extended Kalman filter) or the so-called unscented transformation.

und damit die gesuchten Freiheitsgrade schrittweise geschätzt. Die für eine linearisierte Variante eines Kalman-Filters durchgeführten Berechnungsschritte lauten beispielsweise:The condition factor is determined using several calculation steps $\overrightarrow{x}$

and thus the desired degrees of freedom are estimated step by step. For example, the calculation steps carried out for a linearized variant of a Kalman filter are:

$$P_0=\mathbb{E}\left[\left(\overrightarrow{x_0}-\overrightarrow{{\widehat{x}}_0}\right){\left(\overrightarrow{x_0}-\overrightarrow{{\widehat{x}}_0}\right)}^T\right]$$

Initialization: $$\overrightarrow{\widehat{x}}=\mathbb{E}\left[{\overrightarrow{x}}_0\right]$$

$$P_0=\mathbb{E}\left[\left(\overrightarrow{x_0}-\overrightarrow{{\widehat{x}}_0}\right){\left(\overrightarrow{x_0}-\overrightarrow{{\widehat{x}}_0}\right)}^T\right]$$

$$P_k^{-}=\frac{\partial F}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{x}}_{k-1}}{P}_{k-1}{\left(\frac{\partial F}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{x}}_{k-1}}\right)}^T+\frac{\partial F}{\partial \overrightarrow{p}}|{}_{{\overrightarrow{x}}_{k-1}}{R}^p{\left(\frac{\partial F}{\partial \overrightarrow{p}}|{\overrightarrow{x}}_{k-1}\right)}^T$$

Forecast: $${\overrightarrow{\widehat{x}}}_k^{-}-=F\left({\overrightarrow{\widehat{x}}}_{k-1}\mathrm{,0}\right)$$

$$P_k^{-}=\frac{\partial F}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{x}}_{k-1}}{P}_{k-1}{\left(\frac{\partial F}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{x}}_{k-1}}\right)}^T+\frac{\partial F}{\partial \overrightarrow{p}}|{}_{{\overrightarrow{x}}_{k-1}}{R}^p{\left(\frac{\partial F}{\partial \overrightarrow{p}}|{\overrightarrow{x}}_{k-1}\right)}^T$$

$${\overrightarrow{\widehat{x}}}_k={\overrightarrow{\widehat{x}}}_k^{-}+K_k\left(\overrightarrow{y_k}-B\left({\overrightarrow{\widehat{x}}}_k^{-}\mathrm{,0}\right)\right)$$

$$P_k=\left(I-K_k{H}_k\right)P_k^{-}$$

Correction: $${K_k=P_k^{-}{\left(\frac{\partial b}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{\widehat{x}}}_k^{-}}\right)}^T{\left(\frac{\partial b}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{\widehat{x}}}_k^{-}}{P}_k^{-}(\frac{\partial b}{\partial \overrightarrow{x}}|{}_{{\overrightarrow{\widehat{x}}}_k^{-}}\right)}^T+\frac{\partial b}{\partial \overrightarrow{n}}|{}_{{\overrightarrow{\widehat{x}}}_k^{-}}{R}^n{\left(\frac{\partial b}{\partial \overrightarrow{n}}|{}_{{\overrightarrow{\widehat{x}}}_k^{-}}\right)}^T)}^{-}$$

$${\overrightarrow{\widehat{x}}}_k={\overrightarrow{\widehat{x}}}_k^{-}+K_k\left(\overrightarrow{y_k}-b\left({\overrightarrow{\widehat{x}}}_k^{-}\mathrm{,0}\right)\right)$$

$$P_k=\left(I-K_k{H}_k\right)P_k^{-}$$

und die Kovarianzmatrix P₀ ergeben sich durch den Aufbau. Diese können im Beispiel zu ${\overrightarrow{\widehat{x}}}_0=\overrightarrow{0}$

bzw. P₀=0_6,6 gewählt werden. Die Parametermatrizen Rⁿ, R^p entsprechen dem zu erwartenden Sensorrauschen bzw. der Unsicherheit über den Bewegungsprozess. Die Funktion $B\left(\overrightarrow{x},\overrightarrow{n}\right)$

stellt hierbei die Messfunktion bzw. das Messmodell dar. Eingangsparameter sind die Position $\overrightarrow{x}$

und das Messrauschen $\overrightarrow{n}.$

Die Übergangsfunktion $F\left(\overrightarrow{x},\overrightarrow{p}\right)$

beschreibt die Dynamik des Systems abhängig von der Position $\overrightarrow{x}$

und dem Prozessrauschen $\overrightarrow{p}.$

The initialization values for ${\overrightarrow{\widehat{x}}}_0$

and the covariance matrix P ₀ result from the structure. These can be used in the example ${\overrightarrow{\widehat{x}}}_0=\overrightarrow{0}$

or P ₀ =0 _6.6 can be selected. The parameter matrices R ⁿ , R ^p correspond to the expected sensor noise or the uncertainty about the movement process. The function $b\left(\overrightarrow{x},\overrightarrow{n}\right)$

represents the measurement function or the measurement model. Input parameters are the position $\overrightarrow{x}$

and the measurement noise $\overrightarrow{n}.$

The transition function $F\left(\overrightarrow{x},\overrightarrow{p}\right)$

describes the dynamics of the system depending on the position $\overrightarrow{x}$

and the process noise $\overrightarrow{p}.$

ausgibt. Dies ist im unteren Teil der 3 dargestellt.The next example explains position determination with neural networks in more detail, which is used in the proposed method in combination with an optimal estimator. Neural networks consist of relatively simple signal processing units, called neurons, and connections between them. Under certain conditions, a map f:R ⁿ →R ^m (n, m from N) can be approximated with any precision by a neural network if the topology of the network and the weighting of the connections between the neurons are chosen appropriately. A typical neural network can, for example, be implemented with five inputs and one output. Each neuron calculates a weighted sum from the signal values of the incoming connections and a constant offset and applies a so-called activation function σ:R→R to this. The function value determined in this way can be available as input to other neurons or it can be used as the output value of the network. 2 shows an example of signal processing within a neuron 4. The signals arriving via the inputs 5 are first weighted with the weighting factors w ₁ ..., w _p and added up. During the summation, an offset 6 is taken into account, which is incorporated into the summation. The activation function σ is then applied to the result and the result is output at output 7. In the neural network-based approach, the inversion of the measurement function is carried out a priori by training the neural network. This is in 3 illustrated. The training 12 takes place in the laboratory 8. In order to determine the location and position data r belonging to a measured value vector B, the components of B from the measurement 10 are then fed into the trained neural network 11 as the input data in the application 9, which then at its outputs an approximation for the desired location and position vector $\overrightarrow{r}$

outputs. This is in the lower part of the 3 shown.

The neural network therefore contains an implicit model of the inverse measurement function. Such an implicit model can be evaluated with relatively little computational effort and very quickly during the measurement.

Mit Hilfe des sog. Trainingsalgorithmus werden die Gewichte w_j der Verbindungen des neuronalen Netzes so optimiert, dass die Ausgabe ${\overrightarrow{r}}^i$

des Netzes für alle 1 ≤ i ≤ K möglichst genau mit rⁱ übereinstimmt.For training 12, a large amount of training data M{(B ⁱ , r ⁱ )l1 ≤ i ≤ k} is generated by simulation or measurement 13, where the magnetic field values B ⁱ correspond to the position r ⁱ . When the components of one of the vectors B ^k are fed into the neural network as input, its outputs then form the components of a vector ${\overrightarrow{r}}^k.$

With the help of the so-called training algorithm, the weights w _j of the connections of the neural network are optimized so that the output ${\overrightarrow{r}}^i$

of the network matches r ⁱ as closely as possible for all 1 ≤ i ≤ K.

Reference symbol list

1

IC chip

2

Magnetic field sensor

3

Permanent magnet

4

Neuron

5

Inputs of the neuron

6

offset

7

Output of the neuron

8th

laboratory

9

Application

10

Measurement

11

neural network

12

training

13

Measurement series/simulation

Claims (13)

Method for determining the position of a magnetic body (3) by means of one or more magnetic field sensors (2), which moves relative to the one or more magnetic field sensors (2), in which the one or more magnetic field sensors (2) repeatedly locally one or more of three directional components of a magnetic flux density generated by the magnetic body (3). Magnetic field are detected and evaluated in order to determine the respective position of the magnetic body (3), wherein - the one or more magnetic field sensors (2) are arranged in the near field of the magnetic body (3) and - the evaluation at least partially with an optimal estimator based on a magnetic field model, characterized in that during the evaluation the position is either first roughly determined using a neural network and then further refined using the optimal estimator, or first roughly determined using the optimal estimator and then further refined using a neural network becomes. Procedure according to Claim 1 , characterized in that a Kalman filter is used as the optimal estimator. Procedure according to Claim 1 or 2 , characterized in that at least one 3D magnetic field sensor (2) is used, with which all three directional components of the magnetic flux density are detected. Procedure according to Claim 1 or 2 , characterized in that at least three magnetic field sensors (2) are used, each of which only detects one directional component of the magnetic flux density. Procedure according to one of the Claims 1 until 4 , characterized in that after the position has been determined, a plausibility check is carried out using a method that was not used to determine the position. Procedure according to one of the Claims 1 until 5 , characterized in that other variables influencing the magnetic flux density at the location of the measurement or the measurement itself are determined during the evaluation from measured values that are recorded with the magnetic field sensors (2). Procedure according to Claim 6 , characterized in that a homogeneous interference field and/or sensor parameters and/or one or more parameters of the magnetic body (3) are determined as further variables. Arrangement for determining the position of a magnetic body (3), which - the magnetic body (3), - one or more magnetic field sensors (2) in the near field of the magnetic body (3), and - has an evaluation and measuring device which, via the one or more magnetic field sensors (2), repeatedly locally detects and evaluates one or more of three directional components of a magnetic flux density of a magnetic field generated by the magnetic body (3) in order to determine the respective position of the magnetic body (3) to determine - wherein the evaluation and measuring device is designed in such a way that it carries out the evaluation at least partially with an optimal estimator based on a magnetic field model and the position is either first roughly determined using a neural network and then further refined with the optimal estimator or initially with the The optimal estimator is roughly determined and then refined using a neural network. Arrangement according to Claim 8 , characterized in that at least a subset of the magnetic field sensors (2) are arranged at a distance from one another that is less than twice the characteristic length of the magnetic body (3). Arrangement according to Claim 8 or 9 , characterized in that at least one of the magnetic field sensors (2) is a 3D magnetic field sensor. Arrangement according to Claim 8 or 9 , characterized in that at least three of the magnetic field sensors (2) are magnetic field sensors, each of which can only detect one directional component of the magnetic flux density. Arrangement according to one of the Claims 8 until 11 , characterized in that the magnetic field sensors (2) are arranged monolithically integrated on a sensor substrate. Arrangement according to one of the Claims 8 until 12 , characterized in that the evaluation and measuring device is formed by a processor.

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