150 with respect to the radar system 110.

An important task for the combination of the radar system 110 and the processing unit 120 is the determination of the height 152 of the object 150 in order to assess whether the object 150 is potentially dangerous for the vehicle 100. In order to determine the height 152 of the object 150, the elevation angle 154 may be used. However, the elevation angle 154 of the object 150 is determined with respect to the radar system 110, i.e. in a radar coordinate system being centered at the radar system 110. Two axes of the radar coordinate system may extend within the imaginary plane 132 extending in parallel to the road surface 130 at the mounting height 134 of the radar system 110. These two axes are aligned, for example, with a longitudinal axis and a lateral axis of the vehicle 100, respectively.

In order to determine the height 152 of the object 150 with respect to the road surface 130, a spatial transformation is required between the radar coordinate system and a ground coordinate system which has its origin at the road surface 130. In addition, for determining the height 152 of the object 150 with respect to the ground plane or road surface 130 correctly, it is necessary to know the current pitch angle of the radar system 110 relative to the road surface 130.

During an acceleration of the vehicle 100, for example, the front of the vehicle 100 may move upward slightly with respect to the rear of the vehicle. Accordingly, the radar system 110 may have a positive pitch angle 162 with respect to the ground plane or road surface 130 and with respect to the parallel imaginary plane 132. Conversely, during braking maneuvers of the vehicle 100, the front of the vehicle 100 may move downward with respect to the rear of the vehicle 100 such that the radar system 110 may have a negative pitch angle 164 with respect to the road surface 130 and to the imaginary parallel plane 132. The pitch angles 162, 164 are depicted in FIG. 1 by respective small arrows.

During driving of the vehicle 100, the pitch angle may change by 2 degrees or even more. Such a pitch angle change may cause an error when determining the height 152 of the object 150 which may be approximately 3.5 m for a range or distance of 100 m of the object 150 with respect to the vehicle 100. Therefore, it is important to have a reliable estimation of the current pitch angle of the radar system 110 during the operation of the vehicle 100 at every time step. For dynamically determining the pitch angle 162, 164 of the radar system 110 in a reliable manner, a method according to disclosure is provided. Steps of this method are schematically depicted in FIG. 2.

The signals received by the radar sensor of the radar system 110 are transformed to points in spherical coordinates, i.e. including a range, an azimuth angle and an elevation angle of a respective reflection of the radar waves. These points are associated with a respective radar intensity and are denoted as radar detections 210 (see FIG. 2). At 220, the radar detections 210 are separated into road detections 230 and context detections 240.

The road detections 230 are generated by the received signals from the predefined area or region of interest 136 (see FIG. 1) of the road surface 130. In contrast, the context detections 240 are generated by signals received from objects like the object 150 (see FIG. 1) which are located at positions being different from the road surface 130, for example. The road detections 230 and the context detections 240 can be distinguished and separated from each other based on their respective range and elevation angle with respect to the radar system 110.

For example, radar detections 210 which are generated at the predefined range of e.g. 5 to 10 m and which have a corresponding elevation angle 140 which fits to the region of interest 136 are regarded as road detections 230, whereas other radar detections 210 providing a range outside the region of interest 138, i.e. smaller than e.g. 9 m or greater than 10 m and having a corresponding elevation and azimuth angle 152 which does not fit to the region of interest 136 are regarded as context detections 240. In addition, the radar cross-section of objects 150 which are not part of the road surface 130 is expected to be much greater than the radar cross-section of a typical road surface 130. In other words, a larger amount of radar energy is usually reflected by stationary objects like the object 150 above the road surface 130 than by an area or region of the road surface 130. Generally, there are different criteria in order to separate the road detections 230 from the context detections 240.

If there is a plurality of N road detections 230 generated by radar reflections from the road surface 130 within the region of interest 136 (see FIG. 1), respective “theoretical” or expected angles are calculated for respective measured ranges r_i,Road^Mlike the range 138 (see FIG. 1) of the N road detections 230 by applying the known mounting height 134 of the radar system 110 which is denoted by h_Radar. In detail, the sine of this theoretical angle is given by the ratio of the mounting height h_Radarand the respective measured range r_i,Road^M, i.e. by h_Radar/r_i,Road^M. The “theoretical angle” of the N road detection 230 corresponds to an expected pitch angle of about 0 degrees, i.e. for a situation in which the longitudinal axis of the vehicle 100 is aligned in parallel with the road surface 130 (see FIG. 1).

The theoretical angles which are determined as described above based on the mounting height 134 of the radar sensor 110 and the range 138 of the road detections 230 are subtracted from respective measured angles θ_i,Road^Mat 250 which is denoted as subtraction procedure. The N measured angles are determined for the N road detections 230 by standard angle finding procedures known in the field of radar sensors, e.g. as angles from range rate or via more sophisticated procedures using Fourier transforms or an iterative adaptive approach (IAA). For the N road detections 230, a mean value and a variance are calculated for the above-described differences as follows:

θ
ˆ

Road
M

=

∑

i
=
1

N

⁢

(

θ

i
,
Road

M

-

sin

-
1

(

h
Radar

r

i
,
Road

M

)

)

/
N

(
1
)

var
⁢

(

θ
Road
M

)

=

∑

i
=
1

N

⁢

❘
"[LeftBracketingBar]"

θ

i
,
Road

M

-

sin

-
1

(

h
Radar

r

i
,
Road

M

)

-

θ
ˆ

Road
M

❘
"[RightBracketingBar]"

2

/
N

(
2
)

θ_Road^Mdenotes the estimated pitch angle of the radar system 110 relative to the road surface which may be denoted as a primary pitch angle.

The mean value denoted by 262 and the variance denoted by 264 (see FIG. 2) for the estimation of the primary pitch angle based on the road detection 230 are transferred as an input to a recursive filter 280 which will be described in detail below.

In some circumstances, the region of interest 136 on the road surface 130 may be blocked for the radar system 110 or may have a low reflectivity for the transmitted radar waves. Therefore, a small amount of road detections 230 is available in this case for the estimation of the mean value 262 and the variance 264 of the pitch angle. Therefore, the variance 264 may strongly increase if a small amount of road detections 230 is available due to a blocked radar system 110 or a low reflectivity of the road surface 130.

Therefore, the context detections 240 are also used for the estimation of a so-called relative pitch angle. The context detections 240 are generated, as already mentioned above, by objects like the object 150 (see FIG. 1) which do not belong to the road surface 130. In detail, a plurality or almost all static objects 150 available in the external environment of the vehicle 100 are considered for determining a respective measured angle θ_i,Context^Mwhich may also be determined by standard angle finding procedures as described above for the road detections 230. By calculating the respective range rate or Doppler based on the context radar detection 240 it may be determined whether the respective object 150 is stationary or not.

In a similar manner as for the primary pitch angle determined based on the road detections 230, a mean value 272 and a variance 274 are calculated based on a plurality of L context detections 240 as follows:

θ
ˆ

Context
M

=

∑

i
=
1

L

⁢

θ

i
,
Context

M

/
L

(
3
)

var
⁢

(

θ
Road
M

)

=

∑

i
=
1

L

⁢

❘
"[LeftBracketingBar]"

θ

i
,
Context

M

-

θ
ˆ

Context
M

❘
"[RightBracketingBar]"

2

/
L

(
4
)

In contrast to the primary pitch angle determined from the road detections 230, the estimated angle provided by the mean value 272 does not provide a correct estimation of an absolute pitch angle since this angle does not refer to the road surface 130 or ground plane. The mean value 272 which is determined based on the context detections 240 also varies over time since it depends on the available stationary objects 150 in the external environment of the vehicle 100.

In order to remove the incorrect absolute angle information from the mean value 272 of the angles determined from the road detections 240, the difference between two consecutive angles which are determined for two different measurement cycles or time steps is calculated as follows:

Δ
⁢

θ
Context
M

(
t
)

=

θ
Context
M

(
t
)

-

θ
Context
M

(

t
-
1

)

(
5
)

This angle difference is denoted as a relative pitch angle. Besides, a pitch angle rate may be determined by dividing the angle difference from equation (5) by the corresponding time interval. In summary, the mean value 272 and the corresponding variance 274 of the measured angle from context on which the relative pitch angle relies are transferred to recursive filter 280.

The recursive filter 280 is configured as a Kalman filter for the present embodiment. For the Kalman filter, a state space x is defined as follows:

x
=

(

θ
Road
S

Δθ
Context
S

)

,

(
6
)

- wherein θ_Road^Sis an estimation of a final pitch angle with respect to the road surface 130, and Δθ_Context^Sis the relative pitch angle as described above.

In addition, a measurement vector of the Kalman filter is defined by

z
=

(

θ
Road
M

Δθ
Context
M

)

,

(
7
)

- wherein θ_Road^Mis the measured or primary pitch angle relative to the road, and Δθ_Context^Mis relative pitch angle given by the difference between two consecutive estimations from the context detections 240.

The state transition model or predictor step of the Kalman filter is given by the following matrix which combines the pitch angle estimation based on the road detections 230 which is estimated at 250, and the relative pitch angles or pitch angle rates which are based on the context detections 240 and which are estimated at 270. The matrix is given by:

A
=

(

1

1

0

1

)

(
8
)

Finally, the observation model of the Kalman filter is given by the identity matrix:

H
=

(

1

0

0

1

)

(
9
)

The output of the recursive filter 280 or Kalman filter includes a final pitch angle 290 which is given as a fused estimation of the pitch angle based on the road and context detections 230, 240. In addition, the output of the recursive filter 280 or Kalman filter includes a confidence value or uncertainty measure 292 which is based at least partly on the variances 264, 274.

In FIG. 3, a diagram is depicted which shows different curves for the pitch angle of the radar system 110 with respect to the road surface 130 (see FIG. 1). The respective pitch angle is represented in degrees on the y-axis over a consecutive row of about 400 radar scans on the x-axis which therefore corresponds to a time axis. That is, the curves of the pitch angle are depicted over time in FIG. 3.

The diagram includes a curve 310 which represents the primary pitch angle, i.e. the pitch angle estimated based on the road detections 230 as the result of block 260 in FIG. 2, i.e. according to formula (1). As emphasized by the ellipses 312, the curve 310 includes strong outliers 314 in the region after the scan number 250. As described above, these outliers may be caused by a low reflectivity of the road surface 130 (see FIG. 1) or by a partial blocking of the region of interest 136 with respect to the radar system 110.

In addition, the curve 320 represents the respective mean values of angle detections over all available stationary objects 150 in the external environment of the vehicle 100. These mean values for the curve 320 are estimated in block 270 of FIG. 2 based on the context detections 240 according to formula (3). As can be recognized in FIG. 3, the angle 320 as determined by the context detections 240 has an offset with respect to the pitch angle 310 as determined from the road detections 230. In addition, the angle 320 determined from context detections 240 varies over time in a much stronger manner than the pitch angle 310 determined from the road detections 230.

The curve 310 for the primary pitch angle determined from road detections 230 has a quite constant value of about −0.7 degrees for most of the radar scans, i.e. for most of the time up to scan 250 and after scan 300. Between the scan 250 and 300, however, the variance of the pitch angle determined from the road detections 320 strongly increases, wherein this variance is calculated according to formula (4).

Due to this increase of the variance for the estimation of the primary pitch angle from the road detections 230, the recursive filter 280 configured as a Kalman filter compensates the unreliable estimation of primary pitch angle from road detections 230 by the context-based pitch angle estimation as provided by block 270 in FIG. 2. In other words, the Kalman filter reduces the weight for the mean value 262 representing the estimation of the primary pitch angle from the road detections 230 and increases the weight for the context-based estimation of the pitch angle as provided via the mean value 272 generated by block 270 as the relative pitch angle Δθ. This compensation is denoted by 332 in FIG. 3

The result of the recursive filter 280 is shown in FIG. 3 as curve 330. This curve 330 represents the final pitch angle or fused estimation 290 (see FIG. 2) of the pitch angle which is provided as an output of the recursive filter 280 together with a confidence value or uncertainty measure 292. As mentioned above, the uncertainty measure 292 for the pitch angle is determined based on the variance 264 and the variance 274 which are input to the recursive filter 280 together with the respective mean values 262, 272.

In addition, the curve 340 as shown in FIG. 3 represents a ground truth provided for the pitch angle of the radar system 110. As can be recognized in FIG. 3, the curve 330 being the output of the recursive filter 280 shows a good agreement with the curve 340 for the ground truth. In detail, the outliers 340 of the curve 310 are removed from the curve 330 for the pitch angle which is output by the recursive filter 280 by additionally considering the context detections 240. In summary, a reliable and stable estimation of the pitch angle of the radar system 110 with respect to the road surface 130 is provided by the method according to the disclosure.

FIG. 4 shows a flow diagram 400 illustrating a method for determining a pitch angle of a perception system of a vehicle with respect to a road surface on which the vehicle is located. The perception system may be configured to detect perception information from an external environment of the vehicle.

At 402, road perception information from the road surface may be detected via the perception system. At 404, object perception information from objects being different from the road surface may be detected via the perception system. At 406, a primary pitch angle may be determined via a processing unit of the vehicle by using the road perception information. At 408, a relative pitch angle may be determined via the processing unit by using the object perception information. At 410, the primary pitch angle and the relative pitch angle may be combined via the processing unit in order to determine a final pitch angle of the perception system.

According to various embodiments, the primary pitch angle and the relative pitch angle may be combined via a recursive filter.

According to various embodiments, a first variance may be calculated for the primary pitch angle, a second variance may be calculated for a raw pitch angle which may be determined based on the object perception information and which may be used for determining the relative pitch angle, and an input for the recursive filter may include the first variance and the second variance.

According to various embodiments, a confidence value may be determined for the final pitch angle by applying the recursive filter.

According to various embodiments, the recursive filter may include a Kalman filter, and a measurement vector of the Kalman filter may include the primary pitch angle and the relative pitch angle.

According to various embodiments, a region of interest may be predefined on the road surface in front of the vehicle, and the road perception information may be determined by using detections received from the region of interest only via the perception system.

According to various embodiments, the perception system may include a radar system, the road perception information may include road radar detections received from the road surface, and the object perception information may include object radar detections received from stationary objects being different from the road surface in the external environment of the vehicle.

According to various embodiments, a respective measured angle may be determined for each of the road radar detections within a region of interest on the road surface, a respective theoretical or expected angle may be determined based on a respective measured range of each of the road radar detections with respect to the radar system and based on a mounting height of the radar system, and the primary pitch angle may be determined based on at least one difference between the respective measured angle and the respective theoretical angle.

According to various embodiments, the primary pitch angle may be determined by estimating a mean value of respective differences between the measured angles and the theoretical angles determined for a plurality of road radar detections for the region of interest on the road surface, and the relative pitch angle may be determined based on at least one mean value of raw pitch angles determined for a plurality of object radar detections from the stationary objects.