阅读说明：本技术 确定估计速度的不确定性估计的方法 (Method for determining an uncertainty estimate of an estimated velocity ) 是由 M·斯塔希尼克 D·凯斯拉尔 于 2019-08-14 设计创作，主要内容包括：确定估计速度的不确定性估计的方法,其中该方法包括：确定不确定性估计的第一部分,该第一部分表示相对于对象的速度分布方程的第一估计系数和第二估计系数的不确定性,第一估计系数被分配至估计速度的第一空间维度,并且第二估计系数被分配至估计速度的第二空间维度,其中,速度分布方程根据第一估计系数和第二估计系数来表示估计速度；确定不确定性估计的第二部分,该第二部分表示相对于对象的角速度、对象在第二空间维度中的第一坐标以及对象在第一空间维度中的第二坐标的不确定性；以及基于第一部分和第二部分确定不确定性估计。(A method of determining an uncertainty estimate of an estimated velocity, wherein the method comprises: determining a first portion of an uncertainty estimate representing uncertainty of a first estimation coefficient and a second estimation coefficient of a velocity profile equation with respect to the object, the first estimation coefficient being assigned to a first spatial dimension of the estimated velocity and the second estimation coefficient being assigned to a second spatial dimension of the estimated velocity, wherein the velocity profile equation represents the estimated velocity in terms of the first estimation coefficient and the second estimation coefficient; determining a second portion of the uncertainty estimate, the second portion representing an uncertainty with respect to the angular velocity of the object, the first coordinate of the object in the second spatial dimension, and the second coordinate of the object in the first spatial dimension; and determining an uncertainty estimate based on the first portion and the second portion.)

1. Determining an estimated velocity of an object (2)

wherein the method comprises the following steps:

determining the uncertainty estimateFirst part of

Determining a second portion of the uncertainty estimate

based on the first part

2. The method of claim 1, wherein the first and second light sources are selected from the group consisting of,

wherein the uncertainty estimate

Wherein the second part

3. The method according to claim 1 or 2,

wherein the uncertainty estimate

4. The method according to any one of the preceding claims,

wherein the first portion is determined based on

-representing the first estimation coefficient

-representing the first estimation coefficient

5. The method of claim 4, wherein the first and second light sources are selected from the group consisting of,

wherein a plurality of detection points (6, 6') and at least one constant (k) based on the object (2)_{ols_bias_scale}、k_{c_var_bias}、k_{s_var_bias}) To determine the deviation portion

Wherein each of the plurality of detection points (6, 6') comprises an estimated velocity assigned to a detection position on the object (2)

6. The method according to any one of the preceding claims,

wherein the estimated speedA position (x) assigned to the object (2)_t,i，y_t,i) By the first coordinate (x) of the object (2) in the first spatial dimension (x)_t,i) And the second coordinate (y) of the object (2) in the second spatial dimension (y)_t,i) Represents said position (x)_t,i，y_t,i) And wherein the bit according to the object (2)Is arranged (x)_t,i，y_t,i) Determining the uncertainty estimate.

7. The method according to any one of the preceding claims,

wherein the reference is based on representing only the angular velocity (ω) with respect to the_t) Intermediate second part of uncertainty of

8. The method of claim 7, wherein the first and second light sources are selected from the group consisting of,

wherein the angular velocity (ω) through the object (2)_t) Variance of distribution of

9. The method of claim 8, wherein the first and second light sources are selected from the group consisting of,

wherein the distribution is with the angular velocity (ω) of the object (2)_t) At least one predetermined extreme value (ω)_{t_max}) Is uniformly distributed.

10. The method according to any one of claims 7 to 9,

wherein the angular velocity (ω) of the object (2) is represented by_t) Extreme value of (ω)_{t_max}) Is predetermined by at least one parameter ofThe intermediate second part

11. The method according to any one of the preceding claims,

wherein based on the first part

12. The method according to any one of the preceding claims,

the method further comprises determining an estimated velocity of the object (2)

13. Storage device with software, in particular firmware, for carrying out the method according to one of the preceding claims.

14. A system comprising the storage device of claim 13 and a vehicle,

wherein the vehicle (4) comprises a sensor (5') and a control unit configured to cooperate with the storage means,

wherein the control unit is further configured to determine a plurality of detection points (6, 6') of at least one object (2) in the vicinity of the sensor (5'), each detection point (6, 6') comprising an estimated velocity on the object (2) or at a position in the vicinity of the object (2)

Wherein the control unit is further configured to determine the estimated speed of at least one of the detection points (6, 6') by using the software stored in the storage means

15. The system of claim 14, wherein the first and second sensors are configured to sense the temperature of the fluid,

wherein the control unit is further configured to: estimating based on the uncertainty

Estimating based on the uncertainty

Estimating based on the uncertainty

Wherein the sensor and the control unit form a pulsed Doppler radar system.

Technical Field

The invention relates to a method of determining an uncertainty estimate of an estimated velocity of an object, wherein the uncertainty estimate represents an uncertainty of the estimated velocity relative to a true velocity of the object.

Background

Uncertainty estimation is useful for quantifying the effectiveness of estimated velocities. In other words, the uncertainty metric represents the degree to which the estimated speed can be trusted, or the likelihood that the estimated speed matches the true speed. That is, the uncertainty may be interpreted as a range of potential errors between the true and estimated velocities. According to one definition, uncertainty represents a range of speeds within which the true speed is assumed to fall. Thus, the uncertainty estimate is an estimate of the range.

In general, the higher the potential error between the estimated speed and the true speed, the higher the uncertainty. Preferably, the uncertainty estimate is at least related to uncertainty, which may be manifested as uncertainty proportional to the uncertainty estimate.

In modern automotive applications, particularly in automated or autonomous driving applications, there is a need to accurately determine the motion characteristics of any object in the vicinity of the host vehicle. Such objects may be other vehicles, but may also be pedestrians or stationary objects like traffic signs or walls. The environment of the vehicle can be determined in a generally perceptual sense by means of sensor technology operatively installed in the host vehicle, depending on the position and movement characteristics of any object in the vicinity of the host vehicle. It should be understood that the host vehicle (i.e., the control unit of the host vehicle) needs to have accurate information about the speed of surrounding objects in order to be able to safely control the vehicle through automatically generated driving commands. However, as described above, it is generally not possible to estimate the velocity of surrounding objects with complete accuracy. In order to still allow a safe autonomous driving of the host vehicle, an uncertainty estimation for the respective estimated speed is very helpful, since the control unit of the host vehicle can easily adapt itself to the validity of the estimated speed, thus enabling an optimal use of the available technical information.

An important motion characteristic is the velocity of a given object, which usually needs to be estimated by the host vehicle by means of sensors, and is therefore subject to estimation errors, i.e. the estimated velocity deviates from the true velocity of the object. One way to determine the estimated velocity is by using one or more radar sensors installed in the host vehicle, wherein a plurality of detection points are determined with a radar system, each detection point representing an estimated velocity at a given position in the vicinity of the host vehicle. The detection point may also be located on the object and may therefore be used to estimate the velocity of the object. Preferably, a plurality of detection points on a single object are jointly evaluated in order to derive an estimated velocity that is more accurate than the estimated velocity of a single detection point. The estimated velocity may include a magnitude and a direction, such that the estimated velocity is a vector having two components, i.e., the velocity is quantized with respect to two spatial dimensions. However, it is also possible that the estimated speed comprises only amplitude values.

Due to the inherent limitations of obtaining accurate estimated speeds using modern sensor technology, especially radar technology, knowledge about the potential error of the estimated speed needs to be obtained. In this regard, the uncertainty metric may be used to further process the estimated velocity, such as for a tracking algorithm configured to track the object such that the host vehicle has accurate information about the motion of the particular object. That is, a given value of the estimated velocity is processed along with the uncertainty estimate. In this way, it can be ensured that the estimated speed affects a given application in terms of its effectiveness. More simply stated, an estimated velocity with a high uncertainty estimate should have less impact than another estimated velocity with a low uncertainty estimate.

An accurate uncertainty estimate (or metric) is needed that quantifies as much as possible the true uncertainty of the estimated velocity, especially when the object is rotating at an angular velocity that cannot or should not be estimated. In some applications, the variance of the estimated velocity may be used as an uncertainty estimate. However, it has been found that in many motion situations occurring in real traffic scenarios, such uncertainty estimates are inaccurate. In particular, if a given object does not move along a straight line (linear motion), the variance is typically a very poor uncertainty estimate. Furthermore, the variance typically shows systematic errors that severely impact any further processing of the estimated speed, thus resulting in reduced performance for the autonomous driving application. This is intolerable because the safety of any traffic participant cannot be compromised.

Disclosure of Invention

The problem to be solved by the present invention is to provide an improved method of determining an uncertainty estimate of an estimated velocity of an object.

A method of determining an uncertainty estimate of an estimated velocity of an object comprises the steps of: (a) a first portion of an uncertainty estimate is determined, the first portion representing uncertainties of first and second estimation coefficients of a velocity distribution equation with respect to the object, the first estimation coefficient assigned to a first spatial dimension of the estimated velocity and the second estimation coefficient assigned to a second spatial dimension of the estimated velocity. A velocity distribution equation representing an estimated velocity from the first estimation coefficient and the second estimation coefficient;

(b) determining a second portion of the uncertainty estimate, the second portion representing an uncertainty with respect to the angular velocity of the object, the first coordinate of the object in the second spatial dimension, and the second coordinate of the object in the first spatial dimension; and (c) determining an uncertainty estimate based on the first portion and the second portion.

In summary, the uncertainty measure comprises or consists of two dedicated parts. The first part represents the uncertainty of two estimated "speed" coefficients with respect to a so-called speed profile equation, which is generally known in the art (see d. kellner, m. barjen-break, k. dietmayer, j. klappstein, j. dickmann, "instant velocity estimation of a vertical using doppler radar", Information Fusion (Fusion), 201316 th International Conference, eistanbul, 2013). This equation is also known as the approach rate equation (velocity) and generally represents the estimated velocity from two of the coefficients. These coefficients are assigned to respective spatial dimensions, which means that the coefficients typically represent the velocity components of the object in these dimensions. The interpretation is usually associated with a motion scenario where the object moves along a straight line (linear motion). However, if there is a rotational movement of the object about a predetermined axis, i.e. the object has a yaw rate (yawrate) greater than zero, the coefficients do not fully represent a "linear" velocity component, but a mixture of a rotational velocity part and a linear velocity part. However, since the coefficients are preferably used to evaluate the total velocity component in the various dimensions, they are assigned to the dimensions. In the field of estimating the motion of an object by means of sensor technology, in particular radar technology, the skilled person is generally familiar with velocity profile equations. The velocity profile equations are also discussed and further explicitly provided below.

The first estimation coefficient and the second estimation coefficient of the velocity distribution equation are numbers of estimation, and contribute to the overall uncertainty of the estimated velocity. Thus, the first portion of the uncertainty metric may be interpreted to capture uncertainty information related to the coefficients.

The second part of the uncertainty estimate is related to the angular velocity of the object. In particular, the angular velocity is the yaw rate of the object, i.e. the rotational speed of the object in a horizontal plane around a predetermined axis extending perpendicular to said plane. For example, while driving, the yaw rate of an automobile (a type of object) generally corresponds to the lateral movement of the automobile caused by the steering activity of the driver.

The estimation of angular velocity often provides inadequate results when using only one scan of one sensor (i.e. one measurement instance). That is to say that the estimated angular velocity is in most cases not reasonable. The estimation can be improved by filtering the signal over time or by using two sensors (see d.kellner, m.barjenbruch, j.klappstein, j.dickmann and k.dietmayer, "instant full-motion estimation of arbitarrarbobjects using dual Doppler radar", in Proceedings of intelligent vehicles symposium (IV), 2014). However, this solution requires multiple sensors to cover the field of view and results in a significant increase in overall cost.

The angular velocity of the object contributes to the overall uncertainty of the estimated velocity of the object (independent of the underlying estimate of angular velocity). It can be shown that, in general, there is a mathematical link between the estimated velocity, the first and second coefficients and the angular velocity. The association may be represented by a first coordinate of the object in the second spatial dimension and a second coordinate of the object in the first spatial dimension. The first and second coordinates are associated with or represent a point corresponding to a position on the object where the estimated velocity is assumed to be valid. However, for mathematical reasons, the coordinates are inverted between dimensions (inverted), as will be apparent from further detailed description below. The proposed uncertainty estimate takes these coordinates into account, which results in a more accurate uncertainty estimate for the local definition of the second part.

A final uncertainty estimate is formed based on the first and second portions of the uncertainty estimate. It has been found that splitting the uncertainty estimate into two parts results in a higher accuracy of the overall estimate. In particular, processing the angular velocity separately from the coefficients of the approach velocity equation is one aspect of improving the reliability of the proposed uncertainty estimate.

Advantageous embodiments of the invention are described in the dependent claims, the description and the drawings.

According to one embodiment, the uncertainty estimate represents a dispersion of the estimated velocity. Likewise, the first portion of the uncertainty estimate represents a dispersion of the first estimation coefficient and the second estimation coefficient. Further, the second part may represent a dispersion of the angular velocity of the object. The term "dispersion" is to be understood in a sense of dispersion, which means the range of possible values. The known dispersion types are variance and standard deviation, and accordingly the term dispersion is not limited. These types represent the dispersion of values around a mean. An advantage of expressing the uncertainty measure or part thereof in terms of dispersion is an intuitive understanding of the estimation, which is known in the field of statistics. For example, a high dispersion may represent a high uncertainty.

According to a further embodiment, the uncertainty estimate and/or the first part and/or the second part of the uncertainty estimate is determined as a two-dimensional matrix, wherein the two-dimensional matrix represents a dispersion with respect to the first spatial dimension and the second spatial dimension. In particular, the various parts and the resulting uncertainty estimate can be determined, i.e. represented as a two-dimensional matrix. The use of a matrix is advantageous in view of the efficient handling of a given estimated speed for which the uncertainty estimate should be valid. Furthermore, a direct correspondence between the two spatial dimensions and the two dimensions of the matrix may be achieved.

According to another embodiment, the first portion is determined based on:

-a covariance part of a covariance matrix representing the first estimated coefficients and the second estimated coefficients, and

-a deviation portion representing a deviation of the first estimation coefficient and/or the second estimation coefficient.

For example, a first portion of the uncertainty metric may be determined as a sum of the covariance portion and the bias portion. However, other types of combinations are also possible.

The covariance part may be determined as a covariance matrix of the first estimated coefficient and the second estimated coefficient, wherein the covariance matrix comprises the variances of the coefficients and the covariance between them. Such a structure of the covariance matrix is known in the field of statistics and can be calculated efficiently. It has proven to be robust and, in combination with other parts, can improve the accuracy of the uncertainty estimate.

The term "deviation" is generally interpreted as a systematic statistical error. For example, the deviation may be a constant representing the average difference between the estimated average and the true average of the values. The covariance portion may be centered on the estimated mean, where the deviation may represent how far the estimated mean is from the true mean. Thus, the deviation part may be interpreted as a correction part for systematic errors in the covariance part or another (sub-) part with respect to the first part.

It is important to note that the bias (or estimated bias) is not used to correct the estimated velocity, but rather to refine the uncertainty estimate to make it more consistent. The bias is estimated in order to improve the effectiveness of the estimation uncertainty (rather than the estimation speed). An accurate knowledge of the deviation is not necessary and in some cases it cannot even be estimated due to lack of observability. Such defects can be dealt with by introducing a bias part. A similar method can also be used to determine the uncertainty of the angular velocity.

Considering further the deviation part, according to one embodiment, the deviation part may be determined based on a plurality of detection points of the object, each of which comprises an estimated velocity at a detection position on the object, said detection position on the object being defined by at least one angle, and at least one constant. As further indicated above, the detection points may be acquired by means of a radar system, however, other sensor technologies are also possible. In one example, the detection points are preferably acquired, i.e. the plurality of detection points comprises detection points from only one scan, in particular a radar scan of a radar system.

The multiple detection points enable the adjustment of the deviation portion from the actual sensor data, which significantly improves the accuracy of the uncertainty estimate. In particular, the deviation portion may use the same data as the first coefficient and the second coefficient used to determine the velocity profile equation, i.e., use the data from the detection points to determine the coefficients and the deviation portion of the velocity profile equation.

The estimated velocity (for which an uncertainty estimate is determined) may be assigned to the location of the object. The position is preferably represented by a first coordinate of the object in a first spatial dimension and a second coordinate of the object in a second spatial dimension, and wherein the uncertainty estimate is determined from said position of the object. Assigning uncertainty to a particular location on or of an object improves the accuracy of the uncertainty measure, since its "maximum local validity" is explicitly taken into account, so that subsequent processing of the estimated velocity can benefit from this information. The "Lossy averaging" that occurs to provide one single uncertainty estimate for large objects can be avoided.

The estimated velocity (for which an uncertainty estimate is determined) may be equal to the velocity of the velocity profile equation, i.e. the estimated velocity may depend directly on the first estimation coefficient and the second estimation coefficient. However, the estimated velocity may also be determined in other ways, for example by using other sensor technologies.

Hereinafter, embodiments regarding determining the second portion will be discussed.

According to one embodiment, the second portion is determined based on the intermediate second portion. The intermediate second part represents only the uncertainty with respect to the angular velocity, wherein the intermediate second part is predetermined. In other words, the intermediate second part represents only the "angular velocity uncertainty", e.g. assuming a series of values comprising or covering the true unknown angular velocity. In the method, the intermediate second portion is predetermined, i.e. set to one or more predetermined values. It has been found that better results can be achieved with a predetermined intermediate second portion, instead of trying to determine the intermediate second portion based on an actual estimate of the angular velocity. Angular velocity is difficult to estimate with high accuracy, especially when it should be estimated from only one scan ("single processing instance"). Estimation is still difficult when multiple sensors are used to view a single object (see d.kellner, m.barrenbruch, j.klappstein, j.dickmann and k.dietmayer, "instant full-motion estimation of object using dual Doppler front", in Proceedings of intelligent vehicles Symposium (IV), dilberten, michigan), 2014). When only one sensor is used to observe an object, it is very difficult to estimate the angular velocity (i.e., yaw rate) of the object, and in most cases, it cannot even be considered approximately reasonable to estimate the angular velocity. In this case, the proposed uncertainty measure may provide significant advantages, since estimating the angular velocity may be avoided altogether.

Since it has been realized that for most object classes the angular velocity is usually limited to certain limits, relying on a predetermined intermediate second part may lead to even more accurate results. For example, in a traffic scenario, it may be assumed that the angular velocity of any object will typically be below a certain threshold.

In a preferred embodiment, the intermediate second portion is predetermined by a variance of the angular velocity distribution of the object. This is a method of modeling angular velocity by means of a hypothetical distribution. The variance or correlation number can be chosen as the key value (figure) because it fits well to represent the range or dispersion of values, consistent with the general thinking about uncertainty estimation. The intermediate second portion may be equal to a predetermined variance of the angular velocity of the object.

In a particular embodiment, the distribution is a uniform distribution having at least one predetermined extreme of the angular velocity of the object. Thus, explicit model assumptions can be made via the distribution. Other model distributions of angular velocity are also possible, such as triangular or trapezoidal distributions.

In a further embodiment, the intermediate second part is predetermined by at least one parameter representing an extreme value of the angular velocity of the object. For example, the maximum value of the angular velocity may be set manually and used to parameterize the intermediate second part. This may be done, for example, by determining the intermediate second portion as a variance of a model distribution of angular velocities, wherein the model distribution is limited to angular velocities between a negative maximum angular velocity (negative extremum) and a positive maximum angular velocity (positive extremum). As previously mentioned, a uniform distribution may be selected as the model distribution, but other model distributions are possible. This may depend on the specific application. The model distribution may also be selected according to the object type. For example, if the object is automatically classified as a passenger car, a different distribution may be selected than when the object is classified as a truck. Likewise, different extrema may be selected for the intermediate second portion. Thus, in general, the determination of the uncertainty estimate may depend on the class of the object, wherein the class may be determined automatically by using a classification method. Such a classification method may be based on visual data of the object acquired by means of a camera, but may also be based on an estimated speed of the object.

In yet another embodiment, the uncertainty estimate may be determined based on a sum of the first portion and the second portion. Other mathematical combinations are also possible, such as a quotient between the first and second portions of the uncertainty estimate.

In view of the possible use of uncertainty estimates, the method may further comprise controlling the vehicle in the vicinity of the object in accordance with an estimated speed of the object, wherein the estimated speed is processed in accordance with the uncertainty estimate.

The invention also relates to a storage device with software, in particular firmware, for carrying out the method according to one of the preceding embodiments.

The storage device may be part of a system comprising the storage device and a vehicle, wherein the vehicle comprises a sensor and a control unit configured to cooperate with the storage device. The control unit is further configured to determine a plurality of detection points of at least one object in the vicinity of the sensor, each detection point comprising an estimated velocity at a location on or in the vicinity of the object. Furthermore, the control unit is configured to determine an uncertainty estimate of the estimated speed of at least one of the detection points by using software stored in the storage means.

In an embodiment of the system, the control unit may be further configured to track the object based on the uncertainty estimate and/or to classify the object based on the uncertainty estimate. The object may also be distinguished from other objects based on uncertainty estimates. Other applications, in particular automotive applications, in which an estimated speed of an object other than the (host) vehicle is employed, may also be modified such that the uncertainty estimate is taken into account. The reliability and accuracy of such applications can be improved. Examples of such applications are distance control, valet parking, and autonomous driving.

According to another embodiment of the system, the sensor and the control unit may form a so-called pulse doppler radar system, which is a widespread and well-known system for determining a plurality of detection points, each of which represents an estimated velocity at a position on an object and passes at least through an angle θ_iThe position is defined. This angle is typically an azimuth angle, as it represents an angle about the boresight of the radar antenna of the system, wherein the angle is in a horizontal plane corresponding to the ground below the vehicle. As a general aspect of the present disclosure and according to an embodiment of the method, a first estimation coefficient and a second estimation coefficient are determined based on a plurality of detection points, each of which is represented at an objectAt least through an angle theta_iDefining the position, wherein the velocity profile equation is represented by:

wherein the content of the first and second substances,

representing the velocity of the object at the position of the ith detection point,

which represents the first estimated coefficient of the first signal,

representing the second estimated coefficient, theta_iIndicating the position of the i-th inspection point. Preferably in one example a plurality of detection points is acquired, i.e. the plurality of detection points comprises detection points from only one scan, in particular a radar scan of a radar system.

Radar systems, in particular the pulse doppler radar system, are well suited to provide a plurality of detection points, on the basis of which the velocity profile equation can be easily determined. The proposed uncertainty estimate is particularly suitable for accurately representing the uncertainty of the estimated velocity determined by using the velocity distribution equation.

It should be understood that in connection with the mathematical expressions disclosed herein, the mathematical expressions do not necessarily need to be exactly satisfied in a strict mathematical sense. In particular, algebraic expressions can be understood in a conceptual sense. That is, if the equation is only approximately satisfied, the equal sign can still be satisfied. Thus, as understood by those skilled in the art, if an expression is implemented on a computer, any numerical deviation from the narrow meaning of the expression (i.e., an offset or a substantially constant factor) due solely to the technical details of the implementation does not affect the fact that the implementation falls within the meaning of the expression. In particular, any equivalent sign (i.e., "═ o") appearing in any algebraic expression disclosed herein may be replaced with a scale symbol (i.e., "-").

Drawings

The invention is further described, by way of example, with reference to the accompanying drawings, in which:

figure 1 shows a target coordinate system;

figure 2 shows a vehicle coordinate system;

figure 3 shows a sensor coordinate system;

figure 4 shows a target vehicle relative to a host vehicle, wherein the detection point is located on the target vehicle;

figure 5 illustrates how the velocity vector at the location of the inspection point is calculated;

fig. 6 illustrates an embodiment of the method as described herein.

List of reference numerals

1 origin of world coordinate system

2 target vehicle

3 front bumper

3' rear bumper

3' origin of vehicle coordinate system

4 host vehicle

5 origin of sensor coordinate system

5' radar system

6. 6' detection point

7 center of rotation of target

Detailed Description

Typically, the host vehicle 4 (see fig. 2) is equipped with a radar system 5 '(see fig. 2), and reflected radar signals from the targets 2 (fig. 1) in the field of view of the radar system 5' are processed to provide data for determining parameters used in the method.

For this reason, a number of conditions and requirements may be advantageous. The target 2 (rigid body, e.g. vehicle) is preferably an extended target, i.e. the target enables a determination of a number of reflection points 6' (see fig. 4) reflected in real time from the target 2 and this is based on raw radar detection measurements.

Object 2 is an example of an object in the sense of the general part of the detailed description and claims. However, other types of objects are also possible, in particular specific objects that occur in common traffic scenes, such as motorcycles, bicycles, pedestrians, large vehicles and small vehicles. Furthermore, in principle, the object may also be a stationary object.

As used herein, the term "extended target" is used to refer to a target 2 that is capable of providing a plurality (i.e., two, three, or more) of spaced apart scattering points 6 '(which are also referred to as reflection points 6'). The term "extended target" is therefore understood as a target 2 having a certain physical size. In this case, it should be noted that the physical dimensions may be chosen, for example, in the range of 0.3m to 20m, in order to be able to detect the reflection point 6', which reflection point 6' originates from, for example, a moving person to a moving heavy goods vehicle or similar.

It is not necessary to track the scattering points 6 'individually from one radar scan to the next, and the number of scattering points 6' may be different between scans. Furthermore, in a continuous radar scan, the position of the scattering point 6' may be different on the extended target 2.

The radar-reflecting point 6 'may be determined by the host vehicle 4 from radar signals reflected from the target 2, wherein a comparison of a given reflected signal with an associated transmitted radar signal may be performed to determine the position of the radar-reflecting point 6' (e.g. in cartesian or polar coordinates (azimuth, radial range)) relative to the position of a radar-transmitting and/or radar-receiving element/unit on the host vehicle, which may be the position of a radar sensor unit.

The rate of approach is also determined as known in the art, using, for example, doppler radar technology. Notably, the "raw data" from a single radar scan may provide the parameter θ for the ith reflection point of the n reflection points_i(azimuth angle) and

(original approach velocity, i.e. radial velocity). These are parameters used to estimate the speed of the (moving) target, where i ═ 1.

It should also be noted that the term instantaneous radar scan, single radar scan, or single measurement instance may include reflection data from "chirps" in doppler techniques, which may scan for more than, for example, up to 2 ms. As is well known in the art. In the description that follows, the following conventions and definitions are used:

world coordinate system

Conventionally, a world coordinate system is used that has an origin fixed to a point in space-assuming that the world coordinate system does not move and rotate. Conventionally, the coordinate system is a right-hand coordinate system; the Y axis is orthogonal to the X axis and points to the right side; the Z-axis points to the page and defines an azimuth angle in a negative direction (clockwise) with respect to the X-axis; referring to fig. 1, such a coordinate system is shown with an origin 1 and a non-autonomous vehicle 2. Fig. 1 also shows an extended target 2 in the form of a vehicle, for example an object about 4.5 meters long.

Vehicle coordinate system

Fig. 2 shows a vehicle coordinate system having an origin 3 "located in the center of the front bumper 3 of the host vehicle 4 in this example. It should be noted in this respect that the origin 3 "of the vehicle coordinate system may be arranged at different positions of the host vehicle 4.

In the present example, the X-axis is parallel to the longitudinal axis of the vehicle 4, i.e. it extends between the front bumper 3 and the rear bumper 3' and intersects the center of the front bumper 3 if the origin 3 "is located in the center of the front bumper 3 of the host vehicle 4. The vehicle coordinate system is a right-hand coordinate system with the Y-axis orthogonal to the X-axis and pointing to the right, and the Z-axis pointing to the page. The (azimuth) angle is defined as defined in the world coordinate system.

Sensor coordinate system

Fig. 3 shows a sensor coordinate system with an origin 5. In the example of fig. 3, the origin 5 is located in the center of a radar system (in particular a sensor unit) 5', which may be a radome. The X-axis is perpendicular to the sensor radome and points away from the radome. The coordinate system is a right-hand coordinate system: the Y axis is orthogonal to the X axis and points to the right side; the Z-axis points to the page. The (azimuth) angle is defined as defined in the world coordinate system.

It is assumed that the speed and yaw rate of the host vehicle 4 are known from sensor measurements known in the art. An over-the-ground (OTG) velocity vector of the host vehicle 4 is defined as:

V_h＝[u_hv_h]^T，

wherein u is_hIs the longitudinal velocity of the host vehicle 4 (i.e., the velocity in the X-axis direction parallel to the vehicle coordinate system), and v_hIs the lateral velocity of the host vehicle 4 (i.e., the velocity in the Y-axis direction parallel to the vehicle coordinate system). More generally, the longitudinal and lateral velocities are first and second velocity components, respectively, of the host-vehicle 4. The X-axis and the Y-axis generally correspond to a first spatial dimension and a second spatial dimension, respectively. Likewise, the longitudinal direction and the transverse direction correspond to the first spatial dimension and the second spatial dimension, respectively. These are preferably (but not necessarily) orthogonal to each other.

The sensor mounting position and boresight angle relative to the vehicle coordinate system are assumed to be known relative to the Vehicle Coordinate System (VCS), where the following notation is used:

x_s，VCSsensor mounting position relative to a longitudinal (X-) coordinate

y_s，VCS-sensor mounting position relative to the transverse (Y) coordinate

γ_s，VcS-sensor visual axis angle.

The over-ground (OTG) velocity of the sensor may be determined based on a known host vehicle velocity and a known sensor mounting location. It should be understood that more than one sensor may be integrated into a vehicle and designated accordingly.

Define the sensor OTG velocity vector as:

V_s＝[u_sv_s]^T，

wherein u is_sIs the longitudinal velocity of the sensor, and v_sIs the sensor lateral velocity, which normally corresponds to the first velocity component and the second velocity component in the case of a yaw-rate of zero.

At each radar measurement instance (scan), the radar sensor unit captures n (raw) detection points from the target. Each detection point i 1.., n can be described by the following parameters expressed in the sensor coordinate system:

r_i-an approach distance (or radial distance),

θ_i-an azimuth angle,

original closing velocity (or radial velocity).

The target plane motion can be described by the target OTG velocity vector at each of the originally detected positions:

V_t，i＝[u_t，iv_t，i]^T，

wherein u is_t，iRepresents a longitudinal velocity at a position of the i-th detection point, and v_t，iRepresenting the lateral velocity of the target at the location of the ith detection point, both preferably (but not necessarily) relative to the sensor coordinate system.

The object plane motion can also be described by:

V_t，COR＝[ω_tx_t，CORy_t，COR]^T，

wherein, ω is_tRepresenting the yaw rate (angular velocity), x, of the target_t，CORIs the longitudinal coordinate of the center of rotation of the target, y_t，CORIs the lateral coordinate of the center of rotation of the target.

Fig. 4 illustrates the target velocity vector as a line originating from a plurality of detection points 6', illustrated as a cross, wherein the detection points 6' are all located on the same rigid body target 2, and wherein the detection points 6' are acquired using a sensor unit on the host vehicle 4.

The general case is shown in more detail in fig. 5, showing three detection points 6 located on a target (not shown) having a centre of rotation 7. To have an axis x_SCS，Y_SCSShows a sensor coordinate system having an axis x_VCS，Y_VCSThe vehicle coordinate system of (1). Together show in detection point 6(i ═ 1)Velocity vector of one and its component u_t，i，v_t，i。

The approach rate equation for a single detection spot 6 can be expressed as follows:

wherein the content of the first and second substances,

represents the approach rate, i.e., the rate of change in the distance between the origin of the sensor coordinate system and the detection point 6 as illustrated in fig. 5. Can pass through the azimuth angle theta_i＝1And a radial distance r_i＝1The position of the detection point 6 is described by a value of (the approach distance of the detection point, i.e., the distance between the origin and the detection point).

To simplify notation, the compensated approach rate can be defined as:

wherein the content of the first and second substances,

the approach rate of the i-th detection point that compensates for the velocity of the host vehicle 4 is indicated.

The compensated approach rate can also be expressed as:

the compensated approach rate can also be expressed in vector notation as:

the so-called velocity profile equation (or the approach velocity equation) is defined as:

wherein c is_tA first (e.g., longitudinal) coefficient or component representing the closing velocity, and s_tRepresenting a second (e.g., lateral) coefficient or component of the proximity velocity equation. Note that, preferably, the coefficient c_t、s_tIs invariant with respect to azimuth, at least for an azimuth range corresponding to the positions of the targets pointed to by the plurality of detection points, and the coefficients have been determined on the basis thereof. This means that the velocity profile equation is assumed to be valid not only for a specific detection point but also for a range of azimuth angles. Thus, the approach velocity for any azimuth angle relative to a particular angular range can be readily determined using the approach velocity equation. The approach velocity is an example of an estimated velocity in the general sense of the present disclosure.

As will be appreciated by those skilled in the art, in practice, the "true" coefficient c is typically estimated from a plurality of detection points_t、s_t. These estimates are expressed as

And

and estimated using, for example, an iterative (re) weighted least squares method. In the following, the method for estimating the coefficient c is described_t、s_tAn exemplary method of (1).

Step 1

In an initial step, the method comprises transmitting a radar signal and determining a plurality of radar detection points at one measurement instance from a plurality of radar detection measurements captured by said radar sensor unit. Each radar detection point including at least an azimuth angle theta_iAnd closing rate

Wherein the approach rate

Indicating that the distance between the sensor unit and the target is at the i-th detection pointThe rate of change at the location (see fig. 4). It can be understood that the azimuth angle θ_iThe angular position of the ith detection point is depicted. As shown in fig. 4, it is assumed that a plurality of detection points are located on a single target (such a target is generally referred to as a distributed target). The target is an object.

Step 2

Compensating for rate of approach

Is determined as:

wherein u is_sRepresents a first (e.g., longitudinal) velocity component of the sensor unit, and wherein v_sRepresenting a second (e.g., lateral) velocity component of the sensor unit. The compensated approach rate is an approach rate that compensates for the velocity of the host vehicle. Thus, the compensated approach rate can be interpreted as the effective velocity of the target at the position of the ith detection point. The compensated approach rate corresponds to the estimated velocity of the target.

Step 3

From the results of step 1 and step 2, the first coefficient c of the velocity profile equation of the target is determined, preferably by using an Iterative Reweighted Least Squares (IRLS) method (which may also be an ordinary least squares method)_tIs estimated by

And a second coefficient s of the velocity profile equation of the target_tIs estimated by

The iterative weighted least squares (IRLS) method includes at least one iteration and weighting w_iApplied to radar detection points, where the velocity profile equation of the target is represented by:

for example, the IRLS method is initialized by the solution of the ordinary least squares method (OLS). This is done by a first calculation:

wherein the content of the first and second substances,

a compensated approach rate representing i 1, 2

The vector of (2). Calculated using the following equationInitial solution of (a):

then, the initial residual is calculated by:

the variance of the residual is then calculated as:

next, an estimate is calculated

And

estimation of variance of (c):

wherein

Using the initial solution, the weight w can be calculated from the residual_i∈[0；1]Wherein a predefined threshold may be used to ensure that the weights are well defined.

Then the weight w_iArranged in a diagonal matrix W and given the estimates of the coefficients of the first iteration as follows:

step 4

Determining an estimate of the velocity profile from the solution of the first iteration

Represented by the formula:

wherein the azimuth angle theta is determined according to step 1_iAnd determining an estimate of the first coefficient from step 3 (initial solution)

And estimation of the second coefficient

The new residual is calculated as follows:

the variance of the new residual is then calculated as:

wherein

Wherein the content of the first and second substances,

to represent

Relative to residual errorWherein n represents the number of detected points.

Next, the estimate is calculated as follows

And

estimation of variance of (c):

wherein the variance may be compared to a stopping criterion (e.g., a threshold) in order to decide whether to perform further iterations to determine the estimation coefficients

And

in this way, coefficients can be obtainedAnd

the final solution of (2).

It can be shown that if the target 2 moves along a straight line (linear movement), the first and second estimation coefficients correspond to portions of the velocity in the first and second spatial dimensions (i.e. x-and y-directions), respectively, i.e.:

wherein

Is the velocity component of the ith detection point in the x direction,

is the velocity component in the y direction at the i-th detection point. In fig. 5, these velocity components are represented as one of the detection points 6, i.e. i ═ 1, where

And is

In the case of a target with a non-zero yaw-rate, i.e. ω_tInstead of zero, the velocity component relative to the first and second spatial dimensions can be expressed as:

wherein x is_t，iIs the first coordinate of the i-th detection point, y_t，iIs the second coordinate of the i-th detection point.

The approach rate equation for each detection point can then be expressed as:

wherein, due to

y_t，icosθ_i＝r_t，isinθ_icosθ_i＝x_t，isinθ_i，

The equation can be simplified as:

recall that the approach rate equation is generally defined as:

comparison with the equation of the approach rate equation including the yaw rate shows that the estimated first coefficient and second coefficient can be expressed as the estimated first coefficient and second coefficient, respectively

Therefore, the velocity at the ith detection point can be expressed as:

the yaw rate is usually unknown, but can be estimated. In view of this estimation, the estimated velocity at the ith detection point can be expressed as:

wherein the velocity component relative to the yaw rate can be identified as:

wherein the second coordinate-y_t，iIn a first spatial dimension x, and a first coordinate x_t，iIn a second spatial dimension y, i.e. a first coordinate and a second coordinate, the position of the i-th detection point is defined as (x)_t，i，y_t，i) Wherein the second coordinate is inverted.

In a more compact representation (rotation), the estimated velocity at the i-th detection point can be expressed as:

wherein the estimated velocity may be set equal to the estimated compensated approach rate of the velocity profile equation, as further explained above.

The uncertainty estimate of the estimated velocity at the ith detection point is preferably defined as:

wherein the content of the first and second substances,

is a two-dimensional matrix of which the,

is a two-dimensional matrix and is an uncertainty estimate

A first part of, and

is a two-dimensional matrix and is an uncertainty estimate

The second part of (1). This estimate and both parts are preferably squared numbers, which avoids negative values of the estimate. The matrix also preferably represents a dispersion (dispersion) with respect to the first and second spatial dimensions. Although the uncertainty estimate is defined herein as the sum of the first portion and the second portion, other combinations of the first portion and the second portion are possible in order to determine the uncertainty estimate.

The first part

First estimation coefficient representing equation of distribution with respect to velocityAnd a second estimation coefficient

Uncertainty of (2). Thus, the first part may be interpreted to represent the uncertainty of the solution with respect to the velocity profile. This can be expressed as:

wherein the content of the first and second substances,

is an uncertainty estimate of the first estimation coefficient,

is an uncertainty estimate of the second estimation coefficient, and

is a cross uncertainty estimate between the first estimation coefficient and the second estimation coefficient. In this way, the first part generally corresponds to the covariance matrix.

The first portion may be further defined as:

wherein the covariance part

A covariance matrix representing the first estimated coefficient and the second estimated coefficient, and a bias part

Representing the deviation of the first estimation coefficient and the second estimation coefficient.

The covariance part can be expressed as:

wherein the content of the first and second substances,

is an estimate of the variance of the first estimation coefficient,

is an estimate of the variance of the second estimation coefficient, and

is a covariance estimate of the first estimated coefficient and the second estimated coefficient.

As previously mentioned, the covariance part may preferably be determined as:

in view of the deviation part, a general definition can be given:

wherein Y represents the compensated approach rate

k denotes some constants. Furthermore, the matrix X is the same as before, i.e.:

in particular, the deviation part may be defined as:

wherein

Wherein k is_{ols_bias_scale}Is scaling the calibration parameter, k_{c_var_bias}Is an offset calibration parameter of the first estimation coefficient, and k_{s_var_bias}Is an offset calibration parameter for the second estimation coefficient.

Note, the offset part

Preferably a covariance matrix of the first estimated coefficients and the second estimated coefficients

And a function of the additional calibration parameters.

Considering the second part of the uncertainty estimation

The second part may be defined as:

wherein the content of the first and second substances,

is the estimation uncertainty of the yaw rate.

To avoid uncertainty in dynamically estimating the yaw rate, a predetermined uncertainty may be relied upon. This can be done assuming that the yaw rate of the object is bounded. For example, the yaw rate of a typical traffic object (e.g., a vehicle) typically does not exceed 30 degrees per second. The yaw rate can then be modeled as a distribution (probability density function, pdf), e.g. with zero mean and yaw rate ω_tMaximum value ω of_{t_max}The uniform distribution of (2):

the maximum value of the yaw rate (also called the extreme value) can be determined beforehand by means of calibration parameters as:

ω_{t_max}＝k_{max_yaw_rate}。

according to standard mathematics, the variance of a uniform pdf is:

the uncertainty in yaw-rate can then be set to the variance, i.e. to be:

thus, the second part of the uncertainty estimate is predetermined and is represented as:

wherein it is to be understood that the second part represents a first coordinate x of the estimated velocity relative to the angular velocity in a second spatial dimension y_t，iAnd a second coordinate y in the first spatial dimension x_t，iUncertainty of (2).

Fig. 6 gives an overview of some aspects of the above method. Each block corresponds to an exemplary step of the method, wherein the step is represented within the block. The dashed boxes indicate that the corresponding steps are only optional.

The proposed uncertainty estimate has been evaluated in two different example scenarios. To quantify the effectiveness of the uncertainty estimate, the Normalized Estimation Error Squared (NEES) is used as a metric. This metric can be generally interpreted as a measure of consistency between the estimated speed and the estimated variance or uncertainty estimate. A general definition may be:

wherein the content of the first and second substances,

representing the inverse of the estimated covariance matrix, e_iNEES at the i-th detection point is shown. Covariance matrix

Is an estimated covariance matrixOr the proposed uncertainty estimate

If the expected value of NEES is equal to the dimension n of the covariance matrix (where n is 2), then the estimated velocity and the estimated covariance matrix are consistent:

H₀：E(e_i)＝n。

in both example scenarios, simulations of moving objects have been performed using 1000 Monte Carlo iterations. In a first scenario, a linearly moving object is simulated. When using the estimated covariance matrixWhen the expected NEES is E (E)_i) It was inconsistent at a significance level of 95%. When using the mentionedDerived uncertainty estimate E (E)_i) It is consistent at a significance level of 95% when 2.03.

In a second scenario, a yaw object is simulated. When using the estimated covariance matrix

This is completely inconsistent. Using this as an "uncertainty estimate" would be dangerous for tracking applications. However, when using the proposed uncertainty estimate, then E (E)_i) It is well consistent at a significance level of 95% 2.04. Thus, the proposed uncertainty estimate may be used for e.g. security tracking applications.