DE102019204408B4 - Method for determining the yaw rate of a target object based on sensor data, for example from a high-resolution radar - Google Patents

Abstract

A method for determining the yaw rate (ω) of a target object (50), the target object (50) being a vehicle, comprising receiving sensor data comprising a plurality of detections (P1, ... PN) describing the target object (50). , estimating the location of the yaw center (64) of the target object (50) based on the detections (P1, ...PN), and determining the yaw rate (ω) based on the estimated location of the yaw center (64),• wherein the Position of the yaw center (64) is determined by determining the mutually orthogonal main components (61, 62) from the detections (P1, ... PN) by means of main component analysis, determining an orientation (φ) of the target object (50). Based on the main components (61, 62), a shape of the target object (50) is approximated as a rectangle (60) with rectangle sides (a, b), which are orthogonal to the main components (61, 62), the rectangle sides ( a, b) by least square minimization of the error func tion (f)ƒ(a,b)=∑i=1Nmin{|Pi−R(a,b)|2}, which represents the sum over all minimum distances between a detection (Pi) and the rectangle (60), are determined,o the average speed (vi) of the target object (50) is determined from point speeds (vi) of the detections (P1, ...PN),o the rear of the vehicle as the shortest (min(a,b)) of the rectangle sides (a,b), which is in the opposite direction of the mean velocity (vi),o location and orientation of a rear axle (63) is determined to be parallel to the rear at a distance L = 0.2 max{a,b} is determined,o the yaw center (64) is determined as being in the middle of the rear axle (63), and• the yaw rate (ω) is determined by determining the position of the yaw center (64) according to the aforementioned method steps, comprising the determination of the orientation (φ) of the target object (50) on the basis of the principal components (61, 62), and the detections (P1, ... PN) in a model equation that Bewe behavior of the vehicle in the form of the rectangle (60), a system of equations with two unknowns (v, ω) and N equations being obtained, the system of equations being solved with least squares minimization and the calculated yaw rate (ω) being output becomes.

Description

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

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

Solutions from the prior art are already known which are able to determine the yaw rate of a vehicle based on sensor data. So determined in patent disclosure DE 10 2013 019 804 A1 disclosed device the yaw rate of another vehicle using two sensors.

The EP 3 415 945 A1 discloses a method for determining the yaw rate of a target vehicle, a first line perpendicular to the orientation of the target and running through the center of the target being determined from radar data, a second line running through the center of rotation of the target being determined, the intersection of the first and second lines is determined, from which the position of the pivot point is determined and the yaw rate is estimated.

The EP 3 285 230 A1 discloses a vehicle environment detection system comprising at least one detector and at least one processing unit, the vehicle environment detection system being arranged to detect at least two feature points on objects external to a vehicle.

The EP 3 415 948 A1 discloses a method for determining the range of range of a target in a horizontal plane by a radar-equipped lead vehicle.

The EP 3 151 034 A1 discloses a radar system including a radar sensor wherein a yaw rate of a target vehicle at the current time is determined based on a current frequency range of a current azimuth angle.

The DE 10 2008 025 773 A1 discloses a method for estimating a position and movement state of an observed object, in which a distance to the object is determined, a displacement of at least part of the object in the image of a camera is detected and at least one parameter of the position and movement state, taking into account a movement model of the observed object is estimated, one of the parameters being a yaw rate or a lateral velocity.

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

However, the known solutions are limited in terms of the temporal resolution, since a number of measurements that are offset in time have to be evaluated, or there is a need to use a number of sensors, which makes the construction of the measuring apparatus space- and resource-intensive.

Proceeding from this, the object of the invention is to provide a method and an evaluation unit which improves the determination of the yaw rate. This object is achieved by the method according to claim 1 and the evaluation unit according to claim 3. Further advantageous refinements of the invention result from the dependent claims 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, which includes a plurality of detections that describe the target object, estimating the position of the yaw center of the target object based on the detections, and determining the yaw rate based on the estimated location of the craving center. The yaw rate describes the rotational speed of an object around the vertical axis at a defined reference point, here called the yaw center. Preferably, the multiple detections provide a point cloud that describes the target object.

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

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

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

According to the invention, the yaw rate is determined by solving an overdetermined model equation which estimates the movement of the target object. A model equation is used here, which contains the amount of the target object speed and the yaw rate of the target object as unknowns.

The model equation is solved according to the invention by inserting N detections or measurement 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 is solved using a least squares estimation method.

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

The location 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 centroid of the point cloud.

The location of the yaw center is also estimated based on a principal component analysis. The orientation of the target object is determined with a main component analysis of the detections associated with the target object by evaluating the angle of the main components.

According to the invention, the position of the yaw center is 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 executed by a processor of an evaluation unit. The subject matter is therefore also a computer program that executes the methods described here.

The detection, checking and processing, for example the determination of the yaw rate, preferably takes place in real time. This means that the yaw rate of a target object is preferably determined instantaneously on the basis of the sensor data, for example from a high-resolution radar. Instantaneous means here that the yaw rate is estimated within one measurement cycle, i.e. without historical 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 12 is a block diagram schematically showing the configuration of a vehicle according to an embodiment of the present invention;
• 2 Fig. 12 is a block diagram showing an example configuration of an autonomous driving controller;
• 3 schematically represents the data of a vehicle measured by a radar sensor;
• 4 and 5 schematically show the step-by-step determination of the center of rotation of a yawing vehicle from a point cloud provided by a radar sensor;
• 6 in a flow chart, the determination of the center of rotation of a yawring vehicle is shown schematically from a point cloud provided by a radar sensor; and
• 7 shows the determination of the yaw rate of a yawing vehicle from a point cloud provided by a radar sensor with the center of rotation already determined.
• 8th illustrates a possible model equation for calculating the yaw rate.

1 12 is a block diagram schematically showing the configuration of a vehicle according to an embodiment of the present invention. The vehicle includes a number of components which are connected to one another via a vehicle communication network 28 . The vehicle communication network 28 may be, for example, an in-vehicle standard vehicle communication network such as a controller area network (CAN) bus, a local interconnect network (LIN) bus, a local area network (LAN) bus, a MOST bus, and/or a FlexRay bus (registered trademark) or the like.

in the in 1 illustrated example, the autonomous vehicle 1 includes 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 includes a control unit 14 (ECU 2) that controls a braking system. The braking system refers to the components that allow the vehicle to brake. The autonomous vehicle 1 further includes a control unit 16 (ECU 3) that controls a powertrain. The powertrain refers to the drive components of the vehicle. The powertrain may include an engine, transmission, driveshaft/propeller shaft, differential, and final drive.

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

The vehicle also includes one or more sensors 26 which are designed to detect the vehicle's surroundings, the sensors being mounted on the vehicle and capturing images of the vehicle's surroundings, or recognizing objects or conditions in the vehicle's surroundings. Surroundings sensors 26 include, in particular, cameras, radar sensors, lidar sensors, ultrasonic sensors or the like. The surroundings sensors 26 can be arranged inside the vehicle or outside the vehicle (eg 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 human-machine interface (HMI) 32 that allows a vehicle occupant to interact with one or more vehicle systems. This user interface 32 (e.g., a GUI = graphical user interface) may include an electronic display for outputting graphics, symbols, and/or content in text form, and an input interface for receiving input (e.g., manual input, voice input, and input by gestures, head or eye movements). For example, the input interface may include keyboards, switches, touch screens, 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 for autonomous driving 18 determines based on available data over a specified route, environmental data recorded by environmental sensors, and vehicle operating parameters recorded by the vehicle sensors, which are sent to control unit 18 by control units 12, 14 and 16, parameters for the autonomous operation of the vehicle (for example target speed, target torque, distance to the vehicle in front, distance to the edge of the road, steering operation and the like). For example, the control unit for autonomous driving 18 is designed to analyze and assess the driving path of surrounding vehicles, for example vehicles of other road users.

2 12 is a block diagram showing an example configuration of an autonomous driving control unit 18 (ECU 4). The control unit for autonomous driving 18 can be, for example, a control device (electronic control unit ECU or electronic control module ECM). The autonomous driving control unit 18 (ECU 4) includes a processor 40. The processor 40 may be, for example, a computing unit such as a central processing unit (CPU) that executes program instructions. The processor of the control unit for autonomous driving 18 is designed to calculate an optimal driving position (following distance, lateral offset) when 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 permissible lane area. The calculated optimal driving position is used to control actuators of the vehicle subsystems 12, 14 and 16, for example brake, drive and/or steering actuators. The autonomous driving control unit 18 further includes a memory and an input/output interface. The memory may be one or more non-transitory computer-readable media and includes at least a program storage area and a data storage area. The program memory area and data memory area may include combinations of different types of memory, such as read-only memory (ROM) 43 and random access memory (RAM) 42 (e.g., dynamic RAM ( "DRAM"), synchronous DRAM ("SDRAM"), etc.). Further, the autonomous driving control unit 18 may include 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 18 also includes a communication interface 45, via which the control unit communicates with the vehicle communication network (28 in 2 ) can communicate.

3 shows schematically the data of a vehicle measured by an environment sensor 26 . A high-resolution radar, for example, is used as the environmental sensor 26, which generates a plurality of detections P ₁ to P _N (“targets”) for a target object, which 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 applied to data from other types of sensors, such as ToF, lidar, ultrasonic or camera sensors. The target object here is, for example, a vehicle 50 with a rear axle 51. The radar is able to determine the position of the detections P ₁ to P _N , for example in a polar coordinate system (distance r _i and azimuth angle θ _i ), as well as the To capture radial velocity v _r,i of the detections. As a result, the radial velocity distribution v _r,i at various locations of the target object P ₁ to P _N is known for a given measurement time. In the case of a pure translational movement, the measured velocity vector v _i at the given measuring point P _i agrees in magnitude and phase with the mean target object velocity v'=mean value (vi). For these situations, methods are known for determining the object speed vector v _i from the measured radar detections, which will not be discussed in 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 a superimposition of the average target object speed v' with the speed component v _θ,i caused by the rotation of the target object. The superposition of these velocity components affects the radial velocity distribution v _r,i 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 form and functionality of vehicles to simplify the mathematical problem of determining the yaw rate from the measured sensor data.

If one assumes a single-track model with front-axle steering (classic vehicle) to describe the kinematics of the target object, the reference point around which the vehicle rotates can be represented by the cent around the rear axle. This reference point is referred to below as the center of rotation 64 .

4 and 5 show schematically the step-by-step determination of the center of rotation of a yawring 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 by evaluating the angle of the main components.

In 4 an environment sensor 26, for example a radar sensor, detects a target object as a point cloud in its field of view 260. The point cloud consists of individual detections, which are determined from distance measurements and direction measurements in the field of view of the sensor. The point cloud or the individual detections contain not only distance (location) but also (relative) speed information. Therefore, the geometric extent and thus also the orientation of the target object, in this case the vehicle 50, can be determined. For this purpose, according to the invention, the main components 61 and 62, which are orthogonal to one another, are determined from the cloud of points by means of main 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 cloud of points. 4 shows in this regard how, according to the invention, a rectangle 60 is fitted into the point cloud by means of least squares or another error function minimization method. This rectangle 60 is used here as a simplified shape of the target and takes advantage of the knowledge that the target is a vehicle 50 whose shape can be approximated as a rectangle.

The rectangle is fitted to the point cloud under the auxiliary condition that the respective rectangle sides a and b are orthogonal to the principal components 61 and 62. An error function f is then determined, where f sums up the respective shortest distances between a point Pi and the rectangle 60 and this function is minimized using the least squares method.

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 location of the rear axle 63 can be approximately estimated. According to the invention, the location of the rear axle 63 is estimated by assuming that the rear axle 63 is parallel to the rear of the vehicle at a distance L. The distance L is set in advance as L = 0.2 - max {a,b}. The rear of the vehicle is determined from the side lengths a and b of the rectangle 60 and the mean velocity vector v' of the vehicle. 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 running forward. In this case, the tail can be assumed to be the side that is in the opposite direction to the mean velocity v' of the point cloud. With the rear determined in this way, the location and orientation of the rear axle 63 is estimated. Now, as a further assumption, the center of rotation 64 of the target is at the center of the rear axle 63 . In this manner, the location of the axis of rotation 64 is sufficiently estimated to proceed with further yaw rate determination.

Simulations have confirmed that the position of the center of rotation does not need to be known exactly to obtain a robust yaw rate estimate. For the determination of the center of rotation 64, an estimation of the coordinates of the cluster center of the point cloud can therefore alternatively be used, which is already sufficient for the determination of the yaw rate described here. Using the cluster center as the yaw center requires less computing time 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 vi 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 = 0,2 - max {a, b} abgeschätzt. 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. 6 shows in a flow chart the determination of the center of rotation of a yawing 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 (18 in 1 ) or the like executed. In a first step S60, the mutually orthogonal main components 61 and 62 are determined from the point cloud of the radar sensor by means of main component analysis. In an intermediate step S61, an angle φ is determined from the principal components 61 and 62 (see 8th ), which indicates the relative orientation of the vehicle to the sensor 26. In a next step S62, the rectangle lengths a and b are determined using the point cloud and the principal components. For this purpose, the knowledge is used that a and b are orthogonal to their respective main components den and then the error function f is minimized using the least squares method or another error function minimization method, so that the two a and b are determined for which the error function f is minimal. Here, according to the present invention, the error function f can be expressed as follows $$ƒ\left(a,b\right)={\displaystyle \sum _{i=1}^N\text{at least}\left\{{\left|P_i-R\left(a,b\right)\right|}^2\right\}}$$

as the sum over all minimum distances between a measuring point P _i and the rectangle 60 represented by the function R(a,b). Then, in a step S63, the average vehicle speed v` is determined from the point speeds vi 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 shorter rectangular side length min(a,b) is possible as the rear and is assumed becomes that the vehicle is moving forward, hence the tail is the rectangle side length which is in the opposite direction of the mean speed v'. In a next step S65, the position and orientation of the rear axle 63 are estimated as being parallel to the rear and at a distance L=0.2-max {a, b}. In a final step S66, the center of rotation 64 is estimated to be in the center of the rear axle 63. In this way, the location of the center of rotation 64 is now sufficiently known to provide a robust estimate of the yaw rate.

7 shows the determination of the yaw rate of a yawing vehicle from a point cloud provided by a radar sensor with the center of rotation already determined. The method is carried out, for example, by a sensor evaluation unit, such as a control unit for autonomous driving (18 in 1 ) or similar. In a first step S71, the point cloud is initially received, 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), 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 this purpose, according to the invention, the 6 procedures described are used. According to the procedure of 6 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 using 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, the points P ₁ to P _N of the cloud of points are inserted into a model equation that contains the two unknown amounts of the 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 overdetermined with two unknowns and N > 2 measurement points. Therefore, the model equation is evaluated for several detections from one measurement cycle, which results in an overdetermined equation system 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 absolute value of the velocity vector v is obtained. In a fourth step S74, the calculated yaw rate ω is output so that other systems of the vehicle, for example a parking, braking or driving assistant, can use this for their function.

Since there are several spatially distributed detections 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 by evaluating the angle of the main components. For the determination of the center of rotation, the assumption is made that an estimate of the coordinates of the cluster center is sufficient. Simulations have confirmed that the position of the center of rotation does not need to be known exactly to obtain a robust yaw rate estimate. Two unknowns remain (magnitude of target object velocity and yaw rate) for a model equation, so the equation is underdetermined. Therefore, the model equation is evaluated for several detections from one measurement cycle, resulting in an overdetermined 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 absolute value of the velocity vector is obtained.

The exemplary embodiments thus show a combination of a least squares estimation method from several detections with an orientation estimation based on the principal component analysis, together with an estimation of the center of rotation. This means that the speed and yaw rate of the object can be evaluated within a measurement cycle using just one radar sensor. Methods described so far are dependent on at least two radar sensors in one measurement cycle for estimating the yaw rate of a target object, or, when using one radar sensor, require several measurement cycles in order to determine the yaw rate.

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

A model equation for describing the movement, in particular the turning of a vehicle 10, which can be used to estimate the yaw rate, as in step S73 of FIG 7 described, for example: $$v_D=v\cdot \text{cos}\left(\theta -\phi \right)+\omega \cdot \left(y_R\cdot \text{cos}\left(\theta \right)-x_R\cdot \text{sin}\left(\theta \right)\right)$$

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

The point cloud ℘ provided by the sensor consists of N detections with at least the entries r _i , v _D,i and θ _i : $$\mathcal{R}=\left\{P_1\left({\mathrm{right}}_1,v_{D\mathrm{,1}},{\theta }_1\right),...,P_i\left({\mathrm{right}}_i,v_{D,i},{\theta }_i\right),...,P_N\left({\mathrm{right}}_N,v_{D,N},{\theta }_N\right)\right\}$$

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

Equation (1) can be represented as the dot product of two vectors, where the second vector contains the unknowns v and ω: $$v_D=\left[\text{cos}\left(\theta -\phi \right)y_R\cdot \text{cos}\left(\theta \right)-x_R\cdot \text{sin}\left(\theta \right)\right]\cdot \left[\begin{array}{c}v\\ \omega \end{array}\right]$$

und $\overrightarrow{p},$

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

Equation (2) can now be applied to each element of the point cloud P _i ∈ ℘, resulting in an equation system with N equations. This can be written as a vector equation using the vectors $\overrightarrow{y}$

and $\overrightarrow{p},$

and the matrix X can be represented: $$\begin{array}{l}\left[\begin{array}{c}{v}_{D\mathrm{,1}}\\ ⋮\\ v_{D,N}\end{array}\right]=\left[\begin{array}{cc}cOs\left({\mathrm{<figure-callout\; id="1"\; label="\theta "\; filenames="DE102019204408B4\_0014.png,DE102019204408B4\_0016.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_1-\phi \right)& y_R\cdot \text{cos}\left({\theta }_1\right)-x_R\cdot \text{sin}\left({\theta }_1\right)\\ ⋮& ⋮\\ cOs\left({\theta }_N-\phi \right)& y_R\cdot \text{cos}\left({\theta }_N\right)-x_R\cdot \text{sin}\left({\theta }_N\right)\end{array}\right]\cdot \left[\begin{array}{c}v\\ \omega \end{array}\right]\\ \underset{\overrightarrow{y}}{\underbrace{}}\underset{X}{\underbrace{}}\underset{\overrightarrow{p}}{\underbrace{}}\end{array}$$

umgestellt werden. Für die Least-Square-Verfahrensschätzung empfiehlt sich eine weitere Transposition von X, (3) sodass eine weitere Gleichung erhalten wird: $${\overrightarrow{p}}_{LSQ}={\left(X^T\cdot X\right)}^{-1}\cdot X^T\cdot \overrightarrow{y}$$

Equation (3) can be obtained by inverting the matrix X $\overrightarrow{p}$

be switched. For the least squares method estimation, a further transposition of X, (3) is recommended, so that another equation is obtained: $${\overrightarrow{p}}_{LSQ}={\left(X^T\cdot X\right)}^{-1}\cdot X^T\cdot \overrightarrow{y}$$

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 least squares estimation methods from equation (4).

Claims (3)

Method for determining the yaw rate (ω) of a target object (50), the target object (50) being a vehicle, comprising receiving sensor data which include a plurality of detections (P ₁ , ... P _N ) which the target object (50 ) describe estimating the location of the yaw center (64) of the target object (50) based on the detections (P ₁ , ...P _N ), and determining the yaw rate (ω) based on the estimated location of the yaw center (64) , • the position of the center of yaw (64) being determined in that o the mutually orthogonal main components (61, 62) are determined from the detections (P ₁ , ... P _N ) by means of principal component analysis, o a determination of an orientation (φ ) of the target object (50) on the basis of the main components (61, 62), o a shape of the target object (50) as a rectangle (60) is approximated with rectangle sides (a, b), which are orthogonal to the main components (61, 62 ) where the rectangle sides (a, b) are determined by least square minimization g of the error function (f) $$ƒ\left(a,b\right)={\displaystyle \sum _{i=1}^N\text{at least}\left\{{\left|P_i-R\left(a,b\right)\right|}^2\right\}}$$

, which represents the sum of all minimum distances between a detection (P _i ) and the rectangle (60), can be determined, o from point velocities (vi) of the detections (P ₁ , ...P _N ) the mean velocity (vi) of the target object (50) is determined, o the rear of the vehicle is determined as the shortest (min(a,b)) of the rectangle sides (a, b), which is in the opposite direction of the mean speed (vi), o position and orientation of a rear axle (63) is determined to be parallel to the rear at a distance L = 0.2 · max{a,b}, o the yaw center (64) is determined to be at the center of the rear axle (63), and • where the yaw rate (ω) is determined by determining the position of the yaw center (64) according to the aforementioned method steps, including determining the orientation (φ) of the target object (50) on the basis of the main components (61, 62), and the detections (P ₁ , ...P _N ) into a model equation that describes the movement behavior of the describes the vehicle in the form of the rectangle (60), a system of equations with two unknowns (v, ω) and N equations being obtained, the system of equations being solved with least squares minimization and the calculated yaw rate (ω) being output. procedure after claim 1 , the location of the yaw center (64) being determined by estimating the coordinates of the cluster center of the detections (P ₁ ,...P _N ). Apparatus comprising a processor adapted to perform the method of any one of Claims 1 , 2 to perform.

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