DE102022200750A1 - Ultrasonic transceiver arrangement for detecting and locating a surrounding object - Google Patents

Abstract

An ultrasonic transmission/reception arrangement for detecting and locating an object in the surroundings of a means of transportation (10) is proposed. The ultrasonic transmission/reception arrangement comprises a large number of ultrasonic sensors (P) and an electronic evaluation unit (3), the evaluation unit (3) being set up to cause a first ultrasonic sensor (P) of the large number of ultrasonic sensors (P) to emit a transmission signal and to detect echoes of the transmission signal by means of a second ultrasonic sensor (P) of the plurality of ultrasonic sensors (P), characterized in that the evaluation unit (3) is further set up to apply a stored first matrix for the detection and localization of the surrounding object to the echo, which matrix consists of a plurality stored matrices has been selected and represents a spatial relationship between the first ultrasonic sensor (P) as transmitting ultrasonic sensor (P) and the second ultrasonic sensor (P) as receiving ultrasonic sensor (P).

Description

State of the art

The present invention relates to an ultrasonic transmission/reception arrangement for detecting and localizing an object in the surroundings of a means of transportation. In particular, the present invention relates to a simplified calculation rule or method for reducing the required processor power or shortening the evaluation time.

Ultrasound-based transceiver arrangements for environment detection are well known in the prior art.

The most commonly encountered approach considers the location of point objects using distance measurements and is known as the lateration problem or point lateration. A point object is any object that transmits all measurement signals sent from a single point back to the receiver. If one uses exactly three measurements, one speaks of a trilateration. Certain approaches are either designed specifically for point lateration or can only use a fixed number of measurements. Furthermore, these methods usually require that the measurement signal is received again at exactly the same point from which it was sent, or that the measurement signal was sent by the object itself. Other methods are based on other physical events, since they are designed for very high speeds and large distances (e.g. GPS localization). In these cases, mathematical models with an explicit time dependency are required. In the automotive sector, the methods currently used 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 (i.e. in a row), the object height can be determined much more precisely. Furthermore, a determination of the object type with 2D approaches is only possible to a limited extent, since there is no spatial resolution along the third dimension.

The invention determines spatial properties, such as the position and angle of objects in the vicinity of a vehicle, using distance measurements. In addition, quality criteria such as B. error measures and covariance matrices can be calculated. The environmental data obtained in this way can e.g. B. in driver assistance systems or in autonomous vehicles for the perception of the close range, e.g. be used for approach clearance and for navigating intersections and footpaths and cycle paths.

It is an object of the present invention to be able to carry out the determination of object coordinates from a distance measurement with the ongoing operation with reduced processor load or simpler calculation steps.

Disclosure of Invention

The above-mentioned object is achieved according to the invention by an ultrasonic transceiver arrangement for detecting and localizing an object in the vicinity of a means of transportation. The ultrasonic transceiver arrangement can have, for example, ultrasonic transceivers arranged on a bumper of the means of transportation for ultrasonic signal conversion. In addition, the signals received by the ultrasonic transceivers can be received and further processed by an evaluation unit (eg an electronic control unit) in order to identify objects within the echoes of the ultrasonic transceivers. The evaluation unit is set up to cause a first ultrasonic sensor of the plurality of ultrasonic sensors to emit a transmission signal and to receive echoes of the transmission signal that have arisen on the surrounding object by means of a second ultrasonic sensor of the plurality of ultrasonic sensors. The second ultrasonic sensor can, for example, be the same sensor that sent out the signal. This does not rule out the possibility that further ultrasound transceivers or ultrasound receivers can be set up to receive the echoes of the transmission signal that have arisen on the surrounding object. Depending on which spatial resolution is required, at least three echoes may have to be evaluated, for example, in order to be able to determine a localization in three-dimensional space (height and direction from the point of view of the ultrasonic transceiver arrangement). The evaluation unit is set up to apply a stored first matrix for the detection and localization of the surrounding object to the received echo or echoes. The matrix is selected from a variety of stored matrices and represents a spatial relationship between the first (transmitting) ultrasonic sensor and the second ultrasonic sensor or other ultrasonic sensors as receiving ultrasonic sensors. By using a pre-stored matrix, the spatial Relationship determined without a complicated arithmetic operation and hereby done the localization of the surrounding object by comparatively low-performance hardware. The cost and energy consumption of a system according to the invention can thus be reduced.

The dependent claims show preferred developments of the invention.

The plurality of stored matrices may include a respective matrix for each combination of transmitting ultrasonic sensors. Due to symmetry considerations, obsolete matrices can sometimes be superfluous in the memory, since identical relative spatial relationships can be mapped by one and the same matrix. The method is not limited to indirect echoes. Indirect echoes only need to be converted in a suitable way (see Equation 3).

The matrix can be stored in a ROM (read only memory) of the evaluation unit or be linked to the evaluation unit in terms of information technology. In other words, the matrix is not a data set calculated by the evaluation unit of the ultrasound transceiver arrangement, but is permanently specified for the evaluation unit. Here, the matrix maps spatial relationships of the ultrasonic sensors to one another, which can be determined, for example, during typing or at the factory and stored as a matrix. This reduces the cost of maintaining the matrix.

For example, the matrix can be a 3xK matrix, where K stands for the received echoes or the number of received echoes. In other words, the matrix can represent the minimizer of the error in localization. The aim of this is to minimize the error in the localization for the given data. The localization, which is simple according to the invention, can be carried out particularly precisely in this way, so that the information ascertained is particularly revealing and/or valuable for localizing the objects in the surroundings.

The matrix can be determined, for example, from the position of the first sensor reduced by the geometric center of gravity of the multiplicity of sensors. The matrix therefore contains all sensor positions that were involved in the measurement. This can take into account protocols or measurement sequences which are provided during operation of the ultrasound transceiver arrangement (e.g. in a means of transportation). In addition, the so-called pseudo-inverse of this matrix can be saved. This can also bring computational advantages. The positions of the individual sensors or ultrasonic transceivers can then no longer be read directly from this pseudo-inverse matrix.

The ultrasonic transmission/reception arrangement can in particular have a multiplicity of sensors which, during operation, have at least two rows arranged essentially parallel to one another or are arranged in corresponding rows. In this case, the two rows can be arranged at different heights relative to the ground on which the means of transportation is standing. This distance enables a particularly good spatial resolution with regard to the height of a localized object in the surroundings. The large number of sensors can in particular have different heights of 2 cm, 5 cm, 8 cm, 10 cm, 20 cm or 30 cm. The greater the distance, the better the local resolution with regard to the height of the localized objects in the environment.

The plurality of sensors provided according to the invention can in particular be set up so that they are all arranged in a front or in a rear bumper of a means of transportation. In other words, the sensors contained in the multiplicity essentially point in a common direction with respect to which they can bring about the greatest possible spatial resolution. In other words, a single matrix according to the invention is used/stored for the multiplicity of sensors aligned in one direction, while a further matrix is stored for a further multiplicity of sensors that may be present on the means of transport. Each matrix thus represents the spatial relationships between the respective plurality of sensors, so that the environment detection can be processed independently with regard to different directions (including cardinal points). In addition, a respective evaluation unit can be provided for a respective multiplicity of sensors, so that, if necessary, different control units can be provided for the inventive evaluation of the multiplicity of sensors present at the rear of the vehicle or at the front of the vehicle. This makes it possible to further reduce the computing capacity of the individual processors, since collisions are usually only relevant to the driver of the means of transport in the direction of travel.

In the multiplicity of ultrasonic sensors, for example eight ultrasonic sensors (for example two rows of four ultrasonic sensors), preferably twelve ultrasonic sensors (for example two rows of six Ult Rapid sound sensors) and particularly preferably sixteen ultrasonic sensors (eg two rows of eight ultrasonic sensors) can be provided. Of course, the aforementioned ultrasonic sensors can also have a plurality of rows (three or even four rows) and in particular more individual ultrasonic transceivers, without no longer realizing the subject matter of the present invention. In particular, at least four sensors or ultrasonic transceivers are used for complete localization of a surrounding object. A higher number of sensors increases the redundancy and spatial resolution, but also the hardware and evaluation effort.

The individual ultrasonic sensors of a large number of ultrasonic sensors or ultrasonic transceivers can each be coupled to the evaluation unit by means of a separate line (e.g. a two-wire line), preferably twisted. This results in a star topology, with information and/or energy for operating the ultrasonic sensors being able to be transmitted via the respective line. The star topology is also particularly advantageous in terms of reliability, since a broken line always paralyzes only a single ultrasonic sensor.

The lines between the respective ultrasonic sensor and the respective evaluation unit are set up to transmit a respective echo or information determined by means of the echo to the evaluation unit. These received echoes can be used to detect and localize the object in the surroundings using the respective matrix or plurality of matrices. In accordance with the invention, the computing power can be kept low because the spatial relationships are mapped using the respective matrix.

The computing power of the evaluation unit used can be kept very low by the inventive use of the stored matrices, based on a number of the large number of sensors. For example, a computing power of 160 MHz, in particular 120 MHz, preferably 100 MHz, per ultrasonic sensor can be assumed to be sufficient to carry out the inventive detection and localization of surrounding objects for conventional applications in means of locomotion. In this way, energy can be saved, which increases the mobility of the means of transportation designed according to the invention.

Further features and feature combinations of the present invention are presented below without any restrictive character and then explained with reference to the accompanying figures.

A core of the invention includes the determination of object coordinates from distance measurements. The advantage of the method shown is that almost all calculations can be carried out in advance and only very few function evaluations are necessary during operation. As a result, the method can even be implemented with very limited computing capacities. The method supports any number of measurements. In addition, quality criteria and error estimates can be specified that reflect the reliability of the measurements. Just as for the position determination, almost all calculations for the calculation of the quality criteria can be carried out in advance.

The procedure consists of a multi-stage process. First, the data is pre-processed. In the next step, the position is then determined using the converted data. In the last step, the quality criteria are determined.

Möglichkeiten Paare zu bilden. Somit würden sich im schlimmsten Fall $\text{n}+\frac{1}{2}\text{n}\left(\text{n}-1\right)=\frac{1}{2}\text{n}\left(\text{n}+1\right)$

mögliche reale und virtuelle Sensorpositionen für direkte Abstandsmessungen ergeben (anstatt von nur n). Würde man nur Kombinationen von exakt 3 Messungen betrachten, dann müsste man $$\left(\begin{array}{c}\frac{1}{2}n\left(n+1\right)\\ 3\end{array}\right)=\frac{1}{48}\left(n^6+3n^5-3n^4-11n^3+2n^2+8n\right)$$

The algorithm described below requires direct distance measurements, i.e. measurements where the transmitter and receiver positions match. For each possible tuple of sensors that can perform a measurement, a certain amount of data must be stored for the algorithm or calculated on the fly. If only indirect measurements are available (i.e. measurements for the transmitter and receiver position do not match), then these must first be converted into direct measurements. Previous approaches have used virtual sensors for this conversion. Such sensors are not physically present in the system, but one can determine their position and distance to the object. However, important properties such as the viewing direction and opening angle of the virtual sensor are mostly unknown and can only be estimated. This can lead to inaccuracies and errors. In addition, there are actually existing sensors in a system of n $\frac{1}{2}\text{n}\left(\text{n}-1\right)$

opportunities to form pairs. Thus, in the worst case $\text{n}+\frac{1}{2}\text{n}\left(\text{n}-1\right)=\frac{1}{2}\text{n}\left(\text{n}+1\right)$

possible real and virtual sensor positions for direct distance measurements (instead of just n). If one were only to consider combinations of exactly 3 measurements, then one would have to $$\left(\begin{array}{c}\frac{1}{2}n\left(n+1\right)\\ 3\end{array}\right)=\frac{1}{48}\left({\mathrm{<figure-callout\; id="6"\; label="n"\; filenames="DE102022200750A1\_0029.png,DE102022200750A1\_0030.png"\; state="\{\{state\}\}">n</figure-callout>}}^6+3{\mathrm{<figure-callout\; id="5"\; label="n"\; filenames="DE102022200750A1\_0029.png,DE102022200750A1\_0030.png"\; state="\{\{state\}\}">n</figure-callout>}}^5-3{\mathrm{<figure-callout\; id="4"\; label="n"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">n</figure-callout>}}^4-11{\mathrm{<figure-callout\; id="3"\; label="n"\; filenames="DE102022200750A1\_0029.png,DE102022200750A1\_0031.png"\; state="\{\{state\}\}">n</figure-callout>}}^3+2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+\mathrm{8th}n\right)$$

investigate cases. With a system consisting of n = 12 sensors, this would be 76076 combinations (instead of 220). This places significant demands on memory consumption.

Fälle. Für n = 12 wären dies 220 Fälle.For this reason, one embodiment uses the following approach to convert indirect measurements into direct measurements. Here the conversion into a direct distance measurement is always relative to a real sensor. If one also considers combinations of three sensors as an example, only $$\left(\begin{array}{c}n\\ 3\end{array}\right)=\frac{1}{6}\left({\mathrm{<figure-callout\; id="3"\; label="n"\; filenames="DE102022200750A1\_0029.png,DE102022200750A1\_0031.png"\; state="\{\{state\}\}">n</figure-callout>}}^3-3{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+2n\right)$$

Cases. For n = 12, this would be 220 cases.

The conversion must be translation-invariant. So, without loss of generality, we can assume that the sender is in the coordinates (0, 0, 0) and the receiver is in the coordinates (±c, 0, 0). The transit time, i.e. the measured distance from the transmitter to the object and back to the receiver, is 2a (a > c). If you now express the distance from the transmitter to the object in polar coordinates, you get the expression for the radius $$\mathrm{right}\left(\theta \right)=\frac{a\left(1-e^2\right)}{1\pm \text{cos}\left(\theta \right)}$$

The constant e depends only on the distance between the sensor positions and the measured distance and is given by $$e=\frac{c}{a}$$

The sign in the denominator depends on whether the receiver is to the left or right of the sender. The parameter θ specifies the angle between the transmitter-receiver axis and the straight line that goes through the transmitter and the object (see 1 ). The formula also applies if the sender and receiver are in the same place. In that case e = 0 and θ = 0 and thus $\text{right}=\frac{a}{2}.$

Für entfernte Objekte wäre sogar mit einem festen Winkel der Fehler sehr gering (siehe 2).In the following we only consider the case of direct distance measurements. If there are indirect distance measurements, they can be converted to direct distance measurements using equation (3). In most cases, a rough estimate is sufficient for the angle θ. For example, with a moving car, one might assume that the object is in front of the vehicle. In that case would be $\mathrm{\theta }=\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}.$

For distant objects, even with a fixed angle, the error would be very small (see 2 ).

For the position coordinates O ∈ R ³ of a reflection point, measured with m sensors with coordinates P _i ∈ R ³ , i = 1, ..., m, the formula in Equation (5) applies for the direct distance measurements d _i ≥ 0 $${\Vert O-P_i\Vert }_2={\mathrm{i.e}}_i,\forall i=\mathrm{1,}...,m$$

If you square both sides of equation (5) and subtract the arithmetic mean of all equations from each individual equation, you get the linear system of equations in equation (6). $$2〈P_i-\frac{1}{m}{\displaystyle \sum _{j=i}^m{P}_j,O}〉=\left({\Vert P_i\Vert }^2-\frac{1}{m}{\displaystyle \sum _{j=1}^m{\Vert P_j\Vert }^2}\right)-\left({\mathrm{i.e}}_i^2-\frac{1}{m}{\displaystyle \sum _{j=1}^m{\mathrm{i.e}}_j^2}\right),{\forall }_i$$

In the following we denote the system matrix from equation (6) with A and the right-hand side of the linear system of equations with b. The linear system of equations can then be written as AO = b. It is known that all solutions O of this system can be expressed as in equation (7). $$O=A^{†}b+\left(I-A^{†}A\right)\omega$$

Here A ^† denotes the Moore-Penrose pseudo-inverse of the matrix A. With I we denote the identity matrix in R ³ and the vector ω ∈ R ³ is a free variable that parameterizes all possible solutions. The matrix (I - A ^† A) ∈ R ^3,3 describes the orthogonal projection onto the null space of the matrix A. For any matrix Q ∈ R ^k,l its null space ker(Q) is defined as in equation (8). $$\text{ker}\left(Q\right):=\left\{x\in {ℝ}^{\mathcal{l}}|Qx=0\in {ℝ}^k\right\}$$

The system matrix A from equation (6) depends only on the sensor positions. Your Moore-Penrose pseudoinverse A ^† as well as your null space ker(A) can be stored in advance for all possible combinations of sensor positions. A maximum of 3m numbers for the pseudo-inverse and 9 numbers for the zero space must then be stored per combination (so a total of 3m + 9 numbers). The number m stands for the number of sensors involved in the measurement. In a sensor system with M sensors are accordingly $${\displaystyle \sum _{m=0}^M\left(\begin{array}{c}M\\ m\end{array}\right)\left(3m+9\right)=3\cdot 2^{M-1}\left(M+6\right)}$$

Numbers saved considering all possible sensor combinations. In an exemplary system consisting of 12 sensors and a 32-bit representation for the numbers, this would be 110592 numbers. This would require 432 kB of memory. If, as previously mentioned, one had to use virtual sensors, then the system would consist of a total of 78 sensors. In that case it would be impossible to store all the combinations, since this requires more than ^10-25 kB of memory.

The Moore-Penrose pseudoinverse can be determined numerically, for example using a singular value decomposition. The null space ker(A) can be calculated using the Gaussian elimination method, among other things.

1. a) Der Nullraum lässt sich durch drei linear unabhängige Vektoren beschreiben.

The further course of the procedure depends on the size of the null space ker(A). We distinguish the following cases.

1. a) The null space can be described by three linearly independent vectors.

• b) Der Nullraum lässt sich durch zwei linear abhängige Vektoren beschreiben.

This case can only occur when m = 0, ie when there is no measurement. In this case, no position determination is possible.

• b) The null space can be described by two linearly dependent vectors.

• c) Der Nullraum lässt sich durch exakt einen vom Nullvektor verschiedenen Vektor beschreiben.

This case can only occur if m = 1, ie if there is exactly one measurement. In this case, a complete position determination is not possible and the method presented here is not applicable.

• c) The null space can be described by exactly one vector different from the zero vector.

This case occurs in a 3D position determination when the m ≥ 3 sensor positions are in one plane. In a 2D position determination, this case occurs when the m ≥ 2 sensors are on a line. In this case, the null space of the matrix A is one-dimensional and orthogonal to the plane/line spanned by the sensor positions. If the vector that describes the null space is denoted by v, then the solution set from Equation (7) is reduced to the parameterization in Equation (10). $$O=A^{†}b+\theta v,\theta \in ℝ$$

The variable θ is initially a free parameter. If the squared equations from equation (5) are averaged, the representation in equation (11) is obtained. $${\Vert O\Vert }^2-2〈O,\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}〉+\frac{1}{m}{\displaystyle \sum _{j=1}^m{\Vert P_j\Vert }^2=\frac{1}{m}}{\displaystyle \sum _{j=1}^{\mathrm{<figure-callout\; id="2"\; label="m\; i.e\; j"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">m</figure-callout>}}{\mathrm{i.e}}_j^{}{}_2^{}}$$

$$q=2\langle A^{†}b,v\rangle -2\langle v,\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}\rangle ,$$

$$\begin{array}{l}r={\Vert A^{\text{†}}b\Vert }^2-2\langle A^{\text{†}}b,\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}\rangle \\ +\frac{1}{m}{{\displaystyle \sum _{j=1}^m\Vert P_j\Vert }}^2-\frac{1}{m}{\displaystyle \sum _{j=1}^m{d}_j^2}\end{array}$$

Substituting the representation of Equation (10) into Equation (11) gives a quadratic equation pθ ² +qθ+r = 0. The parameters p, q and r are given by $$p={\Vert v\Vert }^2,$$

$$q=2〈A^{†}b,v〉-2〈v,\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}〉,$$

$$\begin{array}{l}\mathrm{right}={\Vert A^{\text{†}}b\Vert }^2-2〈A^{\text{†}}b,\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}〉\\ +\frac{1}{m}{{\displaystyle \sum _{j=1}^m\Vert P_j\Vert }}^2-\frac{1}{m}{\displaystyle \sum _{j=1}^{\mathrm{<figure-callout\; id="2"\; label="m\; i.e\; j"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">m</figure-callout>}}{\mathrm{i.e}}_j^{}{}_2^{}}\end{array}$$

The zeros of the polynomial can now be obtained using the midnight formula. $${\theta }_{+/-}=\frac{-q\pm \sqrt{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">q</figure-callout>}}^2-4p\mathrm{right}}}{2p}$$

• d) Der Nullraum besteht ausschließlich aus dem Nullvektor

The two solutions are symmetrical with respect to the plane/line spanned by the sensor positions. Since the object is usually located in front of the sensors, there is no ambiguity. The object position is given by A ^† b + θ _L v where θ _L is the solution chosen in equation (15). The calculation effort for the determination of θ _L and the coefficients p, q and r is minimal. Most of the quantities used in these expressions are already needed to find the right-hand side b. The vector v can also be chosen such that its length is 1. In this case, the calculation of p is omitted.

• d) The null space consists exclusively of the null vector

This case occurs with a 3D position determination if the m ≥ 4 sensor positions are not all in one plane. This case occurs in a 2D position determination if the m ≥ 3 sensors are not all in one line. In this case, the null space of the matrix A is the zero vector. The solution of equation (7) therefore reduces to the matrix-vector multiplication O = A ^† b.

For a given procedure f : R ^m → R ³ one can calculate the corresponding covariance matrix C _f ∈ R ^3,3 at the point p ₀ by a first-order approximation: $$C_{ƒ}=D\left[ƒ\right]\left(p_0\right)C_{p}D\left[ƒ\right]{\left(p_0\right)}^{\top }$$

$$D\left[q\right]\left(d\right)=2{\upsilon }^{\top }{A}^{\text{†}}D\left[b\right]\left(d\right),$$

$$D\left[r\right]\left(d\right)=2{\left(A^{\text{†}}b-\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}\right)}^{\top }{A}^{\text{†}}D\left[b\right]\left(d\right)-\frac{2}{m}{d}^{\top },$$

$$D\left[\theta \right]\left(d\right)=\frac{-D\left[q\right]\left(d\right)}{2p}\pm \frac{2qD\left[q\right]\left(d\right)-4pD\left[r\right]\left(d\right)}{2p\sqrt{q^2-4pr}}$$

Here D[f](p ₀ ) ∈ R ^3,m is the Jacobian matrix of the method f at the point p ₀ and C _p ∈ R ^m,m is the covariance matrix of the input parameters. In the method described here, the input parameters are the measured distances. Only the right-hand side b and the scaling parameter θ depend on the distance measurements. Because of the linearity of the derivation, the Jacobi matrix for the lateration approach presented here is therefore given by A ^† D[b](d) + vD[θ](d). It still applies $$D\left[b\right]\left(\mathrm{i.e}\right)=2{\left({\delta }_{ij}{\mathrm{i.e}}_i-\frac{1}{m}{\mathrm{i.e}}_j\right)}_{i,j=1}^{i,j=m},$$

$$D\left[q\right]\left(\mathrm{i.e}\right)=2{\upsilon }^{\top }{A}^{\text{†}}D\left[b\right]\left(\mathrm{i.e}\right),$$

$$D\left[\mathrm{right}\right]\left(\mathrm{i.e}\right)=2{\left(A^{\text{†}}b-\frac{1}{m}{\displaystyle \sum _{j=1}^m{P}_j}\right)}^{\top }{A}^{\text{†}}D\left[b\right]\left(\mathrm{i.e}\right)-\frac{2}{m}{\mathrm{i.e}}^{\top },$$

$$D\left[\theta \right]\left(\mathrm{i.e}\right)=\frac{-D\left[q\right]\left(\mathrm{i.e}\right)}{2p}\pm \frac{2qD\left[q\right]\left(\mathrm{i.e}\right)-4pD\left[\mathrm{right}\right]\left(\mathrm{i.e}\right)}{2\mathrm{<figure-callout\; id="2"\; label="p\; q"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">p</figure-callout>}\sqrt{q^{}}\sqrt{{}^2-4p\mathrm{right}}}$$

The symbol δ _ij is 1 if i = j and 0 otherwise. Knowing the covariance matrix of the distance measurements, one can also determine the covariance matrix of the lateration.

In principle, it can be assumed that all measuring sensors have the same error behavior. Each distance measurement d _i is measured with an error that can be at most ±ε _i . In the overdetermined case, the position determination results from a single matrix-vector multiplication. The measured distance d _i can then be represented as the sum of the correct distance δ _i and the error ±ε _i (i.e. d _i = δ _i ± ε). In the overdetermined case, the measured distances only enter our equations (6) at a single point. This results in the representation in Equation (21) in a first-order approximation of the error. $${\mathrm{<figure-callout\; id="2"\; label="i.e\; i"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">i.e</figure-callout>}}_i^{}-\frac{1}{m}{\displaystyle \sum _{j=1}^{\mathrm{<figure-callout\; id="2"\; label="m\; i.e\; j"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">m</figure-callout>}}{\mathrm{i.e}}_j^{}{}_2^{}\approx {\delta }_i^2}-\frac{1}{m}{\delta }_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DE102022200750A1\_0029.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+2\left(\pm {\delta }_i{e}_i\mp \frac{1}{m}{\displaystyle \sum _{j=1}^m{\delta }_j{e}_j}\right)$$

In the overdetermined case, the solution can be represented as O = A ^† b. Using the approximation from equation (21), one obtains the following representation for the position of the reflection point. $$O=A^{\text{†}}{b}_k\pm A^{\text{†}}{\delta }_e$$

The term A ^† b _k represents the exact solution here. The term A ^† δ _ε represents the error. The vector δ _ε is defined as $${\delta }_e:=2{\left({\delta }_i{e}_i-\frac{1}{m}{\displaystyle \sum _{j=1}^m{\delta }_j{e}_j}\right)}_{i=1}^{i=m}$$

If one places all errors ±ε _i in a vector ε ∈ R ^m and assumes that the errors follow a continuous uniform distribution, then this vector is in an m-dimensional hypercube. Provided that all distances δ _i are positive, linear ones exist and S which map the vector ε to the vector δε. The linear mapping S represents the scaling with the δ _i . The subtracts from each δ _i ε _i the mean of all δ _j ε _j . The calculation of the error can thus be expressed as 2A ^† LSε. The linear mapping 2A ^† L does not depend on the measured distances and can be pre-calculated and stored. The mapping S is just a column-by-column scaling of A ^† L and can be done very efficiently. The error can thus be estimated by determining the image of the m-dimensional hypercube under A ^† LS. In general, the region thus obtained will be a convex polygon. The shape of this polygon can be calculated and saved in advance, since its shape only depends on the error behavior of the sensors and the sensors involved in the measurement. Only the scaling, which results from the measured distances, cannot be pre-calculated. Assuming that |ε _i | << δ _i then one can use d _i instead of δ _i to calculate the scaling. The overall computational effort is very low. 4 represents an error estimate with four distance measurements.

In the case of an m-dimensional measurement with n sensors, the matrix A ^† L has a total of mn entries. Accordingly, mn numbers must be stored for each possible combination of sensors. For example, if you assume a system of 12 sensors in 3D space, this would be a maximum $$3{\displaystyle \sum _{k=4}^{12}k}\left(\begin{array}{c}12\\ k\end{array}\right)=71316$$

Numbers that need to be saved. This corresponds to a memory consumption of about 2.2 MB if all numbers are saved with 32-bit precision.

If the measurement is not overdetermined, for example if you only have 3 measurements for a 3D position determination, a more complex error pattern results from superimposed circular disks, which is not so easy to represent in a closed form.

character list

• 1 zeigt die geometrischen Zusammenhänge zwischen Sensoren und Objekt mittels einer indirekten Abstandsmessung für einen zweidimensionalen Ansatz;
• 2 stellt den Fehler dar, der bei der Konvertierung einer indirekten Abstandsmessung in eine direkte Abstandsmessung unter Annahme eines festen Winkels von θ = π/2 auftritt;
• 3 stellt direkte Abstandsmessungen in einem dreidimensionalen Ansatz dar; und
• 4 zeigt eine Fehlerabschätzung mit 4 Abstandsmessungen. Die unskalierte Region kann vorab berechnet werden, da sie nur von den Sensoren abhängt. Die Skalierung ergibt sich aus den gemessenen Abständen.

Exemplary embodiments of the invention are described in detail below with reference to the accompanying drawings. In the drawing:

• 1 shows the geometric relationships between sensors and object using an indirect distance measurement for a two-dimensional approach;
• 2 represents the error involved in converting an indirect distance measurement to a direct distance measurement, assuming a fixed angle of θ = π/2;
• 3 depicts direct distance measurements in a three-dimensional approach; and
• 4 shows an error estimate with 4 distance measurements. The unscaled region can be precomputed since it only depends on the sensors. The scaling results from the measured distances.

Embodiments of the invention

1 shows the principle of a distance measurement with a transmitter P ₁ and a receiver P ₂ at different positions in relation to a surrounding object O. An ellipse E, which describes the possible positions of the object O, can be derived from the measured transit time. The length 2a corresponds to the transit time from the transmitter P ₁ to the object O and back to the receiver P ₂ . The length 2c corresponds to the distance between the transmitter P ₁ and the receiver P ₂ . The angle θ measures the angle between the ray lines P ₁ -P ₂ and P ₁ -O.

2 shows the errors in converting an indirect distance measurement to a direct distance measurement when the object O is placed directly in front of the sensor (θ = π/2). The error of the echo distance conversion or the calculated distance reduced by the actual distance (correct distance) is shown. The object position is given here by its x and y coordinates. The sensors of a large number of ultrasonic transceivers extend over a length of 0.6 m. The error falls very quickly. From a distance of 1 m, it is a maximum of 0.05 m, from a distance of 2 m only 0.025 m. These errors can be accepted without any problems for practical applications.

3 shows a point model with an object O and three distance sensors P ₁ , P ₂ , P ₃ . The measured distances are d ₁ , d ₂ , d ₃ . The position of the object O is to be determined from the known sensor positions and the measured distances. For this purpose, the predefined matrix is used in accordance with the above explanations in order to keep the computing power required low.

4 shows the estimation of an error for the x and y coordinates in the case of a measurement with four sensors (and corresponding object distances). The sensors have the positions (-0.3.0), (0.3.0), (0.3.0.3) and (-0.1.0.2). The measured distances are 1.6m, 1.75m, 2.1m and 1.75m respectively. The unscaled region (5) can be calculated in advance as it only depends on the sensors. The scaled region (6) results from the measured distances.

5 FIG. 1 shows a schematic diagram of an exemplary embodiment of an ultrasonic transmission/reception arrangement arranged in a means of transportation 10. FIG. Ultrasonic sensors 2 are arranged in a front and a rear bumper and are connected to an electronic control unit as an evaluation unit 3 in terms of information technology and energy. The calculation steps performed by the evaluation unit correspond to the above explanations and provide an information technology basis in an energy-efficient manner in order to display information on the extension and position of surrounding objects of the means of transport 10 to a user on a central information display 4 . Of course, the determined information on the positions and extensions of the surrounding objects can also be used by other driver assistance systems or self-propelled means of transportation without the need for an interpretation by a user.

Claims (12)

Ultrasonic transceiver arrangement for detecting and locating a surrounding object (O) of a means of locomotion (10) comprising: - a plurality of ultrasonic sensors (P) and - an electronic evaluation unit (3), wherein - the evaluation unit (3) is set up to cause a first ultrasonic sensor (P) of the plurality of ultrasonic sensors (P) to emit a transmission signal and to receive echoes of the transmission signal produced on the surrounding object (O) by means of a second ultrasonic sensor (P) of the plurality of ultrasonic sensors (P), characterized in that the evaluation unit (3) is further set up to apply a stored first matrix for the detection and localization of the surrounding object (O) to the echo, which matrix is selected from a plurality of stored matrices has been selected and represents a spatial relationship between the first ultrasonic sensor (P) as a transmitting ultrasonic sensor (P) and the second ultrasonic sensor (P) as a receiving ultrasonic sensor (P). Ultrasonic transmit-receive arrangement claim 1 , wherein the plurality of stored matrices comprises a respective matrix for each combination of transmitting ultrasonic sensors (P). Ultrasonic transmit-receive arrangement claim 1 or 2 , wherein the matrix is stored in a ROM of the evaluation unit (3). Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the matrix is a 3xK matrix and/or represents the minimizer of the error of the localization. Ultrasonic transmission/reception arrangement according to one of the preceding claims, in which the matrix is determined from the position of the first ultrasonic sensor (P) reduced by the geometric center of gravity of the plurality of ultrasonic sensors (P). Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the plurality of ultrasonic sensors (P) are set up to be arranged at different heights on the means of locomotion (10). Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the plurality of ultrasonic sensors (P) are arranged to be all arranged in a front or rear bumper. Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the plurality of ultrasonic sensors (P) has 8 ultrasonic sensors, preferably 12 ultrasonic sensors (P), particularly preferably 16 ultrasonic sensors (P). Ultrasonic transmission/reception arrangement according to one of the preceding claims, wherein each of the plurality of ultrasonic sensors (P) is coupled in terms of information technology and energy to the evaluation unit (3) by means of a respective separate line, in particular by means of a preferably twisted electrical line. Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the plurality of ultrasonic sensors (P) are set up to carry out analog-to-digital conversion of received echoes. Ultrasonic transceiver arrangement according to one of the preceding claims, wherein the evaluation unit (3) is set up to detect and localize a surrounding object (O) based on the received echoes and the plurality of matrices, wherein the evaluation unit (3) is set up in particular to receive a respective echo via a respective line. Ultrasonic transmission/reception arrangement according to one of the preceding claims, in which the evaluation unit (3) has a computing power, based on a number of the plurality of ultrasonic sensors (P), which does not exceed 160 MHz, in particular 120 MHz, preferably 100 MHz.

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