Method of determining the yaw rate of a target vehicle

1. A method of determining a yaw rate ({circumflex over (ω)} t ) of a target vehicle in a horizontal plane by a host vehicle equipped with a radar system, said radar system including a radar sensor unit adapted to receive signals emitted from said host vehicle and reflected by said target vehicle, estimated values being denoted by a hat ({circumflex over ( )}) said method comprising:

a) emitting a radar signal at a single time-point instance and determining, from a plurality (m) of point radar detections measurements captured from said target vehicle by said radar sensor unit in said single time-point instance, values for each point radar detection including range, azimuth, and range rate: [r i , θ i {dot over (r)} i ], to provide results of step (a);

b) determining, by using a Least Square method and in a sensor coordinate system, Least Square solution values of longitudinal and lateral components of a range rate equation of the target vehicle ({tilde over (c)} t,scs ,{tilde over (s)} t,scs ) from the results ({dot over (r)} i ,θ i ,) of step a), where the range rate equation is

r

.

i

,

cmp

=

[

cos

⁢

θ

i

sin

⁢

θ

i

]

[

c

t

s

t

]

and {dot over (r)} i,cmp ={dot over (r)} 1 +u s cos θ i +v s sin θ i , u s is the radar sensor unit's velocity or the host vehicle's longitudinal velocity and vs is the radar sensor unit's velocity or the host vehicle's lateral velocity, to provide results of step (b), an x-axis of the sensor coordinate system being perpendicular to the radar sensor unit and pointing away and ahead of the radar sensor unit, a y-axis of the sensor coordinate system being perpendicular to the x-axis and pointing right of the radar sensor unit, Least Square solution values being denoted by a tilde ({tilde over ( )}) and solution values in the sensor coordinate system being denoted with a scs subscript ( scs );

c) determining an orientation angle (γ t,scs ) of the target vehicle relative to the x-axis of the sensor coordinate system and another line representing an orientation of the target vehicle, to provide results of step (c);

d) determining a center of the target vehicle (x t,c,scs and y t,c,scs ) from the range and azimuth (r i , θ i ) of step a), to provide results of step (d);

e) determining a line l PH perpendicular to the other line representing the orientation of the target vehicle and passing through the center of the target vehicle (x t,c,scs and y t,c,scs ), the determining from the results of step (c) and (d), respectively, to provide results of step (e);

f) determining a line l CA that passes through a center of rotation of said target vehicle using a position of the radar sensor unit of said host vehicle and the longitudinal and lateral components of the range rate equation of the target vehicle ({tilde over (c)} t,scs ,{tilde over (s)} t,scs ), from the result of step b), to provide results of step (f);

g) responsive to a determination that the line l CA and l PH are not parallel, determining an intersection point of the lines l CA and l PH from steps e) and f), the intersection point being a position of the center of rotation [{circumflex over (x)} t,COR,scs , ŷ t,COR,scs ] of the target vehicle, to provide results of step (g);

h) estimating the yaw rate ({circumflex over (ω)} t ) based on the position of the center of rotation found in step g) and based on the components of the range rate equation of the target vehicle ({tilde over (c)} t,scs ,{tilde over (s)} t,scs ) of the results of step b); and

i) operating, by a driving-assistance system of the host vehicle, the host vehicle based on the yaw rate of the target vehicle.

2. A method as claimed in claim 1 , wherein said step c) comprises determining the orientation angle (γ t,scs ) of the target vehicle from the values of range and azimuth (r i , θ i ) of said point detections.

3. A method as claimed in claim 1 , wherein said step c) comprises determining the orientation angle (γ t,scs ) of the target vehicle from L fit or Hough transform.

4. A method as claimed in claim 1 , wherein said line l pH of step e) is determined and defined from the following equation:

y

=

-

1

tan

⁢

γ

t

,

scs

⁢

x

+

1

tan

⁢

γ

t

,

scs

⁢

x

t

,

c

,

scs

+

y

t

,

c

,

scs

=

a

1

⁢

x

+

a

0

.

where

a

1

=

-

1

tan

⁢

γ

t

,

scs

and

a

0

=

1

tan

⁢

γ

t

,

scs

⁢

x

t

,

c

,

s

⁢

c

⁢

s

+

y

t

,

c

,

s

⁢

c

⁢

s

.

5. A method as claimed in claim 4 , wherein said line l CA of step f) is determined by applying a cloud algorithm, the cloud algorithm defined as:

y

=

-

s

~

t

,

scs

c

~

t

,

scs

⁢

x

=

b

1

⁢

x

+

b

0

where {tilde over (s)} t,scs =−{circumflex over (x)} t,COR,scs {circumflex over (ω)} t ;

{tilde over (c)} t,scs =−ŷ t,COR,scs {circumflex over (ω)} t ;

b

1

=

-

s

~

t

,

s

⁢

c

⁢

s

c

~

t

,

s

⁢

c

⁢

s

;

and

b 0 =0.

6. A method as claimed in claim 5 , wherein in step g) the position of the center of rotation [{circumflex over (x)} t,COR,scs , ŷ t,COR,scs ] of the target vehicle is determined from the following equations:

x

^

t

,

COR

,

scs

=

b

0

-

a

0

a

1

-

b

1

⁢

and

,

=

a

1

⁢

b

0

-

a

0

⁢

b

1

a

1

-

b

1

.

7. A method as claimed in claim in 6 , wherein in step h) the yaw rate is determined from the following equations:

ω

^

t

=

s

~

t

,

scs

-

x

^

t

,

COR

,

scs

⁢

or

⁢

ω

^

t

=

c

~

t

,

scs

y

^

t

,

COR

,

scs

.

8. A method as claimed in claim 7 including additionally determining estimates of longitudinal velocity û t,i , and lateral velocity {circumflex over (v)} t,i of a certain point of the target vehicle from the value of yaw rate and coordinates of the center of rotation of the target vehicle using the following equation:

[

u

^

t

,

i

,

scs

v

^

t

,

i

,

scs

]

=

[

(

y

^

t

,

COR

,

scs

-

y

t

,

i

,

scs

)

⁢

ω

^

t

(

x

t

,

i

,

scs

-

x

^

t

,

COR

,

scs

)

⁢

ω

^

t

]

.

9. The method as claimed in claim 1 , wherein the other line representing the orientation of the target vehicle passes through the center of the target vehicle (x t,c,scs and y t,c,scs ).