DE102020214403A1 - Method and device for determining object coordinates of an object - Google Patents

Abstract

The present invention relates to a method for determining object coordinates (112) of an object (200), wherein from a group of measurements (400), including direct measurements (106), each a coordinate of a transceiver (211) of the direct measurement (106) and a direct measurement distance (210) from the transceiver (211) to the object (200), and indirect measurements (108), each containing a transmitter coordinate of a transmitter (204) of the indirect measurement (108), a receiver coordinate of a receiver (208) of the indirect measurement (108) and an indirect measurement distance (210) from the transmitter (204) to the object (200) and from the object (200) to the receiver (208), the direct measurements (106) are used to calculate an estimated area (110) of the object (200), the estimated area (110) identifying an area in which the object (200) is likely to be located, the estimated area (110) using the direct measurements (106) and the indirect me ssungen (108) is numerically optimized, and the object coordinates (112) are determined taking into account the optimized estimation range.

Description

field of invention

The invention relates to a method for determining object coordinates of an object and a corresponding device.

State of the art

A sensor in the form of a distance sensor, for example an ultrasonic sensor or a radar sensor, emits a signal that can be reflected on an object within a detection range of the sensor and can be received again as an echo by the sensor or another sensor. A distance that the signal and the echo have traveled together can be determined from a transit time between the sending and the receiving.

In a direct measurement, i.e. when the signal and the echo are sent and received by the same sensor, a distance between the sensor and the object corresponds to half the distance. In a two-dimensional view, the object is then located on a circle whose center is the sensor and whose radius corresponds to the distance.

In the case of an indirect measurement, i.e. if the signal was sent by a different sensor than the one from which the echo was received, the object is located on an ellipse around the sensors when viewed two-dimensionally. The sensors are each arranged in the focal points of the ellipse.

At least two measurements are used to locate the object. A lateration problem is solved for the localization.

Disclosure of Invention

Against this background, with the approach presented here, a method for determining object coordinates of an object and a corresponding device, and finally a corresponding computer program product and a machine-readable storage medium are presented according to the independent claims. Advantageous developments and improvements of the approach presented here result from the description and are described in the dependent claims.

Advantages of the Invention

Advantageously, embodiments of the present invention may allow an approximate position of an object to be determined quickly. The approximated position can then be determined more precisely in a second step. As a result, the refined search can take place within a limited space and can thus be carried out with a limited computing capacity.

A method for determining object coordinates of an object is proposed, from a group of measurements comprising direct measurements, each comprising a coordinate of a transceiver of the direct measurement and a direct measurement distance from the transceiver to the object and from the object to the transceiver, and indirect Measurements each comprising a transmitter coordinate of a transmitter of the indirect measurement, a receiver coordinate of a receiver of the indirect measurement and an indirect measurement distance from the transmitter to the object and from the object to the receiver, the direct measurements are used to calculate an estimated range of the object, where the estimated area identifies an area in which the object is likely to be located, the estimated area being numerically optimized using the direct measurements and the indirect measurements, and the object coordinates being determined taking the optimized estimated area into account.

Ideas for embodiments of the present invention can be regarded as being based, among other things, on the ideas and findings described below.

In a two-dimensional view, object coordinates can include at least one pair of values from a first coordinate and a second coordinate. The object coordinates can be determined relative to a sensor arrangement. The sensor arrangement can be installed on a vehicle, for example. The first coordinate can identify an x-direction of the vehicle, for example. The second coordinate can identify a y-direction of the vehicle, for example. The sensor arrangement can comprise a plurality of individual sensors. The sensors can have different measuring principles or a uniform measuring principle. The sensors can be distance sensors. For example, the sensors can be ultrasonic sensors.

A direct measurement can be performed by a single transceiver of the sensor array. The transceiver emits a signal and receives a result from an object echo. The direct measurement may include a coordinate of the transceiver and a direct measurement distance from the transceiver to the object. The object is somewhere in a circle or sphere around the transceiver. The circle or the spherical shell has half the measuring distance as a radius. The measurement distance results from the delay between sending the signal and receiving the echo. A distance between the transceiver and the object corresponds to half the measurement distance in direct measurement. Direct measurement does not include directional information.

An indirect measurement can be carried out by a transmitter of the sensor arrangement and a receiver of the sensor arrangement remote therefrom. The transmitter sends the signal and the receiver receives the echo resulting from the object. The indirect measurement can include a transmitter coordinate of the transmitter, a receiver coordinate of the receiver and an indirect measurement distance from the transmitter to the object and from the object to the receiver. The object is somewhere on an ellipse or ellipsoid around the transmitter and the receiver. The emitter and receiver lie at the focal points of the ellipse and ellipsoid, respectively. The hidden measurement does not include any directional information.

An estimated range can be quickly calculated using the direct measurements. The estimation area characterizes an area in which the circles or spherical shells of the direct measurements intersect and in which there is a high probability that the object is located. As a rule, all circles or spherical shells do not intersect at a common point of intersection, since the echoes have been reflected at different locations on the object, i.e. at different parts of a surface of the object. Therefore, available information is ignored to calculate the estimation range. The estimation area specifies a search area in which the object is subsequently searched for in detail using all available information.

During numerical optimization, a quality measure for the object position is formulated based on the measurement data and an object model. This can then be gradually improved, starting from an initial estimate of the object's position. In each step, a new object position is determined that better fulfills the quality measure. The procedure ends as soon as the quality measure cannot be further improved.

Approximate measurements can be approximated from the indirect measurements. The approximated measurements can also be used to calculate the estimation range. An approximate measurement may include a virtual coordinate of a virtual transceiver and a virtual measurement distance from the virtual transceiver to a virtual object and from the virtual object to the virtual transceiver. The virtual transceiver can be assumed to be positioned between the transmitter coordinate of the transmitter of the respective hidden line measurement and the receiver coordinate of the receiver of the respective hidden line measurement. The approximate measurement can be used like a direct measurement. The virtual coordinate may be arranged between the sender coordinate, i.e. the coordinates indicating a position of the sender, the hidden line measurement and the receiver coordinate, i.e. the coordinates indicating a position of the receiver, the hidden line measurement. For example, the virtual coordinate can be in the middle between the transmitter coordinate and the receiver coordinate. The virtual object can be a computational object and not actually exist. The virtual measurement distance can correspond to the indirect measurement distance. The virtual measurement distance may have a distance error. The virtual measurement distance can therefore be too large or too small. The estimation range can be expanded by the distance error.

The approximate measurements can be discarded for numerical optimization. Since the approximate measurements may have the range error, it is advantageous to ignore the approximate measurements for the detailed search of the object coordinates.

Using a first object model and the direct measurements, a first object hypothesis can be calculated with a first estimation range. The first estimation region can be numerically optimized using the first object model, the direct measurements and the indirect measurements to obtain first object coordinates and a first hypothesis error of the first object hypothesis. At least one further object hypothesis with a further estimation range can be calculated using at least one further object model that is different from the first object model and the direct measurements. The further estimation range can be numerically optimized using the further object model, the direct measurements and the indirect measurements in order to obtain further object coordinates and a further hypothesis error of the further object hypothesis. Those object coordinates with the smallest hypothesis error can be output. Different object models can have different reflection properties of different object types represent. The object models can show that, depending on the object type, the echoes arise at different points on the object.

The hypothesis errors of the different object hypotheses can be determined by an iterative optimization process. The hypothesis error can correspond to a residual of the optimization process. The optimization process can try to minimize a residual deviation between the measurements and the object hypothesis. The remaining deviation can be called the residual. The better the object model fits the measurements, the smaller the residual can be.

Object models from a group of object models including at least a point model, a wall model and a line model can be used. The reflections from a point, a wall or a line are very different from each other.

The method can be implemented, for example, in software or hardware or in a mixed form of software and hardware, for example in a control unit.

The approach presented here also creates a device that is designed to carry out, control or implement the steps of a variant of the method presented here in corresponding devices.

The device can be an electrical device with at least one computing unit for processing signals or data, at least one memory unit for storing signals or data, and at least one interface and/or one communication interface for reading in or outputting data that are embedded in a communication protocol, be. The computing unit can be, for example, a signal processor, a so-called system ASIC, or a microcontroller for processing sensor signals and outputting data signals as a function of the sensor signals. The storage unit can be, for example, a flash memory, an EPROM or a magnetic storage unit. The interface can be designed as a sensor interface for reading in the sensor signals from a sensor and/or as an actuator interface for outputting the data signals and/or control signals to an actuator. The communication interface can be designed to read in or output the data in a wireless and/or wired manner. The interfaces can also be software modules that are present, for example, on a microcontroller alongside other software modules.

A computer program product or computer program with program code, which can be stored on a machine-readable carrier or storage medium such as a semiconductor memory, a hard disk memory or an optical memory and for carrying out, implementing and/or controlling the steps of the method according to one of the embodiments described above, is also advantageous used, especially when the program product or program is run on a computer or device.

An at least partially automated robot can be controlled using the object coordinates. For example, a trajectory can be determined for the robot on which a collision with the detected object is avoided. Using the trajectory, control commands for the robot's actuators can be generated in order to guide the robot along the trajectory.

It is noted that some of the possible features and advantages of the invention are described herein with reference to different embodiments. A person skilled in the art recognizes that the features of the control device and of the method can be combined, adapted or exchanged in a suitable manner in order to arrive at further embodiments of the invention.

character list

• 1 zeigt eine Darstellung eines Ablaufs eines Verfahrens gemäß einem Ausführungsbeispiel;
• 2 zeigt eine Darstellung von Messungen an einem Objekt;
• 3 zeigt eine Darstellung einer Annäherung einer angenäherten Messung an eine indirekte Messung gemäß einem Ausführungsbeispiel; und
• 4 bis 6 zeigen Darstellungen von Messungen an unterschiedlichen Objekten.

Embodiments of the invention are described below with reference to the accompanying drawings, neither the drawings nor the description being to be construed as limiting the invention.

• 1 shows an illustration of a sequence of a method according to an embodiment;
• 2 shows a representation of measurements on an object;
• 3 12 is an illustration of an approximation of an approximate measurement to an indirect measurement according to an embodiment; and
• 4 until 6 show representations of measurements on different objects.

The figures are merely schematic and not true to scale. In the figures, the same reference symbols denote the same features or features that have the same effect.

Embodiments of the invention

1 shows an illustration of a sequence of a method according to an embodiment game. The method has a step 100 of estimation and a step 102 of optimization. Before step 100 of estimation, direct measurements 106 and indirect measurements 108 of an object are recorded using a plurality of distance sensors of a sensor arrangement 104 . For the estimation step 100, only the direct measurements 106 are used. Using the direct measurements 106, an estimate range 110 within which the object is likely to be located is calculated. In the optimization step 102, the direct measurements 106 and the indirect measurements 108 are used to limit the estimation range 110 by numerical optimization and to obtain object coordinates 112 of the object.

In one embodiment, in a step 114 of converting, preceding the step 100 of estimating, measurements 116 approximated from the indirect measurements 108 are approximated. The approximate measurements 116 have greater uncertainty than the direct measurements 106 and are used in the estimation step 100 in addition to the direct measurements 106 to calculate the estimation range 110 . The approximate measurements 116 are no longer used in step 102 of optimization.

In one embodiment, in step 100 of estimating, different object models 118 are used to calculate different object hypotheses 120 and different estimation ranges 110 . An object hypothesis 120 and an estimation range 110 are calculated for each object model 118 used. In step 102 of optimization, the respective object model 118 is used in order to optimize the object coordinates 112 of the respective estimation area 110 using the respective object hypothesis 120 , the direct measurements 106 and the indirect measurements 108 . A hypothesis error 122 is assigned to each object hypothesis 120 . In a validation step 124 that follows step 102 of optimization, those object coordinates 112 that have the smallest hypothesis error 122 are selected for further processing.

In one embodiment, object models 118 from a set 126 of object models 118 are used. The group includes at least one point model 128, one wall model 130 and one line model 132.

2 shows a representation of measurements on an object 200. For a measurement, a signal 202 is emitted by a transmitter 204, reflected on the object 200 and an echo 206 of the signal 202 is received by a receiver 208. The signal 202 overcomes a distance between the transmitter 204 and the object 200. The echo 206 overcomes a distance between the object 200 and the receiver 208. A measurement distance 210 of the measurement results from a time duration between the transmission and the reception and a propagation speed of the Signal 202 or the echo 206.

In a direct measurement 106, a single sensor of a sensor array 104 is both the transmitter 204 and the receiver 208. The sensor may be referred to as a transceiver 211. The signal 202 overcomes the same distance as the echo 206. The distance thus corresponds to half the measurement distance 210. The object 200 lies on a surface whose points are all equidistant from the sensor. In a two-dimensional view, that is, a circle 212 and in a three-dimensional view on a sphere.

In the case of an indirect measurement 108 , the signal 202 is sent out by a sensor as a transmitter 204 , reflected on the object 200 and the echo 206 of the signal 204 is received by another sensor as a receiver 208 . The signal 202 can cover a different distance to the object 200 than the echo 206. The object 200 lies on an area on which the measurement distance derived from the time between the transmission and the reception is the same. In a two-dimensional view, therefore, on an ellipse 214. In a three-dimensional view, on an ellipsoid. The sensors are arranged in the focal points of the ellipse 214 or the ellipsoid.

3 11 is an illustration of an approximation of an approximated measurement 116 to an indirect measurement 108 according to an embodiment. The object 200 is located as in 2 on an ellipse 214 around the two sensors involved. The approximate measurement 116 is referenced to a virtual transceiver 300 . The virtual transceiver 300 lies between the transmitter 204 and the receiver 208. The virtual transceiver 300 is not a sensor of the sensor arrangement 104 and does not actually exist. For the approximate measurement 116 it is assumed that a virtual object 302 lies on a circle 212 around the virtual sensor 300 . A radius of the circle 212 corresponds to a virtual measurement distance 304 of the approximate measurement 116. The virtual measurement distance 304 can correspond to the measurement distance of the indirect measurement 108, for example.

4 until 6 show illustrations of measurements 400 on different objects 200. Three measurements 400 from three sensors 402 are shown. Each measurement 400 includes a coordinate of the respective sensor 402 and an Ent distance of the object 200 from the sensor 400. The sensors 402 are not arranged in a line next to each other. In 4 measurements 400 of an essentially punctiform object 200 are shown. In 5 measurements 400 of an essentially wall-shaped object 200 are shown. In 6 measurements 400 of an essentially linear object 200 are shown.

All measurements represent a minimum distance between the object 200 and the respective sensor 402. In the case of the punctiform object 200, all measurements 400 relate to a common point 404. In the case of the wall-shaped object 200 and the linear object 200, the measurements relate to different points 404, each of which has the shortest possible distance from the sensor 402. The respective sensor 402 lies on a normal to the wall or line. The point 404 then lies at a base point of the normal. In the case of the wall-shaped object 200, the points 404 are distributed two-dimensionally over the wall. In the case of the line-shaped object 200, the points 404 are distributed one-dimensionally along the line.

In other words, an efficient object localization and validation of different object models is presented.

The approach presented here can be used to determine the position of objects in 3D space using distance sensors. Any number of distance measurements can be used. It is also not necessary for the transmitter and receiver of the measurement signal to be in the same position or for the direction from which the signal is coming to be known.

A localization of point objects using distance measurements can be referred to as a lateration problem. With exactly three measurements, the localization can be referred to as trilateration. Traditional approaches are either designed specifically for point lateration or can only use a fixed number of measurements. To do this, it may be necessary for the measurement signal to be received again at exactly the same point where it was sent, or for the measurement signal to be sent by the object itself. Processes used in the automotive sector often only work in 2D, since the sensors are usually arranged in a single row. The height is then estimated using the object's reflection properties. If the sensors are no longer arranged collinearly, the object height can be determined much more precisely. Determining the object type is only possible to a limited extent with 2D approaches.

With the approach presented here, spatial properties such as the position and angle of objects in the vicinity of a vehicle are determined. In addition, object hypotheses can be validated in order to be able to draw conclusions about the object types. The environmental data obtained in this way can e.g. B. in driver assistance systems or in autonomous vehicles for the perception of the immediate area, among other things, for approach approval and for navigating intersections and footpaths and cycle paths.

In the approach presented here, object coordinates or a parameterization of an object are determined. Various object types can be localized. The approach presented here is independent of the number and type of distance measurements. It is sufficient that a relatively small number of distance measurements, dependent on the object type, is given. The approach presented here for the precise localization of objects is very efficient and can even be implemented with limited computing capacities.

A generic, three-step process is presented. One possibility for implementation is described below. The individual steps are interchangeable. It is sufficient that the specified tasks of the individual stages are solved accordingly. This allows the approach to be easily extended to different model hypotheses. Several distance measurements are used as input for the presented method. It is irrelevant whether the distance measurements are direct (transmitting and receiving sensors are in the same position) or reflected (transmitting and receiving sensors are in different positions). The necessary minimum number of measurements depends on the object model and the dimension of the search space. For points in 3D z. B. at least three measurements necessary. It is assumed that the measuring sensors are positioned in such a way that the object can be localized. A three-dimensional localization requires z. B. at least three measurement sensors that are not arranged collinear to each other.

In 2 a direct distance measurement and a reflected distance measurement are shown for a post-like object. The direct measurement bounces off the object orthogonally and then hits the transmitting sensor again. The reflected measurement bounces off the object in such a way that it arrives in the sensor. This results in a circle equation for the direct measurement. An elliptical equation can be derived from the reflected distance measurement. The sensors form the focal points of the ellipse.

In one embodiment, the following steps are performed.

Conversion of all reflected distance measurements to direct distance measurements.

Approximate object localization based on the (converted) direct distance measurements.

Refinement of the object localization using a numerical optimization method, which also takes the reflected measurements into account.

In 1 A possible course of the procedure is shown. The conversion and the numerical optimization are independent of the object model and are the same for each approach.

Step 1: If there are reflected measurements among the given measurements, these are replaced by corresponding direct measurements. The reflection point of a reflected measurement on an object always satisfies an elliptical equation with the transmitting and receiving sensor at the respective focal points of the ellipse. If a circle is considered whose center coincides with the center of the ellipse, a direct distance measurement results from the radius of the circle. The radius of the circle can be set in different ways. Thus, the radius can be chosen to match one of the semi-axis lengths of the ellipse. Assuming that the reflex point is exactly in the middle in front of the sensors, the corresponding distance to the center of the ellipse can be selected. In this case, the radius r of the circle results from the formula in Eq. (1). Here P1 is the transmitting sensor, P2 is the receiving sensor and d is half the reflected distance measurement.

In 3 an approximation of reflected measurements by direct measurements is shown. Sensors P1 (204) and P2 (208) are replaced with imaginary sensor Q (300) and the equation of the ellipse (with foci P1 and P2) is replaced with the equation of a circle (with center Q). The radius of the circle results from the indirect measurement distance and the hypothetical object position O' (302), which is assumed to be directly in front of the sensor Q. $$\mathrm{right}=\mathrm{i.e}\sqrt{\frac{{\mathrm{i.e}}^2-{\Vert v\Vert }^2}{{\mathrm{i.e}}^2-a{\Vert v\Vert }^2}}\text{With}v:=\frac{P_2-{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="DE102020214403A1\_0013.png,DE102020214403A1\_0015.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}{2}$$

The in Eq. (1) Given formula is adaptable to other hypothetical positions of the object. The factor α ∈ [0, 1] in the denominator of Eq. (1) determines the relative position between the center of the circle and the object. With α = 1/2 it is assumed that the object is directly in front of the fictitious sensor. It should be emphasized here that the localization considered in step 2 considers the center of the circle as the virtual sensor position in order to obtain a correct result.

Step 2: The object localization based on direct distance measurements is model dependent. An efficient procedure for point, wall and line objects is described below. All methods are suitable for implementation on a control unit. The methods determine the object position with the help of a linear system of equations, which is solved taking the object hypotheses into account. There are closed representations of the solution for essential steps in the approach, or these steps are not dependent on the measurements and can be calculated and saved offline in advance. Complex calculations are thus reduced to a minimum.

The underlying system of equations is also always the same size, regardless of the number of measurements. Accordingly, the memory requirement increases only linearly with the number of measurements.

Point model: For a point object O with m sensors P _i ∈ℝ ³ , i = 1, ... , m the formula in Eq. (2). $${\Vert 0-P_i\Vert }_2={\mathrm{i.e}}_i,{\forall }_i=\mathrm{1,}\cdots ,m$$

Hierbei stellen P̅ die gemittelte Sensorpositionen und d̅² den gemittelten quadrierten Abstand dar. Um etwaige Messungenauigkeiten zu berücksichtigen (z. B. dass sich die Messungen nicht alle in exakt dem gleichen Punkt schneiden) wird Gl. (3) in ein Least-Squares Modell überführt. Die Optimalitätsbedingungen dieses Least-Squares Modells ergeben wiederum ein lineares Gleichungssystem mit einer symmetrischen und positiv semi-definiten 3 × 3 Matrix. Wird die m × 3 Matrix, deren Zeilen die Einträge 2(P_i - P̅)^T enthalten, mit A bezeichnet und der Vektor, der die rechten Seiten aus Gl. (3) enthält, mit b bezeichnet, so ergibt sich die Gleichung A^T AO = A^T b. Dieses System kann sehr effizient mit Hilfe einer Eigenwertzerlegung gelöst werden. Die Eigenwertzerlegung zerlegt die Matrix A^TA in ein Produkt von drei Matrizen wie in Gl. (4) dargestellt. $$\begin{array}{c}{A}^{\text{T}}AO=A^{\text{T}}b\\ \iff V\left(\begin{array}{ccc}{\lambda }_1& 0& 0\\ 0& {\lambda }_2& 0\\ 0& 0& {\lambda }_3\end{array}\right)\\ \iff \left(\begin{array}{ccc}{\lambda }_1{V}_{*\mathrm{,1}}& {\lambda }_2{V}_{*\mathrm{,2}}& {\lambda }_3{V}_{*\mathrm{,3}}\end{array}\right)\underset{=:\tilde{O}}{\underbrace{V^{\text{T}}O}}=A^{\text{T}}b\end{array}{V}^{\text{T}}O=A^{\text{T}}\text{b}$$

If both sides in Eq. (2) squared and the arithmetic mean of all equations subtracted from each individual equation, the result is the linear system of equations in Eq. (3). $$2〈P_i-\overline{P},O〉={\mathrm{i.e}}_i^2-{\overline{\mathrm{i.e}}}^2-\left({\Vert P_i\Vert }^2-\frac{1}{m}{\displaystyle {\sum }_{j=i}^m{\Vert P_j\Vert }^2}\right),{\forall }_i$$

Here, P̅ represents the average sensor positions and d̅ ² represents the average squared distance. In order to take into account any measurement inaccuracies (e.g. that the measurements do not all intersect at exactly the same point), Eq. (3) transformed into a least squares model. The optimality conditions of this least squares model result in a linear system of equations with a symmetric and positive semi-definite 3 × 3 matrix. If the m × 3 matrix whose rows contain the entries 2(P _i - P̅) ^T is denoted by A and the vector that contains the right-hand sides of Eq. (3) contains, denoted by b, the result is the equation A ^T AO = A ^T b. This system can be solved very efficiently with the help of an eigenvalue decomposition. The intrinsic value decomposition decomposes the matrix A ^T A into a product of three matrices as in Eq. (4) shown. $$\begin{array}{c}{A}^{\text{T}}AO=A^{\text{T}}b\\ \iff V\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="\lambda "\; filenames="DE102020214403A1\_0013.png,DE102020214403A1\_0015.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_1& 0& 0\\ 0& {\lambda }_2& 0\\ 0& 0& {\lambda }_3\end{array}\right)\\ \iff \left(\begin{array}{ccc}{\lambda }_1{V}_{*\mathrm{,1}}& {\lambda }_2{V}_{*\mathrm{,2}}& {\lambda }_3{V}_{*\mathrm{,3}}\end{array}\right)\underset{=:\tilde{O}}{\underbrace{V^{\text{T}}O}}=A^{\text{T}}b\end{array}{V}^{\text{T}}O=A^{\text{T}}\text{b}$$

The matrix V is an orthogonal matrix and contains the eigenvectors we are looking for. The eigenvalues λi are all nonnegative. In our case, the system matrix A ^T A depends only on the sensor positions and its eigenvalue decomposition can be calculated and saved in advance.

In the case of exactly three direct distance measurements, a closed representation of the eigenvalues and eigenvectors is also known. By transferring it to eigenspace, the linear system of equations is reduced to a system with a diagonal matrix, which allows a closed representation of its solution. Depending on the number of sensors involved and their relative position to each other, the system A ^T AO = A ^T b can allow several solutions. To take this into account, the system is rewritten as follows using the self-representation. $$\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="\lambda "\; filenames="DE102020214403A1\_0013.png,DE102020214403A1\_0015.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_1^2& 0\\ 0& {\lambda }_2^2\end{array}\right)\left(\begin{array}{c}{\tilde{O}}_1\\ {\tilde{O}}_2\end{array}\right)=\left(\begin{array}{c}{\lambda }_1{V}_{*\mathrm{,1}}^{\text{T}}\\ {\lambda }_2{V}_{*\mathrm{,2}}^{\text{T}}\end{array}\right)\left(A^{\text{T}}b-{\tilde{O}}_3{\lambda }_3{V}_{*\mathrm{,3}}\right)$$

Here V _*,i represents the i-th column of the matrix V. The system in Eq. (5) can be solved very easily for Õ ₁ and Õ ₂ . For the vector Ö, ||O||= ||Õ||. From the averaged equations from Eq. (2) therefore follows Eq. (6).
Equation 6 $${\Vert \tilde{O}\Vert }^2={\overline{\mathrm{i.e}}}^2+2〈\overline{P},\tilde{O}〉-\frac{1}{m}{{\displaystyle {\sum }_i\Vert P_i\Vert }}^2$$

If the representation of Ö from Eq. (5) with that from Eq. (6) combined, the result is a quadratic polynomial in Õ ₃ whose zeros contain the values sought for the solution. If the polynomial has no zeros, it follows that the distances originally considered do not have a common point of intersection. In that case the global minimizer of the polynomial can be taken as the value for Õ ₃ . In this case, the position found corresponds to that which minimizes the distances to all circle equations. By returning the solution Ö to the original coordinate system, the coordinates of the point object O based on the direct distance measurements are obtained.

4 shows a point model with an object O (200) and three distance sensors P1, P2, and P3 (402). The measured distances are d1, d2, and d3 (400).

Wall model: Parameterized wall models are considered, which can be represented as {x ∈ ℝ ³ |〈x,n〉 = 1} with a fixed but unknown normal vector n. For m sensors P _i , i = 1,...,m the signals are reflected orthogonally. From this it follows that the distances d _i satisfy equation (7). $${\mathrm{i.e}}_i=\frac{1-〈P_i,n〉}{〈n,n〉},{\forall }_i=\mathrm{1,}\cdots ,m$$

Da das System in Gl. (8) strukturell identisch zum System in Gl. (2) ist, kann auch hier der gleiche Ansatz verfolgt werden. Die in Gl. (4) und Gl. (5) dargestellten Berechnungen im Eigenraum gelten hier auch für Wände. Aus Gl. (5) ergibt sich dann die Darstellung n = ω + tv mit festen Vektoren ω ∈ ℝ³ und v ∈ ℝ³ und einem beliebigen Skalar t. Aus den gemittelten Gleichungen in Gl. (7) folgt nun $${\Vert \omega +tv\Vert }^2\overline{d}=1-\langle \omega +tv,\overline{P}\rangle$$

Gleichung (9) ist eine quadratische Gleichung in der Unbekannten t. Die Nullstellen dieser Gleichung ergeben den gesuchten Wert für t und damit den Wert für den Normalenvektor n.If the arithmetic mean of all equations from Eq. (7), then (n,n) can be expressed as a function of the normal vector n, the average distance d, and the average sensor position P. This expression is then in turn inserted into each equation from Eq. (7) is used and the formulation in Eq. (8th). $$\begin{array}{l}{\mathrm{i.e}}_i-〈n,\overline{P}{\mathrm{i.e}}_i〉=\overline{\mathrm{i.e}}-〈n,P_i\overline{\mathrm{i.e}}〉\\ \iff 〈n,P_i\overline{\mathrm{i.e}}-\overline{P}{\mathrm{i.e}}_i〉=\overline{\mathrm{i.e}}-{\mathrm{i.e}}_i\end{array}$$

Since the system in Eq. (8) structurally identical to the system in Eq. (2), the same approach can be followed here as well. The in Eq. (4) and Eq. (5) shown calculations in eigenspace also apply to walls. From Eq. (5) the representation n = ω + tv with fixed vectors ω ∈ ℝ ³ and v ∈ ℝ ³ and an arbitrary scalar t then results. From the averaged equations in Eq. (7) now follows $${\Vert \omega +tv\Vert }^2\overline{\mathrm{i.e}}=1-〈\omega +tv,\overline{P}〉$$

Equation (9) is a quadratic equation in the unknown t. The zeros of this equation give the value of t we are looking for and thus the value of the normal vector n.

5 shows a wall model with a wall (200) and with three distance sensors P1, P2, and P3 (402). The measured distances are d1, d2, and d3 (400).

Line model: Lines in ℝ ³ with parameterization {g + λh | λ ∈ R}, where ||h|| = 1 and (g,h)=0 hold. It is assumed that the line is aligned in the "direction" of the sensors. Therefore, as the direction vector h, the normalized eigenvector becomes the eigenvalue with the largest absolute value chosen from the covariance matrix of the sensor positions, ie the matrix in Eq. (10) is considered. $$\frac{1}{m}{\displaystyle {\sum }_{i=1}^m\left(P_i-\frac{1}{m}{\displaystyle {\sum }_{j=1}^m\left(P_j\right)}\right)}{\left(P_i-\frac{1}{m}{\displaystyle {\sum }_{j=1}^m\left(P_j\right)}\right)}^{\text{T}}$$

Then the eigenvalues and eigenvectors of this matrix are calculated. Since this matrix only depends on the combination of sensor positions, the vector h can be calculated and stored in advance for every possible sensor position. In a second step, so-called effective distances are calculated from the given sensor positions and distances as in Eq. (11) calculated. $${\mathrm{i.e}}_{i_{eff}}:=\sqrt{{\mathrm{i.e}}_i^2+〈H,P_i〉}$$

These distances represent the distances to a common point of intersection. This common point of intersection q can now be calculated with the aid of the algorithm for localizing point objects. In a final step, this point is projected onto the line using g := q - (h, q)h, resulting in the parameterization (g, h) for the line.

6 shows a line model with a line (200) and with three distance sensors P1, P2, and P3 (402). The measured distances are d1, d2, and d3 (400).

Step 3.: An error can be specified for each object model by comparing the measured distances with calculated distances. The object coordinates determined in step 2 are used for the calculation. In this step, however, the reflected distance measurements are also taken into account in addition to the direct distance measurements. The direct distance measurements estimated in step 1 are no longer used in this step. The result from step 2 is now improved with the help of an iterative optimization process. Approaches such as the (quasi-)Newton or Levenberg-Marquardt method have very fast convergence rates if they are combined with an initial value that is close to the exact solution. In addition, these algorithms only need a routine that provides a pointwise evaluated error and possibly an estimate for its Jacobian matrix. For the models considered here, there are closed representations for both the error and its Jacobian matrix. Furthermore, the object coordinates calculated in step 2. are in most cases close enough that a convergence down to measurement accuracy can be expected in a few iteration steps.

If step 3 is applied to the given measurements with each model, a statistical analysis can also be used to determine which model best fits the measured distances. For example, the simplest approach is B. Consider the residual from each optimization and assign the model with the smallest residual to the distances.

Finally, it should be noted that terms such as "comprising," "comprising," etc. do not exclude other elements or steps, and terms such as "a" or "an" do not exclude a plurality. Any reference signs in the claims should not be construed as limiting.

Claims (9)

A method for determining object coordinates (112) of an object (200) from a group of measurements (400), comprising direct measurements (106), each containing a coordinate of a transceiver (211) of the direct measurement (106) and a direct measurement distance (210) from the transceiver (211) to the object (200) and from the object (200) to the transceiver (211) include, and indirect measurements (108), each containing a transmitter coordinate of a transmitter (204) of the indirect measurement (108), a receiver coordinate of a receiver (208) of the indirect measurement (108) and an indirect measurement distance (210) from the transmitter (204) to the object (200) and from the object (200) to the recipient (208), the direct measurements (106) are used to calculate an estimated range (110) of the object (200), the estimated range (110) identifying an area in which the object (200) is likely to be located, the estimated range (110) is numerically optimized using the direct measurements (106) and the indirect measurements (108), and the object coordinates (112) are determined taking into account the optimized estimation range. procedure according to claim 1 , in which approximated measurements (116) are approximated from the indirect measurements (108), each of which has a virtual coordinate of a virtual transceiver (300) and a virtual measurement distance (304) from the virtual transceiver (300) to a virtual object (302) and from the virtual object (302) to the virtual transceiver (300), the virtual transceiver (300) being defined as between the transmitter coordinate of the transmitter (204) of the hidden measurement (108) and the receiver coordinate of the receiver (208) of the hidden measurement (108 ) is assumed to be positioned, further using the approximated measurements (116) to calculate the estimation area (110). procedure according to claim 2 , where the approximate measurements (108) are discarded for numerical optimization. Method according to one of the preceding claims, in which a first object hypothesis (120) with a first estimation range (110) is calculated using a first object model (118) and the direct measurements (106), the first estimation range (110) using the first object model (118), the direct measurements (106) and the indirect measurements (108) is numerically optimized in order to obtain first object coordinates (112) and a first hypothesis error (122) of the first object hypothesis (120), using at least one from the first object model (118), further object model (118) and the direct measurements (106), at least one further object hypothesis (120) with a further estimation range (110) is calculated, the further estimation range (110) using the further object model ( 118), the direct measurements (106) and the indirect measurements (108) is numerically optimized to further object coordinates (112) and another n hypothesis error (122) of the further object hypothesis (120), wherein those object coordinates (112) with the smallest hypothesis error (122) are output. procedure according to claim 4 , in which the hypothesis errors (122) of the various object hypotheses (120) are determined by an iterative optimization process, the hypothesis errors (122) each corresponding to a residual of the optimization process. Method according to one of Claims 4 until 5 , wherein object models (118) from a group of object models (118) comprising at least one point model (128), one wall model (130) and one line model (132) are used. Device, wherein the device is designed to carry out, implement and/or control the method according to one of the preceding claims in corresponding devices. Computer program product that is set up to guide a processor when executing the computer program product to perform the method according to one of Claims 1 until 6 to execute, implement and/or control. Machine-readable storage medium on which the computer program product according to claim 8 is saved.

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