DE102019204408A1 - Method for determining the yaw rate of a target object on the basis of the sensor data, for example from a high-resolution radar - Google Patents

Abstract

Method for determining the yaw rate (ω) of a target object (50), comprising receiving sensor data which comprise a point cloud (P1, ... PN) which describes the target object (50), estimating the position of the yaw center (64) of the target object (50) on the basis of the point cloud (P1, ... PN), as well as determining the yaw rate (ω) on the basis of the estimated location of the yaw center (64).

Description

The present disclosure relates to a method for evaluating sensor data, in particular in the field of vehicle sensor technology for driver assistance systems, autonomous vehicles or semi-autonomous vehicles.

Autonomous vehicles and driver assistance systems are becoming more relevant and widespread. For such systems it is particularly important that the vehicle can correctly assess the route of surrounding vehicles, for example vehicles of other road users. In order to estimate the route of other vehicles in road traffic, the yaw rate (rotation) of the vehicle to be assessed is important in addition to the location information and the speed of movement.

Solutions are already known from the prior art which are able to determine the yaw rate of a vehicle based on sensor data. So determined in patent disclosure DE 102013019804 A1 The device disclosed the yaw rate of another vehicle with the help of two sensors.

Other solutions are also known which determine the yaw rate by filtering (tracking) the sensor data over time.

The known solutions are, however, limited in their temporal resolving power, since several measurements offset in time have to be evaluated, or there is a need to use several sensors, which makes the construction of the measuring apparatus space-consuming and resource-intensive.

Proceeding from this, the invention is based on the object of providing a method and an evaluation unit which improve the determination of the yaw rate. This object is achieved by the method according to claim 1 and the evaluation unit according to claim 10. Further advantageous embodiments of the invention emerge from the subclaims and the following description of preferred exemplary embodiments of the present invention.

The exemplary embodiments show a method for determining the yaw rate of a target object, comprising receiving sensor data comprising multiple detections which describe the target object, estimating the position of the yaw center of the target object on the basis of the detections, and determining the yaw rate on the basis of the estimated Location of the greed center. The yaw rate describes the speed of rotation of an object around the vertical axis at a defined reference point, here called the yaw center. The multiple detections preferably provide a point cloud which describes the target object.

The vehicle can in particular be a driverless autonomous vehicle or a partially autonomous vehicle. For example, it can be a land, air or water vehicle, for example a driverless transport system (AGV), an autonomous car, a rail vehicle, a drone or a boat.

The sensor data originate, for example, from one or more sensors which are designed to detect the surroundings of a vehicle. The sensors can in particular be cameras, radar sensors, lidar sensors, ultrasonic sensors or the like.

The method preferably comprises a combination of a least squares estimation method of several detections with an orientation estimation based on the principal component analysis, together with an estimation of the yaw center.

The yaw rate is determined, for example, by solving an overdetermined model equation which estimates the movement of the target object. Here, for example, a model equation can be used which contains the amount of the target object speed and the yaw rate of the target object as unknowns.

The model equation is solved, for example, by inserting N detections or measuring points of the sensor data into the model equation in order to obtain an equation system with two unknowns and N equations.

The system of equations can be solved, for example, with the aid of a least square estimation method.

The sensor data are available, for example, as a point cloud that includes location and speed information of targets of the target object.

The position of the yaw center can be estimated, for example, by estimating the coordinates of the cluster center of the point cloud. For example, the cluster center can be determined as the center of gravity of the point cloud.

The location of the yaw center can also be estimated based on a principal component analysis. The orientation of the target object is determined, for example, with a main component analysis of the detections associated with the target object, in that the angle of the main components is evaluated.

For example, the position of the yaw center can be estimated as the center of a rear axle of the target object.

The exemplary embodiments also show an evaluation unit with a processor which is designed to carry out the method described here. The processor can be, for example, a computing unit such as a central processing unit (CPU) that executes program instructions.

The method can be implemented, for example, as a computer-implemented method that is carried out by a processor of an evaluation unit. The subject matter is therefore also a computer program that executes the method described here.

The detection, checking and processing, for example the determination of the yaw rate, is preferably carried out in real time. That is, the determination of the yaw rate of a target object on the basis of the sensor data, for example from a high-resolution radar, is preferably instantaneous. Instantaneous means here that the yaw rate is estimated within a measurement cycle, i.e. without any history information.

• 1 ein Blockdiagramm zeigt, das schematisch die Konfiguration eines Fahrzeugs gemäß einem Ausführungsbeispiel der vorliegenden Erfindung darstellt;
• 2 ein Blockdiagramm ist, das eine beispielhafte Konfiguration eines Steuergeräts für autonomes Fahren zeigt;
• 3 die von einem Radarsensor gemessenen Daten eines Fahrzeugs schematisch darstellt;
• 4 und 5 schematisch die schrittweise Bestimmung des Drehzentrums eines girierenden Fahrzeugs aus einer von einem Radarsensor bereit gestellten Punktwolke zeigen;
• 6 in einem Flussdiagram die Bestimmung des Drehzentrums eines girierenden Fahrzeugs aus einer von einem Radarsensor bereit gestellten Punktwolke schematisch darstellt; und
• 7 die Bestimmung der Gierrate eines girierenden Fahrzeugs aus einer von einem Radarsensor bereit gestellten Punktwolke bei bereits bestimmtem Drehzentrum zeigt.
• 8 eine mögliche Modellgleichung zur Berechnung der Gierrate verdeutlicht.

Embodiments will now be described by way of example and with reference to the accompanying drawings, in which:

• 1 Fig. 13 is a block diagram schematically showing the configuration of a vehicle according to an embodiment of the present invention;
• 2 Fig. 13 is a block diagram showing an exemplary configuration of an autonomous driving control device;
• 3 shows schematically the data of a vehicle measured by a radar sensor;
• 4th and 5 schematically show the step-by-step determination of the center of rotation of a gyrating vehicle from a point cloud provided by a radar sensor;
• 6th shows schematically in a flow diagram the determination of the center of rotation of a gyrating vehicle from a point cloud provided by a radar sensor; and
• 7th shows the determination of the yaw rate of a yawing vehicle from a point cloud provided by a radar sensor with an already determined center of rotation.
• 8th illustrates a possible model equation for calculating the yaw rate.

1 FIG. 13 is a block diagram schematically showing the configuration of a vehicle according to an embodiment of the present invention. The vehicle includes several components that are connected via a vehicle communication network 28 are connected to each other. The vehicle communication network 28 For example, a standard vehicle communication network installed in the vehicle such as a CAN bus (controller area network), a LIN bus (local interconnect network), a LAN bus (local area network), a MOST bus and / or a FlexRay Be a bus (registered trademark) or the like.

In the in 1 The example shown includes the autonomous vehicle 1 a control unit 12 (ECU 1). This control unit 12 controls a steering system. The steering system refers to the components that enable directional control of the vehicle. The autonomous vehicle 1 further comprises a control unit 14th (ECU 2) that controls a braking system. The braking system refers to the components that enable the vehicle to brake. The autonomous vehicle 1 further comprises a control unit 16 (ECU 3) that controls a power train. The drive train refers to the Drive components of the vehicle. The powertrain may include an engine, a transmission, a drive / propeller shaft, a differential, and a final drive.

The autonomous vehicle 1 further comprises a control unit for autonomous driving 18th (ECU 4). The control unit for autonomous driving 18th is designed to be the autonomous vehicle 1 to be controlled in such a way that it can operate completely or partially without the influence of a human driver in road traffic. The control unit for autonomous driving 18th , in the 2 and the associated description is described in more detail, controls one or more vehicle subsystems while the vehicle is operated in the autonomous mode, namely the braking system 14th , the steering system 12 and the drive system 14th . The control unit for autonomous driving can be used for this 18th for example via the vehicle communication network 28 with the corresponding control units 12 , 14th and 16 communicate.

The vehicle also includes one or more sensors 26th which are designed to detect the surroundings of the vehicle, the sensors being mounted on the vehicle and capture images of the surroundings of the vehicle, or to detect objects or states in the surroundings of the vehicle. The environment sensors 26th include in particular cameras, radar sensors, lidar sensors, ultrasonic sensors or the like. The environment sensors 26th can be arranged inside the vehicle or outside the vehicle (e.g. on the outside of the vehicle). For example, a camera can be provided in a front area of the vehicle for recording images of an area in front of the vehicle.

The vehicle sensor system of the vehicle also includes a satellite navigation unit 24 (GPS / GNSS unit). It should be noted that in the context of the present invention, GPS / GNSS is representative of all global navigation satellite systems (GNSS), such as GPS, A-GPS, Galileo, GLONASS (Russia), Compass (China), IRNSS (India) and the like .

The vehicle also includes a user interface 32 (HMI = Human-Machine-Interface) that enables a vehicle occupant to interact with one or more vehicle systems. This user interface 32 (for example a GUI = graphical user interface) can be an electronic display for outputting graphics, symbols and / or content in text form, and an input interface for receiving input (for example manual input, voice input and input by means of gestures, headers or Eye movements). The input interface can include, for example, keyboards, switches, touch-sensitive screens (touchscreens), eye trackers and the like.

If an operating state for autonomous driving is activated on the control side or on the driver side, the control unit determines for autonomous driving 18th , on the basis of available data about a specified route, environmental data recorded by environmental sensors, and vehicle operating parameters recorded by the vehicle sensors, which the control unit 18th from the control units 12 , 14th and 16 parameters for the autonomous operation of the vehicle (for example, target speed, target torque, distance to the vehicle ahead, distance to the edge of the road, steering process and the like).

For example, the control unit is for autonomous driving 18th designed to analyze and assess the route of surrounding vehicles, for example those of other road users.

2 FIG. 13 is a block diagram showing an exemplary configuration of a control unit for autonomous driving 18th (ECU 4). At the control unit for autonomous driving 18th it can for example be a control device (electronic control unit ECU or electronic control module ECM). The control unit for autonomous driving 18th (ECU 4) includes a processor 40 . At the processor 40 For example, it can be a computing unit such as a central processing unit (CPU) that executes program instructions. The processor of the control unit for autonomous driving 18th is designed to calculate an optimal driving position (following distance, lateral offset) while driving behind a vehicle in front, depending on the planned driving maneuver, based on the information from the sensor-based environment model, taking into account the permitted lane area. The calculated optimal driving position is used to control the actuators of the vehicle subsystems 12 , 14th and 16 , for example of braking, drive and / or steering actuators used. The control unit for autonomous driving 18th further comprises a memory and an input / output interface. The memory can consist of one or more non-transitory computer-readable media and comprises at least a program storage area and a data storage area. The program memory area and the data memory area can comprise combinations of different types of memory, for example read-only memory 43 (ROM = Read-only memory) and a random access memory 42 (RAM = Random Access Memory) (e.g. dynamic RAM ("DRAM"), synchronous DRAM ("SDRAM"), etc.). Furthermore, the control unit can be used for autonomous driving 18th an external storage drive 44 such as an external hard disk drive (HDD), a flash memory drive, or a non-volatile solid state drive (SSD). The control unit for autonomous driving 18th furthermore comprises a communication interface 45 via which the control unit connects to the vehicle communication network ( 28 in 2 ) can communicate.

3 shows schematically that of an environmental sensor 26th measured data of a vehicle. As an environmental sensor 26th For example, a high-resolution radar is used that has multiple detections for a target object P ₁ to P _N (“Targets”) that can be assigned to a target object using methods known to those skilled in the art. The principles of the invention are described below using a radar sensor. However, these principles can also be used for data from other types of sensors, such as ToF, lidar, ultrasound or camera sensors. The target object is, for example, a vehicle 50 with rear axle 51 . The radar is able to track the position of the detections P ₁ to P _N for example, to determine in a polar coordinate system (distance r _i and azimuth angle θ _i ), as well as to detect the radial velocity v _{r, i of} the detections. As a result, the radial speed distribution is v _{r, i} at different location points of the target object P ₁ to P _N known for a given measurement time. In the case of a purely translational movement, the measured speed vector v _i at the given measuring point P _i corresponds in magnitude and phase to the mean target object speed v '= mean value (v _i ). Methods are known for these situations in order to determine the object speed vector v _i from the measured radar detections, which will not be discussed in more detail at this point.

An additional rotation of the target object around the center of rotation (often given in the real environment, for example when cornering) with a yaw rate ω leads to an overlay of the mean target object speed v 'with the speed component v _{θ, i} , which is caused by the rotation of the target object. The superposition of these speed components influences the radial speed distribution v _{r, i} , which is recorded by the sensor. Due to the additional unknown variables (yaw rate ω, center of rotation), a general determination of the vehicle kinematics in a single cycle can no longer be carried out in a meaningful way. For this reason, the following procedure uses some assumptions about the shape and functionality of vehicles in order to simplify the mathematical problem of determining the yaw rate from the measured sensor data.

If a single-track model with front-axle steering is assumed to describe the kinematics of the target object (classic vehicle), the reference point around which the vehicle rotates can be precisely described through the center of the rear axle. This reference point is hereinafter referred to as the center of rotation 64 designated.

4th and 5 show schematically the step-by-step determination of the center of rotation of a gyrating vehicle from a point cloud provided by a radar sensor (also called “detections” or “targets”). Since there are several spatially distributed detections for a target object, the geometric extent and also the orientation of the target object can be determined. The orientation of the target object is determined, for example, with a main component analysis of the detections associated with the target object, in that the angle of the main components is evaluated.

In 4th an environmental sensor detects 26th , for example a radar sensor, in its field of view 260 a target object as a point cloud. The point cloud consists of individual detections, which are determined from distance measurements and direction measurements in the field of vision of the sensor. The point cloud or the individual detections contain not only distance (location) but also (relative) speed information. Therefore, the geometric extension and thus also the orientation of the target object, in this case the vehicle 50 , be determined. For this purpose, for example, the main components that are orthogonal to one another are used 61 and 62 determined from the point cloud using principal component analysis. Algorithms for this purpose are well known from the prior art. Furthermore, conclusions can also be drawn about the geometric extent of the target object from the point cloud. 4th shows in this regard how a rectangle is created using Least Square or another error function minimization method 60 is fitted into the point cloud. This rectangle 60 is used at this point as a simplified form of the target object and uses the knowledge that the target object is a vehicle 50 acts whose shape can be approximated as a rectangle.

The rectangle is fitted to the point cloud, for example, under the auxiliary condition that the respective sides of the rectangle a and b are orthogonal to the main components 61 and 62 stand. An error function f can then be determined, where f is the shortest distance between a point P _i and the rectangle 60 summed up and this function is minimized using the least square method or another error function minimization algorithm.

5 . shows the calculated rectangle 60 with side lengths a and b including main components 61 and 62 without the point cloud determined by the radar sensor. Once the rectangle 60 is determined, the position of the rear axle 63 can be estimated approximately. Hence the location of the rear axle 63 can be estimated by the fact that the rear axle 63 is assumed to be parallel to the rear of the vehicle at a distance L. The distance L can be set in advance, for example as L = 0.2 · max {a, b}. The rear of the vehicle can be made up of the side lengths a and b of the rectangle 60 and the mean speed vector v 'of the vehicle can be determined. Since vehicles are longer than they are wide, only one of the two shorter sides can be considered as the rear. So first it is determined whether a or b is shorter. It is now assumed that the vehicle is moving forward. In this case it can be assumed that the stern is the side which is in the opposite direction to the mean velocity v 'of the point cloud. If the rear is determined in this way, the location and orientation of the rear axle can be determined 63 be estimated. A further assumption is now made that the center of rotation 64 of the target object is in the middle of the rear axle 63 is located. In this way the location of the axis of rotation 64 must be assessed sufficiently to proceed with further yaw rate determination.

Simulations have confirmed that the exact position of the center of rotation does not need to be known to get a robust yaw rate estimate. For determining the center of rotation 64 Therefore, as an alternative, an estimate of the coordinates of the cluster center of the point cloud can also be used, which is already sufficient for the determination of the yaw rate described here. Using the cluster center as the yaw center is less computationally time consuming compared to calculating the rear axle.

als die Summe über alle minimalen Abstände zwischen einem Messpunkt P_i und dem Rechteck 60 repräsentiert durch die Funktion R(a,b). Anschließend wir in einem Schritt S63 aus den Punktgeschwindigkeiten v_i der Punktwolke die mittlere Fahrzeuggeschwindigkeit v' bestimmt. Hierbei gilt: $$v\text{'}=\frac{{\displaystyle {\sum }_i^N{v}_i}}{N}$$

wobei N die Anzahl der Punkte der Punktwolke ist. In einem nächsten Schritt S64 wird das Heck des Fahrzeugs aus der Richtung der mittleren Geschwindigkeit v' und den Rechtecksseitenlängen a und b bestimmt, wobei das Wissen ausgenutzt wird, dass nur die kürze Rechtecksseitenlänge min(a,b) als Heck in Frage kommt und angenommen wird, dass das Fahrzeug vorwärts fährt, das Heck folglich die Rechtecksseitenlänge ist, die sich in der entgegengesetzten Richtung der mittleren Geschwindigkeit v' befindet. In einem nächsten Schritt S65 werden Lage und Orientierung der Hinterachse 63 als parallel zum Heck und im Abstand L abgeschätzt. Für L kann zuvor ein Wert festgelegt werden. Zum Beispiel L = 0,2 · max{a,b}. In einem letzten Schritt S66 wird nun das Drehzentrum 64 als in der Mitte der Hinterachse 63 befindlich abgeschätzt. Auf diese Art ist nun der Ort des Drehzentrums 64 ausreichend bekannt, um zu einer robusten Abschätzung der Gierrate zu gelangen. 6th shows in a flow diagram the determination of the center of rotation of a gurgling vehicle from a point cloud provided by a radar sensor. The method is carried out, for example, by a sensor evaluation unit, such as a control unit for autonomous driving ( 18th in 1 ) or the like. In a first step S60 become the main components orthogonal to each other 61 and 62 determined from the point cloud of the radar sensor using principal component analysis. In an intermediate step S61 is made up of the main components 61 and 62 an angle φ is determined (see 8th ), which shows the relative orientation of the vehicle to the sensor 26th indicates. In a next step S62 the rectangle lengths a and b are determined using the point cloud and the main components. For this purpose, use is made of the knowledge that a and b are orthogonal to their respective main component and then the error function f is minimized using the least square method or another error function minimization method, so that the two a and b for which the error function f is determined becomes minimal. Here, the error function f can be expressed as follows, for example $$f\left(a,b\right)={\displaystyle \sum _{i=1}^N\text{min}\left\{{\left|P_i-\mathrm{R.}\left(a,b\right)\right|}^2\right\}}$$

as the sum of all minimum distances between a measuring point P _i and the rectangle 60 represented by the function R (a, b). Then we do it in one step S63 the mean vehicle speed v 'is determined from the point velocities v _{i of} the point cloud. The following applies here: $$v\text{'}=\frac{{\displaystyle {\sum }_i^N{v}_i}}{N}$$

where N is the number of points in the point cloud. In a next step S64 the rear of the vehicle is determined from the direction of the average speed v 'and the rectangular side lengths a and b, using the knowledge that only the short rectangular side length min (a, b) is possible as the rear and it is assumed that the vehicle drives forward, the tail is consequently the length of the rectangle which is in the opposite direction of the mean speed v '. In a next step S65 position and orientation of the rear axle 63 estimated to be parallel to the stern and at a distance L. A value can be specified for L beforehand. For example L = 0.2 * max {a, b}. In a final step S66 becomes the turning center 64 than in the middle of the rear axle 63 currently estimated. In this way is now the location of the turning center 64 known enough to arrive at a robust estimate of the yaw rate.

7th shows the determination of the yaw rate of a yawing vehicle from a point cloud provided by a radar sensor with an already determined center of rotation. The method is carried out, for example, by a sensor evaluation unit, such as a control unit for autonomous driving ( 18th in 1 ) or similar. In a first step S71 the point cloud is received first, which is supplied by a sensor and represents the measurement data of this sensor. The sensor can be a radar, a lidar or a camera sensor. The point cloud consists of distance measurements of a detected object in the field of view of the sensor. In addition to distance (location) information, the point cloud also contains (relative) speed information. In a second step S72 the center of rotation of the object is determined from the point cloud. For example, the in 6th procedure described. According to the procedure of 6th the target object orientation is determined by principal component analysis. In another variant, the target object orientation can be obtained from another source instead of the main component analysis. This can be determined with the help of another sensor in a fusion system (e.g. lidar or camera). Or by using a priori knowledge (e.g. cross traffic at the intersection). In a third step S73 will be the points P ₁ to P _N the point cloud is used in a model equation that contains the two unknowns amount of target object speed v and yaw rate ω. The model equation typically describes the movement behavior of a vehicle, which in turn is approximated as a rectangle with side lengths a and b. The model equation is over-determined with two unknowns and N> 2 measuring points. The model equation is therefore evaluated for several detections from one measurement cycle, which results in an overdetermined system of equations with two unknowns and N equations, where N stands for the number of detections considered (points of the point cloud). This system of equations is solved using a least squares estimation method and an estimate of the yaw rate ω and the magnitude of the speed vector v is obtained. In a fourth step S74 the calculated yaw rate ω is now output so that other systems in the vehicle, for example a parking, braking or driving assistant, can use this for their function.

Since several spatially distributed detections are available for a target object, the geometric extent and thus also the orientation of the target object can be determined. The orientation of the target object is determined, for example, with a main component analysis of the detections associated with the target object, in that the angle of the main components is evaluated. To determine the center of rotation, the assumption is made that an estimate based on the coordinates of the cluster center is sufficient. Simulations have confirmed that the exact position of the center of rotation does not need to be known to get a robust yaw rate estimate. There remain two unknowns (amount of target object speed and yaw rate) for a model equation, so the equation is underdetermined. The model equation is therefore evaluated for several detections from one measurement cycle, which results in an over-determined system of equations with two unknowns and N equations, where N stands for the number of detections considered. This system of equations is solved using a least squares estimation method and an estimate of the yaw rate and the magnitude of the speed vector is obtained.

The exemplary embodiments thus show a combination of a least squares estimation method of several detections with an orientation estimation based on the principal component analysis, together with an estimation of the center of rotation. As a result, the amount of speed and the yaw rate of the object can be evaluated within one measuring cycle with just one radar sensor. The methods described so far are dependent on at least two radar sensors to estimate the yaw rate of a target object in one measuring cycle, or, if one radar sensor is used, require several measuring cycles to determine the yaw rate.

8th illustrates a model equation as described in 7th was used to estimate the yaw rate ω.

Hierbei bezeichnen die einzelnen Variablen folgende physikalische Größen, wie in 8 dargestellt: θ, r und v_D bezeichnen den vom Sensor 26 gemessenen Winkel, Abstand und Radialgeschwindigkeit einer Detektion (vgl. 3). φ bezeichnet den mittels Hauptachsentransformation ermittelten Orientierungswinkel des Fahrzeugs 10 relativ zum Sensor 26 (vgl. Schritt S61 in 6). x_R und y_R bezeichnen die Koordinaten des Gierzentrums 64 (wie beispielsweise gemäß dem Verfahren der 6 ermittelt), ω bezeichnet die gesuchte Gierrate des Fahrzeugs und v die Lineargeschwindigkeit des Fahrzeugs 10, die vom Sensor 26 gemessene Radialgeschwindigkeit des Fahrzeugs 10.A model equation to describe the movement, especially the rotation of a vehicle 10 that can be used to estimate yaw rate, as in step S73 of the 7th is described, for example: $$v_{\mathrm{D.}}=v\cdot \text{cos}\left(\theta -\phi \right)+\omega \cdot \left(y_{\mathrm{R.}}\cdot \text{cos}\left(\theta \right)-x_{\mathrm{R.}}\cdot \text{sin}\left(\theta \right)\right)$$

The individual variables designate the following physical quantities, as in 8th shown: θ, r and v _D denote that of the sensor 26th measured angle, distance and radial speed of a detection (cf. 3 ). φ denotes the orientation angle of the vehicle determined by means of the main axis transformation 10 relative to the sensor 26th (see step S61 in 6th ). x _R and y _R denote the coordinates of the Greed center 64 (such as according to the procedure of 6th determined), ω denotes the searched yaw rate of the vehicle and v the linear velocity of the vehicle 10 taken from the sensor 26th measured radial speed of the vehicle 10 .

The point cloud ℘ that the sensor delivers consists of N detections with at least the entries r _i , v _{D, i} and θ _i : $$=\left\{P_1\left({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="DE102019204408A1\_0012.png,DE102019204408A1\_0014.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,v_{\mathrm{D.}\mathrm{,1}},{\theta }_1\right),\mathrm{...},P_i\left(r_i,v_{\mathrm{D.},i},{\theta }_i\right),\mathrm{...},P_N\left(r_N,{\text{v}}_{\mathrm{D.},N},{\theta }_N\right)\right\}$$

The values x _R and y _R (coordinates of the yaw center 6th ) and the orientation angle <p were obtained from the principal component analysis (see 4th to 6th ) certainly. Thus, only the linear velocity v and the yaw rate ω remain as unknown quantities in the model equation.

Gleichung (2) kann nun auf jedes Element der Punktwolke P_i ∈ ℘ angewendet werden, sodass ein Gleichungssystem mit N Gleichungen entsteht. Dieses kann als Vektorgleichung mit den Vektoren $\overrightarrow{y}$

und $\overrightarrow{p}$

sowie der Matrix X dargestellt werden: $$\underset{\overrightarrow{y}}{\underbrace{\left[\begin{array}{c}{v}_{D\mathrm{,1}}\\ ⋮\\ v_{D,N}\end{array}\right]=}}\underset{X}{\underbrace{\left[\begin{array}{cc}\text{cos}\left({\theta }_1-\phi \right)& y_R\cdot \text{cos}\left({\theta }_1\right)-x_R\cdot \text{sin}\left({\theta }_1\right)\\ ⋮& ⋮\\ \text{cos}\left({\theta }_N-\phi \right)& {\text{y}}_R\cdot \text{cos}\left({\theta }_N\right)-x_R\cdot \text{sin}\left({\theta }_N\right)\end{array}\right]\cdot }}\underset{\overrightarrow{p}}{\underbrace{\left[\begin{array}{c}v\\ \omega \end{array}\right]}}$$

Equation (1) can be represented as the scalar product of two vectors, where the second vector contains the unknowns v and ω: $$v_{\mathrm{D.}}=\left[\text{cos}\left(\theta -\phi \right)y_{\mathrm{R.}}\cdot \text{cos}\left(\theta \right)-x_{\mathrm{R.}}\cdot \text{sin}\left(\theta \right)\right]\cdot \left[\begin{array}{c}v\\ \omega \end{array}\right]$$

Equation (2) can now be applied to every element of the point cloud P _i ∈ ℘, so that an equation system with N equations is created. This can be used as a vector equation with the vectors $\overrightarrow{y}$

and $\overrightarrow{p}$

as well as the matrix X: $$\underset{\overrightarrow{y}}{\underbrace{\left[\begin{array}{c}{v}_{\mathrm{D.}\mathrm{,1}}\\ ⋮\\ v_{\mathrm{D.},N}\end{array}\right]=}}\underset{X}{\underbrace{\left[\begin{array}{cc}\text{cos}\left({\theta }_1-\phi \right)& y_{\mathrm{R.}}\cdot \text{cos}\left({\theta }_1\right)-x_{\mathrm{R.}}\cdot \text{sin}\left({\theta }_1\right)\\ ⋮& ⋮\\ \text{cos}\left({\theta }_N-\phi \right)& {\text{y}}_{\mathrm{R.}}\cdot \text{cos}\left({\theta }_N\right)-x_{\mathrm{R.}}\cdot \text{sin}\left({\theta }_N\right)\end{array}\right]\cdot }}\underset{\overrightarrow{p}}{\underbrace{\left[\begin{array}{c}v\\ \omega \end{array}\right]}}$$

umgestellt werden. Für die Least-Square-Verfahrensschätzung empfiehlt sich eine weitere Transposition von X, sodass eine weitere Gleichung erhalten wird: $${\overrightarrow{p}}_{LSQ}={\left(X^T\cdot X\right)}^{-1}\cdot X^T\cdot \overrightarrow{y}$$

By inverting the matrix X, equation (3) can be obtained from $\overrightarrow{p}$

be changed. For the least square method estimation, another transposition of X is recommended, so that another equation is obtained: $${\overrightarrow{p}}_{\mathrm{L.}\mathrm{S.}Q}={\left(X^T\cdot X\right)}^{-1}\cdot X^T\cdot \overrightarrow{y}$$

und damit v und ω mittels Least-Square-Schätzverfahren aus Gleichung (4) bestimmt/geschätzt werden.Since the system of equations is overdetermined, as already mentioned above, $\overrightarrow{p}$

and thus v and ω are determined / estimated using the least square estimation method from equation (4).

List of reference symbols

10

vehicle

12th

ECU 1 braking system

14th

ECU 2 powertrain

16

ECU 3 steering system

18th

ECU 4 control unit for autonomous driving

20th

Safety ECU

24

GNSS

26th

Environment sensors (radar)

28

Vehicle communication network

30th

Emergency stop ECU

32

HMI

50

Vehicle and target

51

Rear axle of the vehicle 50

61

Main component

62

Main component

60

rectangle

63

Rear axle

64

Greed center

260

Field of view of sensor 26

P ₁ , ... P _N

Point cloud of the target object

QUOTES INCLUDED IN THE DESCRIPTION

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Patent literature cited

• DE 102013019804 A1 [0003]

Claims (10)

Method for determining the yaw rate (ω) of a target object (50), comprising receiving sensor data which include several detections (P ₁ , ... P _N ) which describe the target object (50), estimating the position of the yaw center ( 64) of the target object (50) on the basis of the detections (P ₁ , ... P _N ), as well as determining the yaw rate (ω) on the basis of the estimated location of the yaw center (64). Procedure according to Claim 1 , in which the orientation (<p) of the target object (50) is determined on the basis of a principal component analysis. Procedure according to Claim 1 or 2 which comprises a least square estimation method based on multiple detections (P ₁ , ... P _N ). Method according to one of the preceding claims, wherein the yaw rate (ω) is determined by solving an over-determined model equation (equation (4)) which estimates the movement of the target object (50). Procedure according to Claim 4 wherein a model equation is used which contains as unknowns the magnitude of the target object speed (v) and the yaw rate (ω) of the target object (50). Procedure according to Claim 4 or 5 , solving the model equation by inserting N detections of the sensor data (P ₁ to P _N ) into the model equation to obtain an equation system with two unknowns (v, ω) and N equations. Method according to one of the preceding claims, wherein the position of the yaw center (64) takes place by estimating the coordinates of the cluster center of the detections (P ₁ , ... P _N ). Method according to one of the preceding claims, wherein the position of the yaw center (64) is estimated on the basis of a principal component analysis. Method according to one of the preceding claims, wherein the position of the yaw center (64) is estimated as the center of a rear axle (63) of the target object. Device, comprise a processor which is designed to perform the method according to one of the Claims 1 to 9 perform.

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