Methods and computer devices for determining angular offset of radar system

1. A method of calibrating a radar system based on an angular offset, the radar system having been mounted on a vehicle, the vehicle having a forward direction of travel along a surface, the radar system having a scanning direction, the angular offset being an angle between the scanning direction and the forward direction, the method executable by a computer device, the computer device being communicatively coupled to the radar system, the method comprising:

at a given moment in time during operation of the radar system:

receiving radar data from the radar system, the radar data including point-specific data associated with a plurality of detected objects,

the point-specific data associated with a given detected object being indicative of (i) a position of the given detected object, and (ii) an actual radial speed of the given detected object;

determining, by the computer device, projections of an immobile object velocity in (i) the scanning direction and (ii) a direction perpendicular to the scanning direction by using an iterative process,

the immobile object velocity being associated with a subset of detected objects of the plurality of detected objects, the plurality of detected objects including detected objects that are immobile with respect to the surface and at least one detected object that is non-immobile with respect to the surface, the subset of detected objects having a plurality of objects that are immobile with respect to the surface, the projections of the immobile object velocity being derivable from the actual radial speed of the respective ones of the subset of detected objects,

the determining the projections of the immobile object velocity including:

during a given iteration of the iterative process:

determining candidate projections of velocity (i) in the scanning direction and (ii) in the direction perpendicular to the scanning direction, for the plurality of detected objects based on the point-specific data of the plurality of detected objects;

using the candidate projections of velocity and the respective positions of the plurality of detected objects to determine respective estimated radial speeds for the plurality of detected objects;

in response to a difference between (i) the estimated radial speeds of the plurality of detected objects and (ii) the actual radial speeds of the plurality of detected objects being above a threshold,

 removing the given detected object from the plurality of detected objects thereby generating a reduced set of detected objects, the given detected object corresponding to a non-immobile object with respect to the surface;

during a following iteration of the iterative process:

determining new candidate projections of velocity (i) in the scanning direction and (ii) in the direction perpendicular to the scanning direction, for the reduced set of detected objects based on the point-specific data of the reduced set of detected objects;

using the new candidate projections and the respective positions of the reduced set of detected objects to determine respective new estimated radial speeds for the reduced set of detected objects;

in response to differences between (i) the respective new estimated radial speeds of the reduced set of detected objects and (ii) the respective actual radial speeds of the reduced set of detected objects being below the threshold,

 determining that the reduced set of detected objects is the subset of detected objects and that the new candidate projections are the projections of the immobile object velocity;

determining, by the computer device, the angular offset of the radar system based on at least one of the projections of the immobile object velocity; and

performing, by the computer device, calibration of the radar system based on the angular offset.

2. The method of claim 1 , wherein the method comprises determining the respective estimated radial speeds for the plurality of detected objects by applying a following equation:

V

imob

-

cand

-

x

*

x

i

r

i

+

V

imob

-

cand

-

y

*

y

i

r

i

=

v

i

-

est

3. The method of claim 1 , wherein the determining the angular offset of the radar system is performed by applying a following equation:

θ=π−atan 2( V imob-y ,V imob-x )

4. The method of claim 1 , wherein the radar data is captured when the vehicle is travelling along the forward direction of travel at the velocity of the vehicle.

5. The method of claim 4 , wherein the velocity of the vehicle is substantially constant.

6. The method of claim 4 , wherein the forward direction is a strict forward direction.

7. The method of claim 1 , wherein the position of a given detected object is at least one of:

(i) a distance of the given detected object from the radar system, and (ii) a horizontal angle of the given detected object with the scanning direction of the radar system; and

a distance of the given detected object from the radar system (i) in the scanning direction, and (ii) in the direction perpendicular to the scanning direction.

8. The method of claim 1 , wherein the actual radial speed of a given detected object is a doppler speed of the given detected object as determined by the radar system.

9. The method of claim 1 , wherein the determining the projections of the immobile object velocity is performed by the computer device employing an iterative optimization algorithm.

10. The method of claim 1 , wherein the determining the candidate projections of velocity is performed by the computer device employing an Ordinary Least Squares (OLS) algorithm.

11. The method of claim 10 , wherein the OLS algorithm is employed on a following set of equations:

v

x

1

*

x

1

r

1

+

v

y

1

*

y

1

r

1

=

v

1

v

x

2

*

x

2

r

2

+

v

y

2

*

y

2

r

2

=

v

2

v

x

3

*

x

3

r

3

+

v

y

3

*

y

3

r

3

=

v

3

v

x

1

=

v

x

2

=

v

x

3

=

V

imob

-

cand

-

x

v

y

1

=

v

y

2

=

v

y

3

=

V

imob

-

cand

-

y

12. The method of claim 1 , wherein the subset of detected objects includes at least a pre-determined portion of detected objects of the plurality of detected objects.

13. The method of claim 12 , wherein the method further comprises verifying, by the computer device, that the subset of detected objects includes at least the pre-determined portion of detected objects of the plurality of detected objects.

14. The method of claim 1 , wherein the subset of detected objects includes at least a pre-determined number of detected objects.

15. The method of claim 14 , wherein the method further comprises verifying, by the computer device, that the subset of detected objects includes at least the pre-determined number of detected objects.

16. The method of claim 1 , wherein the determining the angular offset of the radar system is executed in response to the subset of detected objects including at least one of:

at least a pre-determined portion of detected objects of the plurality of detected objects; and

at least a pre-determined number of detected objects.

17. The method of claim 1 , wherein the determining the projections of the immobile object velocity comprises:

iteratively determining, by the computer device, candidate projections based on the point-specific data of respective iteratively-reduced sets of detected objects.

18. The method of claim 17 , wherein detected objects from the subset of detected objects have substantially similar movement patterns relative to the radar system.

19. The method of claim 18 , wherein the movement pattern is being immobile relative to the surface.

20. The method of claim 18 , wherein the movement pattern is moving with a substantially same velocity in a direction opposite to the forward direction of travel.

21. The method of claim 9 , wherein the iterative optimization algorithm is a Random Sample Consensus (RANSAC) algorithm.

22. A computer device for calibrating a radar system based on an angular offset, the radar system having been mounted on a vehicle, the vehicle having a forward direction of travel along a surface, the radar system having a scanning direction, the angular offset being an angle between the scanning direction and the forward direction, the computer device being communicatively coupled to the radar system, the computer device being configured to:

at a given moment in time during operation of the radar system:

receive radar data from the radar system, the radar data including point-specific data associated with a plurality of detected objects,

the point-specific data associated with a given detected object being indicative of (i) a position of the given detected object, and (ii) an actual radial speed of the given detected object;

determine projections of an immobile object velocity in (i) the scanning direction and (ii) a direction perpendicular to the scanning direction by using an iterative process, the immobile object velocity being associated with a subset of detected objects of the plurality of detected objects, the plurality of detected objects including detected objects that are immobile with respect to the surface and at least one detected object that is non-immobile with respect to the surface, the subset of detected objects having a plurality of objects that are immobile with respect to the surface, the projections of the immobile object velocity being derivable from the actual radial speed of the respective ones of the subset of detected objects,

to determine the projections of the immobile object velocity including:

during a given iteration of the iterative process:

determine candidate projections of velocity (i) in the scanning direction and (ii) in the direction perpendicular to the scanning direction, for the plurality of detected objects based on the point-specific data of the plurality of detected objects;

use the candidate projections of velocity and the respective positions of the plurality of detected objects to determine respective estimated radial speeds for the plurality of detected objects;

in response to a difference between (i) the estimated radial speeds of the plurality of detected objects and (ii) the actual radial speeds of the plurality of detected objects being above a threshold,

 remove the given detected object from the plurality of detected objects thereby generating a reduced set of detected objects, the given detected object corresponding to a non-immobile object with respect to the surface;

during a following iteration of the iterative process:

determine new candidate projections of velocity (i) in the scanning direction and (ii) in the direction perpendicular to the scanning direction, for the reduced set of detected objects based on the point-specific data of the reduced set of detected objects;

use the new candidate projections and the respective positions of the reduced set of detected objects to determine respective new estimated radial speeds for the reduced set of detected objects;

in response to differences between (i) the respective new estimated radial speeds of the reduced set of detected objects and (ii) the respective actual radial speeds of the reduced set of detected objects being below the threshold,

 determine that the reduced set of detected objects is the subset of detected objects and that the new candidate projections are the projections of the immobile object velocity;

determine the angular offset of the radar system based on at least one of the projections of the immobile object velocity; and

perform calibration of the radar system based on the angular offset.