DE102023134894A1 - DETERMINING THE POSITION OF A LINEAR OBJECT - Google Patents

Abstract

A method (160) for determining a position of a linear object (170) based on echo information from a vehicle ultrasonic transducer arrangement (140) containing at least one ultrasonic transducer (130) is proposed, which method includes: providing (S3) the echo information describing at least three echo signals, wherein transmission and reception positions of the echo signals are distributed two- or three-dimensionally; and determining (S5, S6, S7) a position of a linear object (170) based on the echo information and an echo-based position determination model of a linear object (170).

Description

The present invention relates to a method for determining the position of a linear object, such as a curb, a handrail, a barrier, and/or a lamppost, based on echo information from a vehicle ultrasonic transducer arrangement containing at least one ultrasonic transducer. Furthermore, the present invention relates to a computer program product, a control device, and a vehicle.

Vehicle ultrasonic transducer arrays are characterized, among other things, by the fact that the individual ultrasonic transducers can receive echo signals in response to transmitted pulses from different ultrasonic transducers and make them available for analysis. However, ultrasonic information describing multiple echo signals typically does not contain an indication of the measured angle at which the respective echo signal was received by the respective receiving ultrasonic transducer. This makes it difficult to determine the position of an object in space.

For example, the JP 2 969 202 B2 A method for recognizing the shape of a three-dimensional object. For this purpose, from a set of distance signals from several distance sensors arranged in a plane, those distance signals that do not correspond to a background distance are selected. The selected distance signals are referenced to a center of gravity of the selected distance signals and thus fed to a neural network to recognize the shape as an outline of a three-dimensional object in a plane.

The KR 101 408 089 B1 discloses a method for determining the position of an object in space using an ultrasonic transducer arrangement. For this purpose, an ultrasonic transducer arrangement is proposed which provides a transmitter and at least three receivers. The position of the object is then determined by means of a propagation time comparison. This patent specification apparently assumes that all echoes emanate from the same reflection point. This only applies to a point-like object. For extended objects, this greatly simplifying assumption generally leads to a non-negligible error in position determination. Furthermore, it is not possible to easily distinguish between point-like and line-like objects, and consequently, information about the position of a line-like object in space is not explicitly available.

The DE 10 2020 121 064 A1 discloses a method for tracking an object in an environment of a vehicle, wherein a plurality of detection points are detected as a point cloud, and wherein the point cloud is evaluated by means of a mathematical model which approximates an object as a polygonal shape.

Against this background, one object of the present invention is to provide means for determining a position of a line-like object on the basis of echo information.

A linear object is understood here to mean, in particular, a curb, a handrail, a barrier and/or a lamppost.

A position of a linear object can, for example, contain or be specified by a position and an orientation or principal axis direction of the linear object. A position of a linear object can, for example, contain or be specified by multiple positions along the linear object.

Accordingly, a method for determining a position of a linear object based on echo information from a vehicle ultrasonic transducer arrangement, which vehicle ultrasonic transducer arrangement contains at least one ultrasonic transducer, is proposed. The proposed method includes: providing echo information that describes at least three echo signals, wherein the transmission and reception positions of the echo signals are distributed two- or three-dimensionally. The proposed method also includes: determining a position of a linear object based on the echo information and an echo-based position determination model of a linear object.

It is therefore proposed to use, provide, and apply a special attitude determination model, or a model specifically designed to determine the position of a linear object from echo information. This allows the position of a linear object to be detected with high accuracy while requiring relatively little computational effort.

The proposed method is preferably a computer-implemented method so that the position of the linear object can be determined frequently and quickly. A computer can preferably be understood as a control device for a vehicle.

The echo information may, in particular, be in the form of a data set and preferably a digital data set, to facilitate interchangeability between different devices or methods.

The echo information may, for example, contain a time series with multiple echo signals. The echo information may, for example, contain multiple time series, each with one echo signal. The echo information may, for example, contain at least one time series, each with one echo signal, and at least one time series, each with multiple echo signals.

Preferably, a transmission position is known for each echo signal, which is a position of a transmitting ultrasonic transducer at the time of transmission of an ultrasonic signal, after which the echo signal is received. Preferably, a reception position is known for each echo signal, which is a position of a receiving ultrasonic transducer at the time of reception of the echo signal.

A linear object can also be understood, for example, as an object whose ultrasonic reflection points have a main axis, where, for example, an extension along the main axis is at least 4 times, preferably at least 8 times, and more preferably at least 12 times an extension perpendicular to the main axis. A linear object can also be understood, for example, as an object whose ultrasonic reflection points are approximately distributed along a straight line in space, where this straight line can be regarded as a first main axis of a reflection point cloud. A linear object can also be understood, for example, as a reflection point cloud in which perpendicular distances between reflection points and the first main axis of the reflection point cloud are less than 10 cm, preferably less than 6 cm, and particularly preferably less than 2 cm. One can also speak, for example, of a characteristic distribution of reflection points influenced by an object geometry of a linear object.

The proposed method may optionally include: providing position information describing the relative positions of the transmitting and receiving positions to one another, in particular—if multiple ultrasonic transducers are present—the relative positions of the ultrasonic transducers of the vehicle ultrasonic transducer arrangement to one another. The proposed method may optionally include: determining the position of the linear object based on the position information. In other words, the proposed method may optionally include: determining the position of the linear object based on the echo information, the position information, and an echo-based attitude determination model for linear objects. By knowing the relative positions of the transmitting and receiving positions precisely, it is possible to determine the position of the linear object.

This proposed method can be reliably implemented, for example, for a stationary vehicle with three ultrasonic transducers in at least a two-dimensional arrangement. This proposed method can be reliably implemented, for example, for a moving vehicle with two ultrasonic transducers. This proposed method can be reliably implemented, for example, for a stationary vehicle with an ultrasonic transducer moving in at least two dimensions, such as an ultrasonic transducer in a moving windshield wiper. This list is not exhaustive. It is therefore a method with broad utility.

The position information, such as a relative position of several ultrasonic transducers of the vehicle or of the vehicle's ultrasonic transducer arrangement, can be included, for example, as a parameter in the attitude determination model. The position information, such as information indicative of vehicle movement between the transmission and reception positions, can be acquired and provided, for example, together with the echo information. Mixed forms are also conceivable, such as a combination of known installation positions and additional vehicle movement. Information indicative of vehicle movement between the transmission and reception positions can, for example, be a vector by which the vehicle has moved between two transmission and reception positions. The method is preferably used for parking operations or the like at a correspondingly low speed, so that vehicle movement between transmitting an ultrasonic wave and receiving a reflection thereof can be negligible.

For ease of availability, the position information may in particular be in the form of a data record, preferably a digital data record.

For example, the proposed method may take the form of: a method for determining a position of a linear object based on echo information from a vehicle ultrasonic transducer arrangement, which vehicle ultrasonic transducer arrangement contains at least two ultrasonic transducers, wherein the proposed method includes: providing echo information describing at least three echo signals, wherein transmission and reception positions of the echo signals are distributed two- or three-dimensionally; and determining a position of a linear object based on the echo information and an echo-based position determination model of a linear object. Thus, a preferred embodiment includes two or more ultrasonic transducers in the ultrasonic transducer arrangement. In this method, the provided echo information preferably describes echo signals received during a journey of a vehicle having the vehicle ultrasonic transducer arrangement. Furthermore, the provided position information preferably contains a relative position of the at least two ultrasonic transducers of the vehicle ultrasonic transducer arrangement to one another, and it is preferably indicative of a relative movement of the journey.

According to a preferred embodiment, the proposed method takes the form of a method for determining a position of a linear object based on echo information from a vehicle ultrasonic transducer arrangement containing at least three ultrasonic transducers, comprising: providing echo information describing at least three echo signals, wherein the transmission and reception positions of the echo signals are distributed two- or three-dimensionally; and determining a position of a linear object based on the echo information and an echo-based position determination model of a linear object. The method may include providing position information describing the relative positions of the ultrasonic transducers to one another; wherein the position of the linear object is also determined based on the position information. This embodiment can be reliably implemented, for example, even with a stationary vehicle or stationary ultrasonic transducers.

The proposed method can optionally include: providing at least one initial position for the linear object. The proposed method can optionally include: repeatedly executing an approximation step, wherein an end position for the linear object is determined in each case based on a starting position for the linear object and the echo information using the position determination model, wherein the initial position is used first as the starting position and the end position of the previous execution is used for each subsequent execution. It has been found that repeatedly executing or applying the position determination model results in a significantly more accurate determination of the position of the linear object. Preferably, three to eight, in particular four to six, initial positions are provided. Preferably, one initial position is provided after the other, and then the approximation step is repeatedly executed. This can be terminated after a position of the linear object has been determined with sufficient quality according to a termination criterion without trying out the remaining initial positions.

The attitude determination model is preferably equation-based or formula-based. The attitude determination model preferably contains an equation or a set of equations that describes at least one linear object based on an echo signal. Thus, one or more equations or formulas can be provided as calculation rules to deterministically and/or comprehensibly determine the position of the linear object.

The term "transmitter-receiver combination" is used below. This refers to a selected combination of a transmitting ultrasonic transducer and a receiving ultrasonic transducer, which can be the same ultrasonic transducer or different ultrasonic transducers. The transmitter-receiver combination can be referred to as a permutation. In other words, a transmitter-receiver combination can define one of the ultrasonic transducers as the transmitting ultrasonic transducer and one of the ultrasonic transducers as the receiving ultrasonic transducer. In other words, the transmitter-receiver combination means, for example, a selection of one ultrasonic transducer of the vehicle ultrasonic transducer arrangement as a transmitting ultrasonic transducer and another or different ultrasonic transducer or the same ultrasonic transducer of the vehicle ultrasonic transducer arrangement as a receiving ultrasonic transducer for subsequent consideration or examination.

In the proposed method, a reflection position or reflection point can be assigned to several, and preferably all, transmitter-receiver combinations. In particular, a reflection position is assigned to all transmitter-receiver combinations considered in the further course of the method. The reflection position can be understood in particular as a position of an ultrasonic reflection of an ultrasonic signal from the transmitting ultrasonic transducer on the linear object to the receiving ultrasonic transducer of the transmitter-receiver combination. The reflection position is in particular a position in three-dimensional space that is located on and/or at the linear object. The reflection position can mean the point to which the strongest echo signal of the transmitter-receiver combination corresponds. The reflection position can mean the point to which the strongest echo signal in a time series of the transmitter-receiver combination corresponds. The reflection position can mean the location corresponding to the strongest echo signal in a time window and/or in a signal strength window of a time series of the transmitter-receiver combination.

In the proposed method, the echo information may identify or designate the transmitting ultrasonic transducer and the receiving ultrasonic transducer for each echo signal. For example, the transmitter-receiver combination may be explicitly specified in a data set of the echo information. For example, the transmitter-receiver combination may result from frequency information and/or time information, which can be extracted from the echo information for the respective echo signal.

In the proposed method, a set of all reflection positions may have a centroid and/or a first principal component. The centroid is, for example, a position in space that corresponds to the arithmetic mean of all reflection position coordinates. The first principal component is, for example, a vector in space for which the sum of the squared perpendicular distances of all reflection positions to this vector is minimal.

In the proposed method, it may optionally be possible for the attitude determination model to contain several equations, formulas, or terms, each of which compares two signal path lengths for a transmitter-receiver combination or specifies a signal path length difference between them. The first of the two signal path lengths is a path length from the transmitting ultrasonic transducer of this transmitter-receiver combination to the reflection position of this transmitter-receiver combination and further to the receiving ultrasonic transducer of this transmitter-receiver combination. The second of the two signal path lengths is a path length based on a propagation time of the echo signal of this transmitter-receiver combination. The second signal path length can be determined, in particular, using an ambient temperature provided to the method. The equations of this option therefore limit the position of the respective reflection position using the signal propagation time between the ultrasonic transducers of the respective transmitter-receiver combination.

In the proposed method, the attitude determination model can optionally contain multiple equations, formulas, or terms, each of which specifies, for a transmitter-receiver combination, a deviation of a) a vector between the center of gravity and the reflection position of the transmitter-receiver combination from b) the first principal component. The equations of this option are therefore suitable for constraining the positions of the respective reflection positions so that they coincide with the first principal component or are as close as possible to and/or on a straight line. These equations can be described as a collinearity requirement.

In the proposed method, it may optionally be possible for the attitude determination model to contain several equations, formulas, or terms, each of which specifies an angular difference between two angles. A first of these two angles is an angle between, on the one hand, a vector from the transmitting ultrasonic transducer of the respective transmitter-receiver combination to the reflection position of the respective transmitter-receiver combination and, on the other hand, the first principal component of the set of reflection positions. A second of these two angles is an angle between, on the one hand, a vector from the reflection position of this transmitter-receiver combination to the receiving ultrasonic transducer of this transmitter-receiver combination and, on the other hand, the first principal component of the set of reflection positions. These equations therefore restrict the positions of the respective reflection positions so that they satisfy the reflection law with respect to the respective transmitter-receiver combination. In other words, it may be required that an angle of incidence of an ultrasonic pulse from the transmitting ultrasonic transducer to the line-like object should be equal to an angle of reflection of an ultrasonic echo from the line-like object to the receiving ultrasonic transducer.

The proposed method can optionally provide for the attitude determination model to be a trained attitude determination model. A trained attitude determination model is preferably trained using a plurality of training data sets to determine the position of a linear object. For example, each training data set contains echo information describing multiple echo signals, as well as a training position. An objective function of the training can be to minimize a difference between the training position of a training data set and a position determined by the attitude determination model based on the echo information of the same training data set.

According to one aspect of the invention, a computer program product is proposed, comprising instructions which, when executed by a computer, cause the computer to carry out the described method for determining the position of a linear object based on echo information from a vehicle ultrasonic transducer arrangement. A computer program product, such as a computer program means, can be provided or delivered, for example, as a storage medium, such as a memory card, USB stick, CD-ROM, DVD, or in the form of a downloadable file from a server in a network. This can be done, for example, in a wireless communications network by transmitting a corresponding file with the computer program product or the computer program means.

According to one aspect of the invention, a control device for a vehicle is proposed, which is configured to carry out the described method for determining the position of a linear object based on echo information from a vehicle ultrasonic transducer arrangement. The embodiments and features described for the proposed method apply accordingly to the proposed control device.

According to one aspect of the invention, a vehicle with a proposed control device is proposed. The vehicle preferably carries or contains the vehicle ultrasonic transducer assembly. The vehicle ultrasonic transducer assembly and the control device are preferably interconnected for data exchange.

Further possible implementations of the invention also include combinations of features or embodiments described above or below with respect to the exemplary embodiments that are not explicitly mentioned. In this case, the person skilled in the art will also add individual aspects as improvements or additions to the respective basic form of the invention.

• 1 zeigt eine schematische Draufsicht auf ein Fahrzeug, das eine Steuervorrichtung hat, die zum Ausführen eines Verfahrens zum Bestimmen einer Lage eines linienartigen Objekts eingerichtet ist, und zwar gemäß einer Ausführungsform der Erfindung;
• 2-4 zeigen in schematischer Weise ein Konvergieren mehrerer beispielhafter Reflexionspositionen zu einem beispielhaften linienartigen Objekt in drei Schritten eines Verfahrens zum Bestimmen einer Lage eines linienartigen Objekts gemäß der Ausführungsform der Erfindung; und
• 5 zeigt in schematischer Weise ein Ablaufdiagramm für das Verfahren zum Bestimmen einer Lage eines linienartigen Objekts gemäß der Ausführungsform der Erfindung.

Further advantageous embodiments and aspects of the invention are the subject of the dependent claims and the exemplary embodiments of the invention described below. The invention will be explained in more detail below using preferred embodiments with reference to the accompanying figures.

• 1 shows a schematic plan view of a vehicle having a control device configured to carry out a method for determining a position of a line-like object, according to an embodiment of the invention;
• 2-4 schematically show a convergence of several exemplary reflection positions to an exemplary line-like object in three steps of a method for determining a position of a line-like object according to the embodiment of the invention; and
• 5 shows schematically a flowchart for the method for determining a position of a line-like object according to the embodiment of the invention.

In the figures, identical or functionally identical elements have been given the same reference numerals unless otherwise stated.

1 shows a schematic view of a vehicle 100 from a bird's eye view. The vehicle 100 is, for example, a car arranged in an environment 150. The car 100 has a control device 110, which can be, for example, part of a parking assistance system. In addition, a plurality of environmental sensor devices 120, 130 are arranged on the car 100, which are, for example, optical sensors 120 and ultrasonic transducers 130 or ultrasonic sensors. The optical sensors 120 comprise, for example, visual cameras, a radar, and/or a lidar. The optical sensors 120 can each capture an image of a respective area from the environment 150 of the car 100 and output it as an optical sensor signal. The ultrasonic transducers 130 are configured to detect a distance to objects arranged in the environment 150 and to output a corresponding sensor signal. By means of the sensor signals detected by the sensors 120, 130, the control device 110 is able to drive the vehicle 100 semi-autonomously or fully autonomously. In addition to the 1 In addition to the optical sensors 120 and ultrasonic transducers 130 shown, the vehicle 100 may be provided with various additional sensor devices 120, 130. Examples of these include a microphone, an acceleration sensor, an antenna with a coupled receiver for receiving electromagnetically transmittable data signals, and the like.

Some of the ultrasonic transducers 130 of the vehicle 100 are combined, for example, to form a vehicle ultrasonic transducer arrangement 140. The ultrasonic transducers 130 of the vehicle ultrasonic transducer arrangement 140 are preferably not all distributed along a single straight line, but rather they are preferably arranged in a two-dimensional plane or, more preferably, spatially distributed in/on the vehicle 100. The vehicle ultrasonic transducer arrangement 140 preferably has only ultrasonic transducers 130 whose detection ranges overlap.

The following is based on the 2 to 5 An embodiment of a method 160 is described that is suitable for determining a position of a line-like object 170 based on (ie, as a function of) echo information from the vehicle ultrasonic transducer arrangement 140, which includes at least one ultrasonic transducer 130. The described method 160 includes optional steps.

In a step S1, a check is performed to determine whether the speed of vehicle 100 does not exceed a speed threshold. The threshold may, for example, be up to 50 km/h and preferably up to 35 km/h. If vehicle 100 is traveling too fast, method 160 is preferably not executed further.

In a next step S2, echo information describing at least part of the environment 150 is acquired by means of the ultrasonic transducers 130 of the vehicle ultrasonic transducer arrangement 140. In a step S3, this echo information is provided. The echo information is in the form of a digital data set, for example. The echo information describes a plurality of echo signals. An echo signal can be understood as an ultrasonic echo indicating a reflection. For example, the echo information for each of the ultrasonic transducers 130 contains a time series of an ultrasonic level, wherein individual echo signals can be derived or read out from the time series. For example, the echo information contains a plurality of echo signals, each of which is identified by time information, such as a timestamp or a propagation time.

Each echo signal is uniquely assigned to a transmitting ultrasonic transducer 130 and a receiving ultrasonic transducer 130. The transmitting ultrasonic transducer 130 and the receiving ultrasonic transducer 130 form a transmitter-receiver combination. These can be different ultrasonic transducers 130 or the same ultrasonic transducer 130.

In a next step S4, position information is provided. For example, the position information is read from a memory after starting the vehicle 100 or the control device 110 and/or at periodic intervals. The position information can be provided as a data set, in particular as a digital data set.

In a next step S5, a position of the line-like object 170 is determined based on the echo information and an echo-based position determination model of a line-like object 170.

The derivation of the exemplary location determination model is described below. This derivation is intended to facilitate understanding.

"k" ultrasonic transducers 130 are considered for the attitude determination model. Preferably, all ultrasonic transducers 130 of the vehicle ultrasonic transducer array 140 are considered.

$${\text{S}}^{\text{T}}={\left(\begin{array}{ccc}{\text{S}}_1^{\text{T}}& \cdots & {\text{S}}_{\text{k}}^{\text{T}}\end{array}\right)}_{1\times 3\text{k}}$$

Thus, there are k relative positions S _i of the ultrasonic transducers 130 to each other or within a vehicle's own coordinate system, wherein each relative position S _i is preferably defined by three Cartesian coordinates x _i , y _i , z _i : $${\text{S}}_{\text{i}}^{\text{T}}=\left(\begin{array}{ccc}{\text{x}}_{\text{i}}& {\text{y}}_{\text{i}}& {\text{z}}_{\text{i}}\end{array}\right);\text{ i}=1\dots \text{k}$$

$${\text{S}}^{\text{T}}={\left(\begin{array}{ccc}{\text{S}}_1^{\text{T}}& \cdots & {\text{S}}_{\text{k}}^{\text{T}}\end{array}\right)}_{1\times 3\text{k}}$$

$${\text{p}}^{\text{T}}={\left(\begin{array}{cccccccccc}{\text{p}}_{\mathrm{1,1}}{}^{\text{T}}& {\text{p}}_{\mathrm{1,2}}{}^{\text{T}}& \cdots & {\text{p}}_{\mathrm{1,}\text{k}}{}^{\text{T}}& {\text{p}}_{\mathrm{2,1}}{}^{\text{T}}& {\text{p}}_{\mathrm{2,2}}{}^{\text{T}}& \cdots & {\text{p}}_{\mathrm{2,}\text{k}}{}^{\text{T}}& \cdots & {\text{p}}_{\text{k},\text{k}}{}^{\text{T}}\end{array}\right)}_{1\times 3{\text{k}}^2}$$

All transmitter-receiver combinations of the ultrasonic transducers 130 under consideration are considered. Including the identity, k ² transmitter-receiver combinations are thus possible. For each transmitter-receiver combination, a reflection position p _i,j or a reflection point is considered, where "i" denotes the transmitter 130 and "j" the receiver 130: $${\text{p}}_{\text{i},\text{j}}{}^{\text{T}}=\left(\begin{array}{ccc}{\text{x}}_{{\text{p}}_{\text{i},\text{j}}}& {\text{y}}_{{\text{p}}_{\text{i},\text{j}}}& {\text{z}}_{{\text{p}}_{\text{i},\text{j}}}\end{array}\right);\text{ i}=1\dots \text{k},\text{j}=1\dots \text{k}$$

$${\text{p}}^{\text{T}}={\left(\begin{array}{cccccccccc}{\text{p}}_{\mathrm{1,1}}{}^{\text{T}}& {\text{p}}_{\mathrm{1,2}}{}^{\text{T}}& \cdots & {\text{p}}_{\mathrm{1,}\text{k}}{}^{\text{T}}& {\text{p}}_{\mathrm{2,1}}{}^{\text{T}}& {\text{p}}_{\mathrm{2,2}}{}^{\text{T}}& \cdots & {\text{p}}_{\mathrm{2,}\text{k}}{}^{\text{T}}& \cdots & {\text{p}}_{\text{k},\text{k}}{}^{\text{T}}\end{array}\right)}_{1\times 3{\text{k}}^2}$$

The totality or set p ^T of reflection positions p _i,j can be understood as a point cloud or reflection point cloud.

$${\text{w}}^{\text{T}}={\left(\begin{array}{cccccccccc}{\text{w}}_{\mathrm{1,1}}& {\text{w}}_{\mathrm{1,2}}& \cdots & {\text{w}}_{\mathrm{1,}\text{k}}& {\text{w}}_{\mathrm{2,1}}& {\text{w}}_{\mathrm{2,2}}& \cdots & {\text{w}}_{\mathrm{2,}\text{k}}& \cdots & {\text{w}}_{\text{k},\text{k}}\end{array}\right)}_{1\times {\text{k}}^2}$$

From the echo information, a path length w _i,j can be determined for each echo signal based on a transit time TOF of the echo signal of this transmitter-receiver combination and preferably an ambient air temperature ϑ: $${\text{w}}_{\text{i},\text{j}}=\text{f}\left({\text{TOF}}_{{\text{s}}_{\text{i}},{\text{p}}_{\text{i},\text{j}},{\text{s}}_{\text{j}}},\mathrm{\vartheta }\right);\text{ i}=1\dots \text{k},\text{j}=1\dots \text{k}$$

$${\text{w}}^{\text{T}}={\left(\begin{array}{cccccccccc}{\text{w}}_{\mathrm{1,1}}& {\text{w}}_{\mathrm{1,2}}& \cdots & {\text{w}}_{\mathrm{1,}\text{k}}& {\text{w}}_{\mathrm{2,1}}& {\text{w}}_{\mathrm{2,2}}& \cdots & {\text{w}}_{\mathrm{2,}\text{k}}& \cdots & {\text{w}}_{\text{k},\text{k}}\end{array}\right)}_{1\times {\text{k}}^2}$$

The set or totality of reflection points p _i,j has a center of gravity p : $$\overline{\text{p}}=\frac{1}{{\text{k}}^2}{\displaystyle \sum _{\text{i}=1}^{\text{k}}{\displaystyle \sum _{\text{j}=1}^{\text{k}}{\text{p}}_{\text{i},\text{j}}}}$$

$$\text{p}*=\left(\begin{array}{c}{\text{p}}_{\mathrm{1,1}}{*}^{\text{T}}\\ {\text{p}}_{\mathrm{1,2}}{*}^{\text{T}}\\ ⋮\\ {\text{p}}_{\text{k},\text{k}}{*}^{\text{T}}\end{array}\right)={\left(\begin{array}{ccc}{\text{x}}_{{\text{p}}_{\mathrm{1,1}}}*& {\text{y}}_{{\text{p}}_{\mathrm{1,1}}}*& {\text{z}}_{{\text{p}}_{\mathrm{1,1}}}*\\ {\text{x}}_{{\text{p}}_{\mathrm{1,2}}}*& {\text{y}}_{{\text{p}}_{\mathrm{1,2}}}*& {\text{z}}_{{\text{p}}_{\mathrm{1,2}}}*\\ ⋮& ⋮& ⋮\\ {\text{x}}_{{\text{p}}_{\text{k},\text{k}}}*& {\text{y}}_{{\text{p}}_{\text{k},\text{k}}}*& {\text{z}}_{{\text{p}}_{\text{k},\text{k}}}*\end{array}\right)}_{{\text{k}}^2\times 3}$$

By means of the center of gravity p of the reflection points p _{i,j ,} reflection points p _i,j * centered on the center of gravity and a correspondingly centered reflection point cloud p* can be determined: $${\text{p}}_{\text{i},\text{j}}*={\text{p}}_{\text{i},\text{j}}-\overline{\text{p}};\text{ i}=1\dots \text{k},\text{j}=1\dots \text{k}$$

$$\text{p}*=\left(\begin{array}{c}{\text{p}}_{\mathrm{1,1}}{*}^{\text{T}}\\ {\text{p}}_{\mathrm{1,2}}{*}^{\text{T}}\\ ⋮\\ {\text{p}}_{\text{k},\text{k}}{*}^{\text{T}}\end{array}\right)={\left(\begin{array}{ccc}{\text{x}}_{{\text{p}}_{\mathrm{1,1}}}*& {\text{y}}_{{\text{p}}_{\mathrm{1,1}}}*& {\text{z}}_{{\text{p}}_{\mathrm{1,1}}}*\\ {\text{x}}_{{\text{p}}_{\mathrm{1,2}}}*& {\text{y}}_{{\text{p}}_{\mathrm{1,2}}}*& {\text{z}}_{{\text{p}}_{\mathrm{1,2}}}*\\ ⋮& ⋮& ⋮\\ {\text{x}}_{{\text{p}}_{\text{k},\text{k}}}*& {\text{y}}_{{\text{p}}_{\text{k},\text{k}}}*& {\text{z}}_{{\text{p}}_{\text{k},\text{k}}}*\end{array}\right)}_{{\text{k}}^2\times 3}$$

In the following, a principal component analysis is performed using singular value decomposition. The matrix p* is factorized: $$\text{p}{*}_{{\text{k}}^2\times 3}={\text{U}}_{{\text{k}}^2\times 3}*{\text{S}}_{3\times 3}*{\text{V}}^{\text{T}}{}_{3\times 3}$$

$${\text{d}}_{{\text{PC1}}_{\text{n}}}=\frac{{\text{d}}_{\text{PC}1}}{\left|{\text{d}}_{\text{PC}1}\right|}=\left(\begin{array}{c}{\text{d}}_{\text{PC}{1}_{\text{n}1}}\\ {\text{d}}_{\text{PC}{1}_{\text{n}2}}\\ {\text{d}}_{\text{PC}{1}_{\text{n}3}}\end{array}\right)$$

From the matrix V, one can determine or extract a direction vector d _PC1 of the 1st principal component of the reflection points p _i,j and then form it into a normalized direction vector d _PC1n : $${\text{d}}_{\text{PC}{1}_{3\times 1}}={\text{V}}_{3\times 3}*{\text{e}}_{1_{3\times 1}}{\text{ mit e}}_1{}^{\text{T}}=\left(\begin{array}{ccc}1& 0& 0\end{array}\right)$$

$${\text{d}}_{{\text{PC1}}_{\text{n}}}=\frac{{\text{d}}_{\text{PC}1}}{\left|{\text{d}}_{\text{PC}1}\right|}=\left(\begin{array}{c}{\text{d}}_{\text{PC}{1}_{\text{n}1}}\\ {\text{d}}_{\text{PC}{1}_{\text{n}2}}\\ {\text{d}}_{\text{PC}{1}_{\text{n}3}}\end{array}\right)$$

Thus, a principal line p _PC1 of the reflection points p _i,j can be drawn through the corresponding center of gravity p determined or formed: $${\text{p}}_{\text{PC1}}=\overline{\text{p}}+\text{s}\ast {\text{d}}_{\text{PC}{1}_{\text{n}}}$$

This straight line in parametric form with its position vector p , the direction vector d _{Pc1 n} and the parameter s represents a potentially detected line-like object.

In this embodiment, a set of a total of ^5k2 system equations is formulated.

$$\begin{array}{c}⋮\\ f_{2k}\left(p\right)=\left|p_{\mathrm{2,}k}-S_2\right|+\left|S_k-p_{\mathrm{2,}k}\right|-w_{\mathrm{2,}k}\\ ⋮\\ f_{k^2-\left(k-1\right)}\left(p\right)=\left|p_{k\mathrm{,1}}-S_k\right|+\left|S_1-p_{k\mathrm{,1}}\right|-w_{k\mathrm{,1}}\\ ⋮\\ f_{k^2}\left(p\right)=\left|p_{k,k}-S_k\right|+\left|S_k-p_{k,k}\right|-w_{k,k}\end{array}$$

For example, the attitude determination model contains several equations, each of which specifies for a transmitter-receiver combination a difference between a) a path length from the transmitting ultrasonic transducer 130 to the reflection position p of this transmitter-receiver combination and further to the receiving ultrasonic transducer 130 and b) a path length based on a travel time of the echo signal of this transmitter-receiver combination: $$\begin{array}{c}{\text{f}}_1\left(\text{p}\right)=\left|{\text{p}}_{\mathrm{1,1}}-{\text{S}}_1\right|+\left|{\text{S}}_1-{\text{p}}_{\mathrm{1,1}}\right|-{\text{w}}_{\mathrm{1,1}}\\ ⋮\\ {\text{f}}_{\text{k}}\left(\text{p}\right)=\left|{\text{p}}_{\mathrm{1,}\text{k}}-{\text{S}}_1\right|+\left|{\text{S}}_{\text{k}}-{\text{p}}_{\mathrm{1,}\text{k}}\right|-{\text{w}}_{\mathrm{1,}\text{k}}\\ {\text{f}}_{\text{k}+1}\left(\text{p}\right)=\left|{\text{p}}_{\mathrm{2,1}}-{\text{S}}_2\right|+\left|{\text{S}}_1-{\text{p}}_{\mathrm{2,1}}\right|-{\text{w}}_{\mathrm{2,1}}\end{array}$$

$$\begin{array}{c}⋮\\ f_{2k}\left(p\right)=\left|p_{\mathrm{2,}k}-S_2\right|+\left|S_k-p_{\mathrm{2,}k}\right|-w_{\mathrm{2,}k}\\ ⋮\\ f_{k^2-\left(k-1\right)}\left(p\right)=\left|p_{k\mathrm{,1}}-S_k\right|+\left|S_1-p_{k\mathrm{,1}}\right|-w_{k\mathrm{,1}}\\ ⋮\\ f_{k^2}\left(p\right)=\left|p_{k,k}-S_k\right|+\left|S_k-p_{k,k}\right|-w_{k,k}\end{array}$$

For example, the attitude determination model contains several equations, each of which determines for a transmitter-receiver combination a deviation a) of a vector between the center of gravity p and the reflection position p _i,j of the transmitter-receiver combination to b) the 1st principal component d _PC1 : $$\begin{array}{c}{\text{d}}_{{\text{p}}_{\text{i}\text{,j}}}=\left|\left({\text{p}}_{\text{i},\text{j}}-\overline{\text{p}}\right)\times {\text{d}}_{\text{Pc}{1}_{\text{n}}}\right|=\left|{\text{p}}_{\text{i},\text{j}}{}^{*}\times {\text{d}}_{\text{PC}{1}_{\text{n}}}\right|\stackrel{!}{{\displaystyle =}}0\\ \\ \begin{array}{ccc}\begin{array}{c}{\text{f}}_{{\text{k}}^2+1}\left(\text{p}\right)={\text{y}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}3}}-{\text{z}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}2}}\\ {\text{f}}_{{\text{k}}^2+2}\left(\text{p}\right)={\text{z}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}1}}-{\text{x}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}3}}\\ {\text{f}}_{{\text{k}}^2+3}\left(\text{p}\right)={\text{x}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}2}}-{\text{y}}_{{\text{p}}_{\mathrm{1,1}}}*{\text{d}}_{\text{PC}{1}_{\text{n}1}}\end{array}& \iff & \left|{\text{p}}_{\mathrm{1,1}}{}^{*}\times {\text{d}}_{\text{PC}{1}_{\text{n}}}\right|=0\\ \begin{array}{c}{\text{f}}_{{\text{k}}^2+4}\left(\text{p}\right)={\text{y}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n}3}}-{\text{z}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n}2}}\\ {\text{f}}_{{\text{k}}^2+5}\left(\text{p}\right)={\text{z}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n1}}}-{\text{x}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n3}}}\\ {\text{f}}_{{\text{k}}^2+6}\left(\text{p}\right)={\text{x}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n2}}}-{\text{y}}_{{\text{p}}_{\mathrm{1,2}}}*{\text{d}}_{\text{PC}{1}_{\text{n1}}}\end{array}& \iff & \left|{\text{p}}_{\mathrm{1,2}}{}^{*}\times {\text{d}}_{\text{PC}{1}_{\text{n}}}\right|=0\\ ⋮& & \\ \begin{array}{c}{\text{f}}_{4{\text{k}}^2-2}\left(\text{p}\right)={\text{y}}_{\text{Pk}\text{,k}}*{\text{d}}_{\text{PC}{1}_{\text{n}3}}-{\text{z}}_{\text{Pk},\text{k}}*{\text{d}}_{{\text{PC1}}_{\text{n2}}}\\ {\text{f}}_{4{\text{k}}^2-1}\left(\text{p}\right)={\text{z}}_{\text{Pk}\text{,k}}*{\text{d}}_{\text{PC}{1}_{\text{n1}}}-{\text{x}}_{\text{Pk},\text{k}}*{\text{d}}_{{\text{PC1}}_{\text{n3}}}\\ {\text{f}}_{4{\text{k}}^2}\left(\text{p}\right)={\text{x}}_{\text{Pk}\text{,k}}*{\text{d}}_{\text{PC}{1}_{\text{n}2}}-{\text{y}}_{\text{Pk},\text{k}}*{\text{d}}_{{\text{PC1}}_{\text{n1}}}\end{array}& \iff & \left|{\text{p}}_{\text{k}\text{,k}}*\times {\text{d}}_{\text{PC}{1}_{\text{n}}}\right|=0\end{array}\end{array}$$

For example, the terms f _{k 2 +1} (p), f _{k 2 +2} (P) and f _{k 2 +3} (P) a group of terms which together represent a deviation of the vector between the center of gravity p and the reflection position p _1,1 on the one hand and the 1st principal component d _PC1 on the other hand. In other words, this group of terms gives the vector product or cross product of the vector between the center of gravity p and the reflection position p _1,1 with the 1st principal component d _PC1 .

For example, the attitude determination model contains several equations, each specifying an angular difference between a) an angle between a1) a vector from the transmitting ultrasonic transducer to the reflection position and a2) the 1st principal component and b) an angle between b1) a vector from the reflection position to the receiving ultrasonic transducer and b2) the 1st principal component: $$\begin{array}{c}{\text{f}}_{4{\text{k}}^2+1}\left(\text{p}\right)=\frac{{\text{p}}_{\mathrm{1,1}}-{\text{S}}_1}{\left|{\text{p}}_{\mathrm{1,1}}-{\text{S}}_1\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}-\frac{{\text{S}}_1-{\text{p}}_{\mathrm{1,1}}}{\left|{\text{S}}_1-{\text{p}}_{\mathrm{1,1}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\\ ⋮\\ {\text{f}}_{4{\text{k}}^2+\text{k}}\left(\text{p}\right)=\frac{{\text{p}}_{\mathrm{1,}\text{k}}-{\text{S}}_1}{\left|{\text{p}}_{\mathrm{1,}\text{k}}-{\text{S}}_1\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}-\frac{{\text{S}}_{\text{k}}-{\text{p}}_{\mathrm{1,}\text{k}}}{\left|{\text{S}}_{\text{k}}-{\text{p}}_{\mathrm{1,}\text{k}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\\ {\text{f}}_{4{\text{k}}^2+\text{k}+1}\left(\text{p}\right)=\frac{{\text{p}}_{\mathrm{2,1}}-{\text{S}}_2}{\left|{\text{p}}_{\mathrm{2,1}}-{\text{S}}_2\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}-\frac{{\text{S}}_1-{\text{p}}_{\mathrm{2,1}}}{\left|{\text{S}}_1-{\text{p}}_{\mathrm{2,1}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\\ ⋮\\ {\text{f}}_{4{\text{k}}^2+2\text{k}}\left(\text{p}\right)=\frac{{\text{p}}_{\mathrm{2,}\text{k}}-{\text{S}}_2}{\left|{\text{p}}_{\mathrm{2,}\text{k}}-{\text{S}}_2\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}-\frac{{\text{S}}_{\text{k}}-{\text{p}}_{\text{2}\text{,k}}}{\left|{\text{S}}_{\text{k}}-{\text{p}}_{\mathrm{2,}\text{k}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\\ ⋮\\ {\text{f}}_{5{\text{k}}^2-\left(\text{k}-1\right)}\left(\text{p}\right)=\frac{{\text{p}}_{\text{k}\mathrm{,1}}-{\text{S}}_{\text{k}}}{\left|{\text{p}}_{\text{k}\mathrm{,1}}-{\text{S}}_{\text{k}}\right|}\cdot {\text{d}}_{{\text{PC1}}_{\text{n}}}-\frac{{\text{S}}_1-{\text{p}}_{\text{k}\text{,1}}}{\left|{\text{S}}_1-{\text{p}}_{\text{k}\mathrm{,1}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\\ {\text{f}}_{5{\text{k}}^2\left(\text{p}\right)}=\frac{{\text{p}}_{\text{k}\text{,k}}-{\text{S}}_{\text{k}}}{\left|{\text{p}}_{\text{k},\text{k}}-{\text{S}}_{\text{k}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}-\frac{{\text{S}}_{\text{k}}-{\text{p}}_{\text{k},\text{k}}}{\left|{\text{S}}_{\text{k}}-{\text{p}}_{\text{k}\text{,k}}\right|}\cdot {\text{d}}_{\text{PC}{1}_{\text{n}}}\end{array}$$

What the above equations have in common is that under ideal conditions, they become zero if the calculated reflection positions p correspond to the actual reflection positions p on/at the linear object 170. Under real conditions, they will approach zero. These equations therefore together form a zero-point problem.

Step S5 has substeps S6 and S7. In step S6, at least one initial position for the linear object 170 is provided. In step S7, an end position for the linear object is determined based on a starting position for the linear object 170, the echo information, and the position information using the position determination model. Step S7 is an approximation step and is repeatedly executed. When the approximation step is executed for the first time, the initial position provided in S6 is used as the starting position. During each subsequent execution of step S7, the end position of the previous execution of step S7 is used.

$${\text{p}}_{\text{n}+1}={\text{p}}_{\text{n}}+{\mathrm{\lambda }}_{\text{n}}\Delta {\text{p}}_{\text{n}}$$

For example, step S7 may include a damped Gauss-Newton method for numerically solving the above equations: $$\text{J}{\left({\text{p}}_{\text{n}}\right)}^{\text{T}}\text{J}\left({\text{p}}_{\text{n}}\right)\Delta {\text{p}}_{\text{n}}=-\text{J}{\left({\text{p}}_{\text{n}}\right)}^{\text{T}}\text{f}\left({\text{p}}_{\text{n}}\right)$$

$${\text{p}}_{\text{n}+1}={\text{p}}_{\text{n}}+{\mathrm{\lambda }}_{\text{n}}\Delta {\text{p}}_{\text{n}}$$

A person skilled in the art chooses the value λ _n according to a damping strategy such that λ _min < λ _n < 1 is satisfied. The Jacobian matrix J(p) is generated, for example, according to the equations described above: $$\text{J}\left(\text{p}\right):={\left(\begin{array}{ccc}\frac{\partial {\text{f}}_1}{\partial {\text{x}}_{\text{p}\mathrm{1,1}}}& \cdots & \frac{\partial {\text{f}}_1}{\partial {\text{z}}_{\text{Pk}\text{,k}}}\\ ⋮& \ddots & ⋮\\ \frac{\partial {\text{f}}_{5{\text{k}}^2}}{\partial {\text{x}}_{{\text{p}}_{\mathrm{1,1}}}}& \cdots & \frac{\partial {\text{f}}_{5{\text{k}}^2}}{\partial {\text{Z}}_{\text{Pk}\text{,k}}}\end{array}\right)}_{5{\text{k}}^2\times 3{\text{k}}^2}$$

In other words, in step S7, for each position value x _{p i,j} ) y _{p i,j} and z _{p i,j} each of the reflection positions p _i,j a solution is approximated for which the terms f ₁ (p) up to _{5k 2} (p) are to be as close as possible to zero. In other words, the zeros of the system of equations are to be approximated, which contains the equations f ₁ (p) to f _{5k 2} (p) contains.

After each execution of an approximation step of the Gauss-Newton method, the fulfillment of a termination condition is checked. If a termination condition is fulfilled, the approximation step is not executed again. A termination condition can be fulfilled, for example, if the reflection points p ^T are no further than a predetermined threshold value from a common main axis according to the last end position. A termination condition can be fulfilled, for example, if the end position has not changed by at least a certain degree of accuracy between the last two executions. A termination condition can be fulfilled, for example, if a computing time threshold is exceeded during step S5. A termination condition can be fulfilled, for example, if a maximum number of executions of the approximation step is reached. Many numerical approximation methods can be used in step S7, and these may require further termination conditions that can be applied by a person skilled in the art.

In the 2 to 4 An exemplary scenario is shown, wherein a position of the line-like object 170 is determined. All three figures show the positions of four ultrasonic transducers 130 of a vehicle ultrasonic transducer arrangement 140. All four ultrasonic transducers 130 serve alternately as transmitting ultrasonic transducers 130 and as receiving ultrasonic transducers 130, so that the indicated line-like object 170 reflects, for example, 16 ultrasonic echoes, which thus correspond to 16 reflection points p. Furthermore, the position of the line-like object 170 is shown for better clarity. 2 shows a position of the reflection points after the first execution of step S7, the 3 shows the position after the second execution of step S7, and the 4 shows the situation after the third and final execution of step S7. The reflection points p _i,j are shown as diamonds. It should be noted that in the 2 to 4 multiple reflection points overlap in the drawing projection. After the third execution of step S7, the position of the line-like object 170 is known with high precision, and therefore step S5 is aborted or terminated.

Finally, the final position of the linear object 170 determined in the last executed step S7 is output as the position of the linear object 170 in a step S8. For example, the position of the linear object 170 can be output, provided, and/or stored as a digital data set.

The position of the linear object 170 to be output can, for example, be or contain the determined reflection points p ^T. The position of the linear object 170 to be output can, for example, be or contain the first principal component p _PC1 based on the determined reflection points p ^T. By deliberately varying the parameter s in the associated straight line equation p _PC1 = p + s ∗ d _{PC1 n} If necessary, additional points lying on the straight line can be calculated in addition to the reflection points already calculated.

Although the present invention has been described using exemplary embodiments, it can be modified in many ways.

LIST OF REFERENCE SYMBOLS

100

vehicle

110

Control device

120

optical sensor

130

Ultrasonic transducer

140

Vehicle ultrasonic transducer assembly

150

Vicinity

160

Method for determining a position of a line-like object based on echo information from a vehicle ultrasonic transducer arrangement containing at least one ultrasonic transducer

170

linear object

S1

Check whether a vehicle speed does not exceed a speed threshold

S2

Acquiring echo information describing at least part of the environment by means of the ultrasonic transducers of the vehicle ultrasonic transducer arrangement

S3

Providing echo information containing multiple echo signals

S4

Providing position information

S5

Determining a position of a line-like object based on the echo information and an echo-based position determination model of a line-like object

S6

Providing at least one initial position for the linear object

S7

Repeatedly executing an approximation step, whereby an end position for the line-like object is determined on the basis of a starting position for the line-like object and the echo information by means of the position determination model, whereby the initial position is used first as the starting position and the end position of the previous execution is used for each subsequent execution

S8

Output the position of the line-like object

QUOTES CONTAINED IN THE DESCRIPTION

This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• JP 2 969 202 B2 [0003]
• KR 101 408 089 B1 [0004]
• DE 10 2020 121 064 A1 [0005]

Claims (12)

A method (160) for determining a position of a linear object (170) based on echo information from a vehicle ultrasonic transducer arrangement (140) containing at least one ultrasonic transducer (130), comprising: providing (S3) the echo information describing at least three echo signals, wherein the transmit and receive positions of the echo signals are distributed two- or three-dimensionally; and determining (S5, S6, S7) a position of a linear object (170) based on the echo information and an echo-based position determination model of a linear object (170). Procedure according to Claim 1 , characterized in that the method includes: providing (S4) position information which describes relative positions (S _i ) of the transmitting and receiving positions to one another; wherein the position of the linear object (170) is also determined on the basis of the position information. Procedure according to Claim 1 or 2 , characterized in that the vehicle ultrasonic transducer arrangement (140) contains at least two ultrasonic transducers (130), wherein the provided (S3) echo information describes echo signals which are received during a journey of a vehicle (100) of the vehicle ultrasonic transducer arrangement (140); and wherein preferably the provided (S4) position information contains a relative position of the at least two ultrasonic transducers (130) of the vehicle ultrasonic transducer arrangement (140) to one another and is indicative of a relative movement of the journey. Method according to one of the Claims 2 until 3 , characterized in that the vehicle ultrasonic transducer arrangement (140) contains at least three ultrasonic transducers (130); wherein the provided (S4) position information preferably describes relative positions (S _i ) of the ultrasonic transducers (130) of the vehicle ultrasonic transducer arrangement (140) to one another. Method according to one of the preceding claims, characterized in that determining (S5) the position includes: providing (S6) at least one initial position for the linear object (170); and repeatedly carrying out (S7) an approximation step, wherein in each case on the basis of a starting position for the linear object (170) and the echo information, an end position for the linear object (170) is determined by means of the position determination model, wherein the initial position is used first as the starting position and the end position of the previous execution is used for each further execution. Method according to one of the preceding claims, characterized in that the attitude determination model is equation-based. Procedure according to Claim 6 , characterized in that a transmitter-receiver combination (130, 130) contains a transmitting ultrasonic transducer (130) and a receiving ultrasonic transducer (130), which can be the same ultrasonic transducer (130) or different ultrasonic transducers (130); several and preferably all transmitter-receiver combinations (130, 130) are each assigned a reflection position (p _i,j ); the echo information for each echo signal identifies the transmitting ultrasonic transducer (130) and the receiving ultrasonic transducer (130); and the attitude determination model comprises several equations (f ₁ (p) to f _{k 2} (p)) which each indicate, for a transmitter-receiver combination (130, 130), a difference between a) a path length from the transmitting ultrasonic transducer (130) to the reflection position (p _i,j ) of this transmitter-receiver combination (130, 130) and further to the receiving ultrasonic transducer (130) and b) a path length based on a propagation time of the echo signal of this transmitter-receiver combination (130, 130). Procedure according to Claim 6 or 7 , characterized in that : a transmitter-receiver combination (130, 130) contains a transmitting ultrasonic transducer (130) and a receiving ultrasonic transducer (130), which can be the same ultrasonic transducer (130) or different ultrasonic transducers (130); several and preferably all transmitter-receiver combinations (130, 130) are each assigned a reflection position (p _i,j ); a set of all reflection positions (p _i,j ) has a center of gravity ( p ) and a 1st principal component (p _PC1 ); and the attitude determination model has several equations (f _{k 2 +1} (p) to f _{4k 2} (p)) or groups of equations, each of which, for a transmitter-receiver combination (130, 130), determines a deviation a) of a vector between the center of gravity ( p ) and the reflection position (p _i,j ) of the transmitter-receiver combination (130, 130) to b) the 1st principal component (p _PC1 ). Method according to one of the Claims 6 until 8 , characterized in that a transmitter-receiver combination (130, 130) contains a transmitting ultrasonic transducer (130) and a receiving ultrasonic transducer (130), which can be the same ultrasonic transducer (130) or different ultrasonic transducers (130); several and preferably all transmitter-receiver combinations (130, 130) are each assigned a reflection position (p _i,j ); a set of all reflection positions (p _i,j ) has a first principal component (p _PC1 ); and the attitude determination model has several equations (f _{4k 2 +1} (p) to f _{5k 2} (p)) or groups of equations which each form, for a transmitter-receiver combination (130, 130), an angular difference between a) an angle between a1) a vector from the transmitting ultrasonic transducer (130) to the reflection position (p _i,j ) and a2) the 1st principal component (p _PC1 ) and b) an angle between b1) a vector from the reflection position (p _i,j ) to the receiving ultrasonic transducer (130) and b2) the 1st principal component (p _PC1 ). Computer program product, comprising instructions which, when executed by a computer, cause the computer to carry out the method (160) for determining a position of a line-like object (170) on the basis of echo information from a vehicle ultrasonic transducer arrangement (140) according to one of the Claims 1 - 9 to execute. Control device (110) for a vehicle (100), which is configured to implement the method (160) for determining a position of a line-like object (170) on the basis of echo information of a vehicle ultrasonic transducer arrangement (140) according to one of the Claims 1 - 9 and/or the computer program product according to Claim 10 to execute. Vehicle (100) with a control device (110) according to Claim 11 .

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